Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging

Derek W. Bartlett; Mark E. Davis

doi:10.1093/nar/gkj439

Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging

Bartlett, Derek W.; Davis, Mark E. 2006-01-01 00:00:00 Published online January 12, 2006 322–333 Nucleic Acids Research, 2006, Vol. 34, No. 1 doi:10.1093/nar/gkj439 Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging Derek W. Bartlett and Mark E. Davis* Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Received December 2, 2005; Revised and Accepted December 23, 2005 discovery in Caenorhabditis elegans in 1998 (1), it has ABSTRACT rapidly attracted attention from researchers in ﬁelds ranging Small interfering RNA (siRNA) molecules are potent from genetics to clinical medicine. A natural intracellular effectors of post-transcriptional gene silencing. process likely involved in cell-based defense against mobile Using noninvasive bioluminescent imaging and a genetic elements such as viruses and transposons (2), RNAi mathematical model of siRNA delivery and function, promises to be an invaluable tool for gene function analysis the effects of target-specific and treatment-specific as well as a powerful therapeutic agent that can be used to silence pathogenic gene products associated with dis- parameters on siRNA-mediated gene silencing are eases including cancer, viral infections and autoimmune monitored in cells stably expressing the firefly disorders (3–8). luciferase protein. In vitro, luciferase protein levels A central component of RNAi is a double-stranded siRNA recover to pre-treatment values within ,1 week in molecule that is 21–23 nt in length with 2 nt long 3 overhangs rapidly dividing cell lines, but take longer than (9). These siRNA effector molecules can be introduced into 3 weeks to return to steady-state levels in nondividing cells directly as synthetic siRNAs or indirectly as precursor fibroblasts. Similar results are observed in vivo, with long dsRNAs or short-hairpin RNAs (shRNAs). RNA poly- knockdown lasting 10 days in subcutaneous tumors merase II- or III-driven expression cassettes can be used for in A/J mice and 3–4 weeks in the nondividing constitutive expression of shRNA molecules (10). Both the hepatocytes of BALB/c mice. These data indicate long dsRNAs and shRNAs are cleaved by Dicer (RNase III that dilution due to cell division, and not intracellular family of endonucleases) into the appropriately sized siRNA effectors. Although the presence of dsRNA >30 nt can elicit an siRNA half-life, governs the duration of gene silencing interferon response in mammalian cells (11), Elbashir and co- under these conditions. To demonstrate the practical workers demonstrated that synthetic 21mer siRNAs evaded use of the model in treatment design, model calcula- the interferon response and yet were still effective mediators tions are used to predict the dosing schedule required of sequence-speciﬁc gene silencing in mammalian cells (9). to maintain persistent silencing of target proteins with Here, we have chosen to focus on the use of synthetic 21mer different half-lives in rapidly dividing or nondividing siRNA duplex molecules in mammalian cells for transient cells. The approach of bioluminescent imaging com- gene silencing. bined with mathematical modeling provides useful Because synthetic siRNA molecules must be transported insights into siRNA function and may help expedite into the cells before they can function in RNAi, successful the translation of siRNA into clinically relevant thera- delivery of siRNA is of central importance. Delivery vehicles peutics for disease treatment and management. must protect the siRNA from nucleases in the serum or extra- cellular media, enhance siRNA transport across the cell membrane and guide the siRNA to its proper location through interactions with the intracellular trafﬁcking machinery. INTRODUCTION While naked siRNA molecules have been shown to enter RNA interference (RNAi) refers to the ability of double- cells, signiﬁcantly more siRNA can be delivered using car- stranded RNA (dsRNA) to cause sequence-speciﬁc degra- rier vehicles (12,13). Both viral and nonviral vectors deli- dation of complementary mRNA molecules. Since its ver siRNA into cells, although viral vectors are limited to *To whom correspondence should be addressed. Tel: +1 626 395 4251; Fax: +1 626 568 8743; Email: [email protected] The Author 2006. Published by Oxford University Press. All rights reserved. The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact [email protected] Nucleic Acids Research, 2006, Vol. 34, No. 1 323 delivering siRNA-expressing constructs such as shRNA. Com- MATERIALS AND METHODS mercially available cationic lipids such as Oligofectamine can Production of luciferase-expressing cell lines by effectively deliver siRNA molecules into cells in vitro with lentiviral transduction transfection efﬁciencies approaching 90% (9). However, the Cell lines were incubated with viral supernatant containing high toxicity of cationic lipids limits their use for systemic SMPU-R-MNCU3-LUC, a lentiviral vector based on HIV-1 delivery in vivo. Recent studies from our laboratory have that transduces the ﬁreﬂy luciferase gene. The backbone vector shown that cyclodextrin-containing polycations (CDPs) can SMPU-R has deletions of the enhancers and promoters of the achieve safe and effective systemic delivery of siRNA in HIV-1 long terminal repeat (SIN), has minimal HIV-1 gag mice (14). Here, we consider the nonviral delivery of sequences, contains the cPPT/CTS sequence from HIV-1, siRNA using cationic lipids or polymers. has three copies of the UES polyadenylation enhancement A challenge for the successful application of siRNA will element from SV40 and has a minimal HIV-1 RRE [gift be to determine the dosing schedule required for efﬁcacy, from Paula Cannon, Children’s Hospital Los Angeles, Los making insights into the kinetics of siRNA-mediated gene Angeles, CA (19)]. The vector has the U3 region from the silencing foundational for the future clinical use of siRNA. MND retroviral vector as an internal promoter driving expres- Without a proper understanding of the kinetics of the pro- sion of the ﬁreﬂy luciferase gene from SP-LUC+ [Promega, cess and the parameters that can affect the resulting gene Madison, WI (20)]. silencing, application of RNAi will be governed largely by trial and error. The ability to speciﬁcally tailor and optimize siRNA duplexes the treatment for each particular system would save signiﬁcant time and resources, especially given the high cost of synthetic All siRNA molecules were ordered puriﬁed and pre-annealed siRNA molecules and the amount of material required for (‘Option C’) from Dharmacon Research, Inc. (Lafayette, CO). 0 0 in vivo studies. Mathematical modeling using simple kinetic siGL3 (sense, 5 -CUUACGCUGAGUACUUCGAdTdT-3 ; 0 0 equations for each step in the RNAi process can shed light antisense, 5 -UCGAAGUACUCAGCGUAAGdTdT-3 )isan on many of these questions regarding the kinetic aspects of unmodiﬁed siRNA duplex that targets the luciferase gene, RNAi. To our knowledge, there are only a few published while siCONTROL non-targeting siRNA #1 (siCON1; sense, 0 0 0 examples of such studies looking at the kinetics of the intra- 5 -UAGCGACUAAACACAUCAAUU-3 ;antisense, 5 -UUG- cellular RNAi process (15–18). Of these studies, none has AUGUGUUUAGUCGCUAUU-3 ) is an unmodiﬁed siRNA combined the delivery process and the interaction with the duplex bioinformatically designed to minimize the potential RNAi machinery in mammalian cells. Bergstrom and for targeting any known human or mouse genes. co-workers (15) proposed a unidirectional ampliﬁcation method in their mathematical model of RNAi-mediated In vitro transfections gene silencing. Because no RNA-dependent RNA polymerase Cells were seeded in 24-well plates 2–3 days prior to trans- has yet been found in mammalian cells, they acknowledged 4 5 fection at 2 · 10 –1 · 10 cells per well and grown in media that their model did not address the silencing mechanisms supplemented with 10% fetal bovine serum (FBS) and anti- observed in mammals. Groenenboom and co-workers (16) biotics (penicillin/streptomycin). siRNA was complexed recently proposed a mathematical model for RNAi that with Oligofectamine (Invitrogen, Carlsbad, CA) according contained several extensions to the core RNAi pathway, pro- to the manufacturer’s instructions and applied to each well viding for siRNA degradation by RNase as well as primed in a total volume of 200 ml OptiMEM (Invitrogen). Trans- ampliﬁcation. Their model aimed to explain transgene- fection medium was removed and replaced with complete or virus-induced gene silencing and avoidance of self- medium after 5 h. reactivity, but did not consider any steps in the delivery process. Similarly, Raab and Stephanopoulos (17) looked at Formation of subcutaneous tumors in mice the dynamics of gene silencing by siRNA given at different Luciferase-expressing Neuro2A (Neuro2A-Luc) cells were doses and at various times relative to plasmid transfection, but grown to conﬂuence in media supplemented with 10% FBS did not incorporate siRNA delivery. Arciero and co-workers and antibiotics (penicillin/streptomycin). Immediately prior to (18) created a mathematical model to investigate tumor- injection, cells were washed with phosphate-buffered saline immune evasion and siRNA treatment. Although this model (PBS), trypsinized and resuspended in serum-free media at provided insights into how siRNA can be used in cancer 2 · 10 cells/ml. Each mouse received 0.5 ml of the resulting treatment, it did not examine the delivery process and there cell suspension by subcutaneous injection. were no experimental data from in vitro or in vivo studies. Here, we use bioluminescent imaging and mathematical Low-pressure tail-vein (LPTV) injection of modeling to investigate the steps of RNAi from siRNA deliv- formulated siRNA polyplexes ery to intracellular function with the aim of enabling the practical application and design of siRNA-based treatment All complexes were made with siRNA and an imidazole- strategies both in vitro and in vivo. Because the imaging is modiﬁed CDP (CDP-Im) synthesized as described previously noninvasive and nondestructive, the same set of cells or ani- (21,22). Before addition to siRNA, CDP-Im was mixed with mals can be followed for the entire study. These results will an adamantane-PEG (AD-PEG) conjugate and an AD- complement investigations using more traditional analytical PEG-transferrin (Tf) conjugate such that the total moles of methods to monitor mRNA or protein knockdown and hope- AD-PEG or AD-PEG-Tf equaled the number of moles of fully serve to encourage the rational design of experimental b-CD. Tf-targeted polyplexes contained 1% AD-PEG-Tf rel- and clinical siRNA-based treatments. ative to AD-PEG. This mixture was added to an equal volume 324 Nucleic Acids Research, 2006, Vol. 34, No. 1 Figure 1. Simplified schematic of the key steps required for siRNA delivery to and function within mammalian cells. Steps 1–3 are unique to in vivo application of siRNA, whereas steps 4–9 represent the general processes on the level of an individual cell and are therefore common to both in vivo and in vitro application of siRNA. of siRNA at a charge ratio (positive charges from CDP-Im to light emission. Mice were anesthetized with an initial dose negative charges from siRNA backbone) of 3:1 (+:). An of 5% isoﬂurane followed by a maintenance dose of 2.5% equal volume of 10% (w/v) glucose in water was added to isoﬂurane. Bioluminescent signal intensities were quantiﬁed the resulting polyplexes to yield a 5% (w/v) glucose (D5W) using Living Image software (Xenogen). solution suitable for injection. Each mouse was injected with 200 ml of this polyplex solution containing 50 mg siRNA per Mathematical model 20 g mouse (2.5 mg/kg siRNA). The model presented here was designed to allow the user High-pressure tail-vein (HPTV) co-injection of to speciﬁcally study the impact of parameter values on plasmid and siRNA gene silencing by RNAi. When designing an siRNA-based treatment, the main controllable parameters are the Hydrodynamic, or HPTV, injection of nucleic acids can delivery method (naked siRNA, formulated with vector, achieve signiﬁcant levels of nucleic acid in the hepatocytes chemically modiﬁed) and dosing schedule. These choices of mice (23,24). A. McCaffrey and M. Kay kindly donated a must be governed by parameters such as the target mRNA plasmid (pApoEHCRLuc) containing the ﬁreﬂy luciferase half-life, target protein half-life, threshold for reduction gene under the control of the human a -antitrypsin promoter (in either target mRNA or protein), number of target cells and the apolipoprotein E locus control region. For HPTV and desired knockdown duration. The model’s design co-injection studies in BALB/c mice, each 20 g mouse criteria therefore included the ability to enable user-deﬁned received a 10% w/v injection of a D5W solution containing values for these parameters that characterize each experi- 0.25 mg/kg of the luciferase-containing plasmid and 2.5 mg/kg mental system. siRNA. A simpliﬁed schematic of the major processes included in the model is shown in Figure 1. Model variables (Table 1) and Bioluminescent imaging parameters (Table 2) were used to develop a set of ordinary Cell culture plates or mice containing the luciferase- differential equations for the steps involved in siRNA delivery expressing cells were imaged using the Xenogen IVIS 100 to and function within mammalian cells in vitro and in vivo. Imaging System (Xenogen, Alameda, CA). D-luciferin The differential equations governing each major process from (Xenogen) was dissolved in PBS at 15 g/l. For in vitro assays the delivery of siRNA to its intracellular interaction with the in 24-well plates, 50 ml of the 15 g/l luciferin solution was RNAi machinery are grouped into modules that can be added to each well containing 1 ml of media. Light emission changed independently to modify the model complexity as was measured 2–3 min after addition of the luciferin. For desired. A detailed description of the mathematical model in vivo experiments, 0.2 ml of the 15 g/l luciferin solution and the rationale for its design are provided in the Supple- was injected intraperitoneally 10 min before measuring the mentary Data. Nucleic Acids Research, 2006, Vol. 34, No. 1 325 Table 1. Model variables Cell growth and target protein production dP Name Model Description (units) ¼ kf ormprot M kdegprot P compartment dt dZ Z Bcf Plasma Free complex in circulation (# vol ) 1 ¼ kgrowth Z 1 Bcb Plasma Bound complex in circulation (# vol ) dt max Ec Extracellular Extracellular complex in local vicinity (# vol ) Enc Intracellular Endosomal complex (# vol ) All of the equations for intracellular siRNA-associated species Enna Intracellular Endosomal free siRNA (# vol ) contain a term to account for dilution due to cell division, Cc Intracellular Cytoplasmic complex (# vol ) where dilution is equal to the ratio of new cells divided by Cna Intracellular Cytoplasmic free siRNA (# vol ) R Intracellular Activated RISC complex (# vol ) the total number of cells. For example, if the number of cells C Intracellular Activated RISC complex bound to doubles in 1 day, then dilution would equal 0.5 and the con- mRNA (# vol ) centration of the intracellular species would likewise be M Intracellular Target mRNA (# vol ) reduced by 50%. For the sake of calculation simplicity, P Intracellular Target protein (# vol ) only species involving the delivered siRNA molecules are Z Intracellular Number of cells (#) diluted by this factor; all other intracellular species (i.e. target mRNA and target protein) are assumed to not change after cell division because they are produced intracellularly by both of Circulation/extracellular transport the daughter cells. The net effect of this is that the siRNA- dBcf associated species are diluted equally between the two daugh- ¼ kblooddis Bcb kbloodbind Bcf dt ter cells after each cell division. The set of ODEs was solved with MATLAB (The Math- ktransblood partition Bcf kelimpl Bcf Works, Inc., Natick, MA) using the stiff ODE15s solver. The dBcb : ODE15s solver is a variable-order solver based on the numeri- ¼ kbloodbind Bcf kblooddis Bcb dt cal differentiation formulas. Parametric sensitivity analysis dEc Vp was performed using SENS_SYS written by V. M. Garcia ¼ ktransblood partition Bcf dt Ve Molla. This MATLAB routine is an extension to the ODE15s solver that calculates the derivatives of the solution kint Ec Z kelimec Ec with respect to the parameters. Cellular uptake and intracellular trafﬁcking dEnc Ve ¼ kint Ec kescendvec Enc RESULTS dt Vi kunpackend Enc dilution Enc In vitro and in vivo experiments were conducted to gain insights into the general kinetics of siRNA-mediated gene dEnna ¼ kunpackend Enc kescendna Enna silencing in cell lines that constitutively express the luciferase dt gene. Constitutively expressed genes, in contrast to genes kdegendna Enna dilution Enna expressed transiently by plasmids, provide a more realistic dCc model for clinical application in which an endogenous ¼ kescendvec Enc kunpackcyt Cc dilution Cc gene, such as an oncogene, is the target for a therapeutic dt siRNA. The Xenogen IVIS 100 Imaging System allowed us dCna ¼ kescendna Enna þ kunpackcyt Cc þ kdisRISC R to monitor luciferase activity in luciferase-expressing cells dt growing in 24-well plates or present in subcutaneous tumors kf ormRISC ðrtot R CÞ Cna or livers in live mice; because the imaging was noninvasive, kdeginna Cna dilution Cna luciferase activity was measured in the same plate of cells or the same animals over the entire duration of the study. Moni- toring the kinetics of siRNA-mediated gene silencing in the RNAi same population of cells helps to avoid variability introduced when using different cell populations for each time point as dR ¼ kf ormRISC ðrtot R CÞ Cna þ kdisRISCm C required in luminometer-based luciferase detection or ﬂow dt cytometry (for ﬂuorescent reporters). Additionally, ﬁreﬂy þ kcleavage C kdisRISC R kdegRISC ðR þ CÞ luciferase has a short half-life of 2 h, so that its level should kf ormRISCm R M dilution R change concomitantly with the level of mRNA (25,26). This enables the use of bioluminescent imaging of luciferase pro- dC ¼ kf ormRISCm R M kdisRISCm C : tein activity as an indicator of mRNA transcript degradation by dt the delivered siRNA molecules. kdegRISC ðR þ CÞ kcleavage Cdilution C dM Effect of siRNA dose on luciferase knockdown in vitro ¼ kf ormmRNA þ kdisRISCm C kdegmRNA M dt The amount of siRNA applied to the extracellular media has a kf ormRISCm R M signiﬁcant impact on the magnitude of the gene silencing but a 326 Nucleic Acids Research, 2006, Vol. 34, No. 1 Table 2. Model parameters Name Description (units) Determination Value max Maximum number of cells (#) Determined experimentally Fit to each system partition Effective fraction of dose available to target cells Estimated from experimental data 1 · 10 1 15 rtot Total available amount of RISC protein complexes (# L ) Literature (42–44) 1.9 · 10 Ve Extracellular volume (L) Specified experimentally in vitro, 2 · 10 Estimated from experimental 1 · 10 data and literature (45,46) Vi Intracellular volume (L) Literature (47) 4 · 10 Vp Plasma volume, mouse (L) Literature (48) 1.5 · 10 1 4 kbloodbind Complex binding to blood components (h ) Estimated from experimental data 1 · 10 1 2 kblooddis Complex dissociation from blood components (h ) Estimated from experimental data 1 · 10 kcleavage Cleavage of target mRNA by activated RISC complex (h ) Literature (44) 7.2 1 1 kdegendna Endosomal siRNA degradation (h ) Literature (32–34,49) 5 · 10 1 2 kdeginna Intracellular siRNA degradation (h ) Estimated from experimental 2.9 · 10 data and literature (33) kdegmRNA Target mRNA degradation (h ) Literature (50–53) 2 1 1 kdegprot Target protein degradation, Luciferase (h ) Literature (25) 3.5 · 10 1 2 kdegRISC Activated RISC complex degradation (h ) Estimated from experimental data 7.7 · 10 1 9 kdisRISC Dissociation of activated RISC complex (h ) Chosen to be negligible once 1 · 10 activated RISC is formed kdisRISCm Dissociation of activated RISC complex and target mRNA (h ) Literature (42–44) 1 1 2 kelimec Extracellular complex degradation (h ) Estimated from experimental data 8.7 · 10 2.9 · 10 1 2 kelimpl Plasma complex degradation (h ) Estimated from experimental data 5.8 · 10 1 2 kescendna Endosomal escape for siRNA (h ) Estimated from experimental 6 · 10 data and literature (54) 1 2 kescendvec Endosomal escape for complex (h ) Estimated from experimental 1 · 10 data and literature (54) 1 1 13 kformmRNA Formation of target mRNA (# L h ) Literature (50,51) 5.2 · 10 1 2 kformprot Formation of target protein (h ) Literature (50,51) 5.2 · 10 1 1 19 kformRISC Formation of activated RISC complex (L # h ) Estimated from experimental data 2 · 10 1 1 14 kformRISCm Formation of activated RISC/mRNA complex (L # h ) Literature (42–44) 1.1 · 10 kgrowth Cell growth rate (h ) Determined experimentally Fit to each system 1 5 kint Internalization (h ) Literature (12,13,55) 1 · 10 5 · 10 1 2 ktransblood Transport from plasma to extracellular fluid (h ) Estimated from experimental data 1 · 10 1 1 kunpackcyt Cytosolic complex unpackaging (h ) Estimated from experimental data 5 · 10 6 · 10 1 4 kunpackend Endosomal complex unpackaging (h ) Estimated from experimental data 1 · 10 1 · 10 For parameters common to both in vitro and in vivo applications, the in vivo parameter values are shown in italics below the in vitro parameter values. minimal impact on the overall duration (Figure 2A). Using the can alter the duration of gene silencing. Consistent with pre- baseline parameters given in Table 2, the mathematical model vious observations, the duration of gene silencing in rapidly predicts the trends observed experimentally (Figure 2B). growing cell lines is 1 week; however, cell lines with slower Similar trends are observed with these siRNA doses in doubling times show a corresponding increase in the duration other luciferase-expressing cell lines (data not shown). of silencing. Figure 3B shows the predicted effect of cell doubling time when the experimental transfection parameters are input into the mathematical model. The model predictions Effect of cell doubling time on luciferase conﬁrm that the dilution effect due to cell doubling time alone knockdown in vitro can account for the decreased duration of gene silencing in The majority of studies examining the kinetics of siRNA- dividing cells. It is interesting to note that the duration of gene mediated gene silencing in vitro have used rapidly dividing silencing in nondividing cells is 3 weeks. This duration is cell lines that typically have doubling times of 1 day. Using consistent with the kinetics observed in two previous reports these cell lines, the silencing effect generally lasts for 1 week looking at siRNA-mediated gene silencing in nondividing (27,28). To investigate whether this duration of silencing is mammalian neurons and primary macrophages (29,30). In intrinsic to siRNA or a result of dilution due to cell division, nondividing cells, the duration of gene silencing is not con- siRNA-mediated gene silencing was monitored in four trolled by dilution from cell division but by the intrinsic sta- luciferase-expressing cell lines with different observed dou- bility of siRNA within the cell. bling times: Neuro2A-Luc (0.8 days), LNCaP-Luc (1.4 days), HeLa-Luc (1.6 days) and CCD-1074Sk-Luc (nondividing). Kinetics of luciferase knockdown by The cells were plated in 24-well plates and transfected siRNA in subcutaneous tumors under identical conditions to enable direct observation of the effect of cell doubling time alone. The experimental results Many tumors exhibit rapid growth with doubling times on the in Figure 3A reveal that the dilution effect from cell division order of only a few days, and the duration of gene silencing Nucleic Acids Research, 2006, Vol. 34, No. 1 327 Figure 2. Effect of siRNA dose on the duration and magnitude of luciferase Figure 3. Effect of cell doubling time on the duration of luciferase knockdown knockdown by siRNA in nondividing cells. (A) Experimental results using by siRNA in vitro.(A) Experimental results using Oligofectamine to deliver Oligofectamine to deliver siRNA to luciferase-expressing, nondividing fibro- 100 nM siRNA to luciferase-expressing cells with a range of doubling times blasts with 1.5 · 10 cells per well in a 24-well plate. Data points represent the (dt). Data points represent the ratio of the average luciferase signal intensity ratio of the average luciferase signal intensity from triplicate wells receiving from triplicate wells receiving siGL3 and siCON1 on day 0. Squares, Neuro2A- siGL3 and siCON1 on day 0. Squares, 10 nM; diamonds, 25 nM; triangles, Luc (dt ¼ 0.8 d); diamonds, LNCaP-Luc (dt ¼ 1.4 d); triangles, HeLa-Luc 50 nM; circles, 100 nM. (B) Luciferase knockdown after siRNA transfection (dt ¼ 1.6 d); circles, CCD-1074Sk-Luc (nondividing). (B) Luciferase knock- predicted by the mathematical model using the baseline in vitro parameters down after siRNA transfection predicted by the mathematical model using the given in Table 2 with the number of cells held constant at 1.5 · 10 , a transfec- baseline in vitro parameters given in Table 2 with the initial number of dividing 4 5 tion time of 5 h, and a transfection efficiency of 90%. and nondividing cells equal to 5 · 10 and 1.5 · 10 , respectively, a transfec- tion time of 5 h, and a transfection efficiency of 90%. should be limited by this rapid cell division. To test this hypothesis, subcutaneous tumors were created in A/J mice By adjusting only the parameters for the circulation/ using luciferase-expressing Neuro2A-Luc cells. Since the extracellular transport of the siRNA polyplexes, very good goal was to observe the kinetics of gene silencing and not agreement was obtained between the model’s predictions and the experimental data. The observed knockdown duration an actual therapeutic effect on the growth rate of the cells, siRNA against the luciferase gene (siGL3) and a control after three consecutive injections was around 10 days, con- siRNA (siCON1) were used to show the sequence- sistent with the in vitro data for cell lines with similar observed speciﬁcity of the luciferase knockdown. Each mouse received growth rates. three consecutive daily LPTV injections of transferrin- targeted polyplexes containing 2.5 mg/kg siRNA. After quan- Kinetics of luciferase knockdown by tifying the luciferase activity in each tumor using the Xenogen siRNA in hepatocytes camera, data were used to create a predicted logistic growth curve (Figure 4A). Because the siRNA targets only the While cells in subcutaneous tumors are dividing rapidly (e.g. luciferase gene, the growth rate of the cells should be unaf- once per day), most of the hepatocytes in a normal mouse liver fected; as a result, a decrease in luciferase signal intensity are in a state of growth arrest (31). Therefore, it was hypothe- indicates a change in the luciferase protein level. Normaliza- sized that gene silencing by siRNA would exhibit different tion to predicted growth curves allowed estimation of the kinetics in hepatocytes versus tumors. Each BALB/c mouse knockdown resulting from siRNA treatment (Figure 4B). received a single HPTV injection of 0.25 mg/kg plasmid and 328 Nucleic Acids Research, 2006, Vol. 34, No. 1 Figure 5. Kinetics of luciferase knockdown by siRNA in nondividing hepatocytes in BALB/c mice. Experimental and predicted results are shown for luciferase knockdown after hydrodynamic tail-vein co-injection of 5 mg pApoEHCRLuc and 50 mg siRNA per 20 g mouse on day 0. Circles represent the ratio of the average luciferase signal intensity from three mice receiving plasmid + siRNA to the luciferase signal intensity from three mice receiving plasmid alone. The predicted luciferase knockdown, given by the solid line, was calculated using the baseline in vivo parameters given in Table 2 with the following modifications to account for hydrodynamic injection of naked siRNA without a delivery vehicle: eliminate steps involving the complexes (kescend- vec, kunpackend, kunpackcyt), modify uptake and intracellular trafficking to match observed kinetics (partition ¼ 1 · 10 , ktransblood ¼ 1, kint ¼ 1 · 3 1 2 1 3 1 10 h , kescendna ¼ 1 · 10 h , kdegendna ¼ 5 · 10 h ), and modify extracellular volume (Ve ¼ 1.5 · 10 L). The kescendna and kdegendna may no longer represent endosomal processes as hydrodynamically injected naked siRNA may be internalized through different vesicles or parti- tioned into a separate intracellular compartment (e.g. nucleus) that exhibits different degradation and release kinetics than in standard or receptor-mediated endocytosis of siRNA-containing complexes. The total number of hepatocytes was chosen to be 5 · 10 , on the same order of magnitude as the number of hepatocytes in a mouse liver (40,41). Figure 4. Kinetics of luciferase knockdown by siRNA in Neuro2A-Luc sub- cutaneous tumors in A/J mice. (A) Experimental and predicted results for ﬁeld of nucleic acid-based therapeutics seek to enhance luciferase knockdown after three consecutive LPTV injections on days 6, 7 the stability of the nucleic acids with the goal of increasing and 8 of transferrin-targeted CDP-Im polyplexes containing 50 mg siRNA per the duration of gene silencing by boosting their bioavailability 20 g mouse. Experimental data points are shown for a mouse receiving siCON1 and possibly prolonging their persistence intracellularly (squares) and a mouse receiving siGL3 (circles). Solid lines represent the predicted luciferase signal with siRNA treatment and dashed lines represent (32–34). Layzer and co-workers studied the kinetics of gene the predicted luciferase signal in the absence of siRNA treatment. (B) Normal- silencing in HeLa cells using 2 -F-modiﬁed siRNA and ization of the observed luciferase signal in the siGL3-treated mouse to the 0 0 unmodiﬁed 2 -OH siRNA. Although the 2 -F-modiﬁed predicted luciferase signal in the absence of treatment. Circles indicate siRNA led to a signiﬁcant increase in serum stability, it the normalized experimental data points, while the solid line represents the response predicted by the mathematical model using the baseline in vivo appeared to have no effect on the duration of gene silencing parameters given in Table 2 and assuming that 50% of the total cells are reached after transfection. This suggests that the intracellular stability with each dose. of siRNA molecules is not the limiting factor controlling the duration of gene silencing in rapidly dividing cells; instead, 2.5 mg/kg siGL3 on day 0, and the Xenogen camera was used dilution due to cell division limits how long gene silencing can to follow the luciferase signal in each mouse liver. Normal- occur under these conditions. If the intracellular half-life of ization to the signal intensity in mice that received plasmid siRNA molecules is already around 24 h, then even modiﬁ- only (no siRNA) allowed quantiﬁcation of the percent knock- cations to increase the half-life to >72 h have an insigniﬁcant down by siRNA. Figure 5 shows the experimental data effect on the duration of gene silencing (Figure 6). These together with the model predictions. Similar to the in vitro model predictions corroborate the experimental results results for gene silencing in nondividing cells, the duration of obtained by Layzer and co-workers (33). On the other gene silencing lasts for 3–4 weeks in the hepatocytes after a hand, the outcome of using modiﬁed siRNA may be different single dose of siRNA. in slowly dividing or nondividing cells since the intracellular siRNA half-life will be shorter than the cell doubling time, meaning dilution due to cell division will no longer be the Effect of siRNA stability on luciferase dominant factor. Increasing the persistence of siRNA within knockdown by siRNA the cell might prolong the duration of gene silencing. Because both double-stranded and single-stranded nucleic Results from such studies in nondividing cells should be inter- acids are rapidly degraded in serum, current efforts in the preted carefully since the apparent intracellular stability of Nucleic Acids Research, 2006, Vol. 34, No. 1 329 Figure 6. Effect of intracellular siRNA half-life on the duration of siRNA-mediated gene silencing in vitro. Curves represent model predictions for luciferase knockdown after transfection with 100 nM siRNA against luciferase on day 0 with a cell doubling time of 1 day (kgrowth ¼ 0.0.029 h ) and intracellular siRNA half-lives of 24, 48 and 72 h (kdeginna ¼ 0.029, 1 4 0.014 and 0.01 h ). The initial number of cells was 5 · 10 , transfection time was 5 h, transfection efficiency was 90%, and all other parameters were kept at their baseline in vitro values given in Table 2. siRNA molecules may be caused by association with other intracellular components or localization to speciﬁc compart- ments, both of which could lead to degradation kinetics inde- pendent of the properties of the siRNA molecules alone. In that case, modiﬁed siRNA would not necessarily increase the dura- tion of gene silencing relative to unmodiﬁed siRNA even in nondividing cells. Multiple doses to prolong luciferase knockdown by Figure 7. Effect of siRNA dose frequency on the duration of luciferase knock- siRNA in nondividing cells down by siRNA in nondividing cells. (A) Experimental results using Oligofectamine to deliver siRNA to luciferase-expressing nondividing fibro- The previous studies have looked at the transient knockdown blasts in vitro. Data points represent the ratio of the average luciferase signal of the luciferase reporter gene by 1–3 injections of siRNA intensity from triplicate wells receiving siGL3 and siCON1. To facilitate com- over a short-term period; even in nondividing cells, the parison of the knockdown kinetics, the data points are normalized such that all three curves exhibit the same magnitude of knockdown for the first four days maximum duration of silencing using typical siRNA doses since all three received the same treatment over this period. This normalization is 3–4 weeks. However, a clinically relevant treatment regi- permits comparison of the kinetics of gene silencing observed with different men using siRNA may require that a gene be silenced for a treatments even though the absolute magnitude of the knockdown varied prolonged period of time. Some have attempted to solve this slightly in each experiment. Squares, 100 nM (day 0); diamonds, 100 nM problem by using lentiviral delivery of expressed short-hairpin (day 0) + 10 nM (day 4); triangles, 100 nM (day 0) + 100 nM (day 4). (B) Luciferase knockdown after siRNA transfection predicted by the siRNAs (shRNAs) to achieve sustained gene silencing in vitro mathematical model using the baseline in vitro parameters given in Table 2 and in vivo (35,36). Precise control of the intracellular level of with the number of cells equal to 1.5 · 10 , a transfection time of 5 h, and a siRNA and having a means to turn off its production when transfection efficiency of 90%. treatment is no longer necessary represent two major chal- lenges to this use of shRNA. On the other hand, the intrinsi- Considerations for siRNA-based treatments that cally transient nature of siRNAs makes them more amenable require a threshold knockdown for efficacy to disease treatments in which the treatment is given over a period of time and then stopped once the desired therapeutic Because siRNA treatment of rapidly dividing cells requires outcome (e.g. regression of a tumor or inhibition of viral treating more cells over time while also having to deal with growth) is achieved. To illustrate how properly timed doses dilution effects, the amount of target gene or protein knock- of siRNA can prolong gene silencing by siRNA, nondividing down will be less than that observed in slowly dividing or CCD-1074Sk-Luc cells were transfected with a second dose of nondividing cells. More frequent dosing is required to over- siRNA 4 days after the initial dose (Figure 7A). With a second come these barriers. Cancer is one example of a disease often dose of 100 nM siRNA, the luciferase protein levels remained characterized by rapid cell division that may require target at <40% of the steady-state value for an additional 4 days. If gene knockdown lasting longer than that which can be the trends continue in such a fashion, a 100 nM dose every achieved with a single dose of siRNA. To address this situ- 4 days could lead to persistent gene silencing as shown by ation, the mathematical model was used to estimate siRNA dosing schedules needed to maintain a given gene below a model calculations in Figure 7B. 330 Nucleic Acids Research, 2006, Vol. 34, No. 1 threshold value for an extended period of time in dividing using mathematical modeling to give insights that help direct cells. While the magnitude of target gene (or protein) reduc- experimental studies. Here, we employed bioluminescent tion or the duration of knockdown relative to the steady-state imaging and mathematical modeling to investigate the effects value in the absence of treatment can be relatively good indi- of target-speciﬁc and treatment-speciﬁc parameters on siRNA- cators of the success of an siRNA treatment, the therapeutic mediated gene silencing in vitro and in vivo. efﬁcacy of an siRNA treatment regimen should perhaps be The experimental data presented here show the effects of judged by the length of time it is able to maintain the target cell doubling time, siRNA dosing schedule, and siRNA deliv- gene or protein level below a given threshold. Although a ery method on luciferase reporter-protein knockdown and aid short, substantial knockdown of certain targets may be sufﬁ- in developing mathematical models of siRNA delivery to and cient to trigger a cascade of downstream effects, other situa- function within mammalian cells. Luciferase knockdown in tions may require considerably longer knockdown to achieve cell lines engineered to constitutively express luciferase was the desired therapeutic effect. Additionally, this therapeutic used to mimic the knockdown of an endogenously expressed effect may only be seen when the target protein is reduced gene, analogous to an oncogene whose presence in a cell can below a threshold, or some fraction of its pre-treatment value. lead to tumorigenicity. The luciferase-expressing cell lines The data in Figure 8 show how the mathematical model can were used in cell culture experiments or injected into mice be used to simulate the effects of cell doubling time and target and then monitored for luciferase expression using noninva- protein half-life during treatment with siRNA. To avoid sive bioluminescent imaging with the Xenogen Imaging unnecessary complications, the calculations ignore the circu- System. The duration of gene silencing lasted for 1 week lation/extracellular transport and consider each siRNA dose in rapidly dividing cells but longer than 3 weeks in nondivid- already in the local extracellular environment of the cells ing cells both in vitro and in vivo, supporting the hypothesis (analogous to the in vitro situation). Figure 8A–D gives results that dilution due to cell division is the major factor controlling the duration of luciferase knockdown in rapidly dividing cells. that demonstrate how target protein half-life can impact the The duration of gene silencing by siRNA can be longer than observed dynamics of protein knockdown with once- or twice- weekly dosing in rapidly dividing or nondividing cells. For a that achieved with other nucleic acid-based gene inhibition target protein with a short half-life in rapidly dividing cells, strategies, such as antisense, whose knockdown typically lasts even twice-weekly dosing still can result in signiﬁcant oscil- only on the order of 1–2 days. Bertrand and co-workers (37) lations which may hinder the ability to cause a phenotypic studied antisense- and siRNA-mediated inhibition of GFP in change in the target cells (Figure 8A). If the target protein has a HeLa cells and showed that while antisense-mediated inhibi- long half-life, then twice-weekly dosing is able to maintain tion diminished after only 1 day, the siRNA-mediated inhibi- steady knockdown at 50% of the steady-state level, but this tion was still increasing. This signiﬁcant difference in the magnitude of protein knockdown is not achieved until about a duration of gene silencing could become important when try- week after the ﬁrst dose of siRNA (Figure 8B). In nondividing ing to use either antisense or siRNA molecules as therapeutic cells, once-weekly dosing is adequate to maintain persistent agents. In fact, the short duration of gene silencing by certain silencing at 20% of the steady-state value (Figure 8C and D). nucleic acid-based gene inhibition strategies could preclude Again, this protein knockdown can only be achieved after their ability to alter cellular behavior if the target gene is not more than a week from the initial siRNA dose if the target silenced for an adequate amount of time. This would be par- protein half-life is very long (Figure 8D). The fraction of the ticularly apparent if the target protein has a long intracellular total treatment time during which a target protein is below a half-life; then, knockdown of the target mRNA may not result threshold (e.g. 50% steady-state value) can be used as a metric in target protein knockdown if the mRNA levels can be res- to compare the efﬁcacy of different treatment regimens. The tored before a signiﬁcant amount of protein has degraded. data illustrated in Figure 8E reveal how cell growth rate and The ﬁndings presented here highlight several key consid- target protein half-life can affect protein knockdown when erations for experimental design when evaluating the efﬁcacy siRNA is administered once on day 0, once-weekly or of siRNA against certain genes that produce proteins with long twice-weekly over the 25-day treatment. As expected, cell half-lives. If the knockdown phenotype does not become apparent until the protein is below a certain threshold, then growth rate has a large impact on the duration of knockdown, observation at early time points may not reveal any effect. This directly affecting the fraction of the total time that the target is crucial for in vitro studies aimed at testing the ability of a protein level can be reduced below the threshold of 50%. therapeutic siRNA to induce apoptosis or growth arrest in certain cell lines. Common practice is to look at time points DISCUSSION within 48 and 72 h; here, model predictions suggest that these A more thorough understanding of the factors affecting the time points may be too early if the target protein half-life is any kinetics of siRNA-mediated gene silencing should prove to be longer than a couple of days. Similar considerations should be invaluable for experimental and clinical applications of made when deciding dosing schedules for in vivo studies using siRNA. Given the relatively recent discovery of RNAi, details siRNA for protein knockdown in tumors (e.g. an oncogenic of its action are still being elucidated, and many of the current fusion protein), since proteins with longer half-lives will show siRNA dosing schedules used in literature are based on prece- a slower initial response to the therapy but will require less dence rather than being optimized for each system. The high frequent dosing for persistent silencing. An important area for cost of siRNA molecules, especially for in vivo studies, limits future research will be to determine to what extent a gene or systematic exploration of the parameter space needed to protein needs to be knocked down before the intended thera- achieve the most effective siRNA dosing schedule for each peutic effect is realized. Such information can be combined model system. This situation can be partially rectiﬁed by with mathematical models like the one presented here to more Nucleic Acids Research, 2006, Vol. 34, No. 1 331 Figure 8. Effect of cell doubling time and target protein half-life on the ability to maintain persistent gene silencing. All plots represent predicted mRNA (dashed lines) and protein (solid lines) knockdown in transfected cells using the baseline in vitro parameters given in Table 2, a transfection time of 5 h, and an initial number 4 5 of dividing and nondividing cells equal to 5 · 10 and 1.5 · 10 , respectively. (A) Dose of 100 nM siRNA every 3 days with a target protein half-life of 1 1 2h (kdegprot ¼ 0.35 h ) in cells with a doubling time of 1 day (kgrowth ¼ 0.029 h ). (B) Dose of 100 nM siRNA every 3 days with a target protein 1 1 half-life of 48 h (kdegprot ¼ 0.014 h ) in cells with a doubling time of 1 day (kgrowth ¼ 0.029 h ). (C) Dose of 100 nM siRNA every 7 days with a target protein half-life of 2 h (kdegprot ¼ 0.35 h ) in nondividing cells. (D) Dose of 100 nM siRNA every 7 days with a target protein half-life of 48 h (kdegprot ¼ 0.014 h ) in nondividing cells. (E) Effect of variations in cell doubling time and target protein half-life on the ability to maintain a target protein level below a threshold of 50% its pre-treatment value over the 25-day period. I, 100 nM (day 0); II, 100 nM (days 0, 7, 14); III, 100 nM (days 0, 3, 7, 10, 14, 17, 21, 24). Surface vertices represent the fraction of the total time during which the relative protein level is below the 50% threshold. 332 Nucleic Acids Research, 2006, Vol. 34, No. 1 accurately determine the required treatment regimen needed to stability enables knockdown that can last for weeks in nondi- achieve efﬁcacy. Although the model in its current form does viding cells. It is shown here that an optimized siRNA-based not allow for treatment effects other than target gene knock- treatment schedule can be designed to achieve prolonged gene down, the simple addition of a death parameter to the cell silencing by properly timed injections of siRNA. Mathemati- growth equation could provide a target cell death rate that cal modeling can help to realize these optimized treatments at depends on the reduction of the target protein level below a a fraction of the time and cost that would be required by certain threshold. Other slightly more complicated modiﬁca- experimentation alone. Although there is no substitute for tions to the current set of equations could incorporate recruit- experimental data, especially for highly variable and not com- ment of immune effector cells, effects on angiogenesis or even pletely deﬁnable biological systems, model calculations can sensitization to other treatments including chemotherapy. help to guide effective experimental design and aid in data While the mathematical model can predict many of the interpretation. With the burgeoning interest in nucleic acid- trends observed experimentally for the systems used here, based therapeutics such as siRNA, development of mathemati- conﬁdence in the actual magnitude and duration of the pre- cal models such as the one presented here may expedite their dicted gene silencing in hypothetical situations can still be translation into clinically relevant therapeutics for disease greatly increased as more accurate parameter values become treatment and management. available. Parametric sensitivity analysis was performed using the SENS_SYS modiﬁcation of the ODE15s solver in MAT- SUPPLEMENTARY DATA LAB. Parameters governing RISC formation (kformRISC) and binding to target mRNA (kformRISCm) have a signiﬁcant Supplementary Data are available at NAR Online. impact on target mRNA or protein levels. Although studies of the RISC complex are rapidly elucidating details of its ACKNOWLEDGEMENTS mechanism and kinetics, these parameters will need to be reﬁned as more data become available. Additional equations The authors are especially grateful to D. Petersen and D. Kohn will be needed to model a multi-step RISC formation process, (Children’s Hospital Los Angeles) for performing the lentiviral or the lumped rate constants currently used can be modiﬁed to transductions of the luciferase-expressing cell lines; A. provide reasonable estimates of the overall kinetics. As McCaffrey and M. Kay (Stanford University) for donating expected, target mRNA and protein levels are also sensitive the luciferase-containing plasmid; and J. Heidel (Calando to parameters governing the siRNA delivery process, such as Pharmaceuticals, Inc.) for performing bioluminescent imaging cellular uptake, endosomal escape and vector unpackaging. It of the mice used in the HPTV studies looking at hepatocyte- will be important to determine these parameters for each indi- specific luciferase expression. This material is based upon work vidual delivery vehicle since such rates will vary from system supported under a National Science Foundation Graduate to system. With knowledge of these different parameters, the Research Fellowship. This publication was made possible by model can be used to mimic delivery by a variety of methods Grant Number 1 R01 EB004657-01 from the National including naked siRNA (by high-pressure or low-pressure tail- Institutes of Health (NIH). Its contents are solely the respon- vein injection) or formulation into liposomes, lipoplexes or sibility of the authors and do not necessarily represent the polyplexes. Such comparisons may reveal how the character- official views of the NIH. Funding to pay the Open Access istics of each delivery method speciﬁcally affect the kinetics of publication charges for this article was provided by the gene silencing. This information may help to focus design California Institute of Technology. improvements for delivery vehicles or improve the efﬁcacy Conflict of interest statement. None declared. of treatment regimens employing them, as suggested in gen- eral for gene delivery by Varga and co-workers (38). Of the parameters intrinsic to the target cells, the most important are REFERENCES the cell growth rate (dilution effect), compartment volumes 1. Fire,A., Xu,S., Montgomery,M.K., Kostas,S.A., Driver,S.E. and (that control the concentration of siRNA available to drive Mello,C.C. 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Publisher: Oxford University Press
Copyright: © The Author 2006. Published by Oxford University Press. All rights reserved  The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact [email protected]
ISSN: 0305-1048
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DOI: 10.1093/nar/gkj439
pmid: 16410612
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Abstract

Published online January 12, 2006 322–333 Nucleic Acids Research, 2006, Vol. 34, No. 1 doi:10.1093/nar/gkj439 Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging Derek W. Bartlett and Mark E. Davis* Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA Received December 2, 2005; Revised and Accepted December 23, 2005 discovery in Caenorhabditis elegans in 1998 (1), it has ABSTRACT rapidly attracted attention from researchers in ﬁelds ranging Small interfering RNA (siRNA) molecules are potent from genetics to clinical medicine. A natural intracellular effectors of post-transcriptional gene silencing. process likely involved in cell-based defense against mobile Using noninvasive bioluminescent imaging and a genetic elements such as viruses and transposons (2), RNAi mathematical model of siRNA delivery and function, promises to be an invaluable tool for gene function analysis the effects of target-specific and treatment-specific as well as a powerful therapeutic agent that can be used to silence pathogenic gene products associated with dis- parameters on siRNA-mediated gene silencing are eases including cancer, viral infections and autoimmune monitored in cells stably expressing the firefly disorders (3–8). luciferase protein. In vitro, luciferase protein levels A central component of RNAi is a double-stranded siRNA recover to pre-treatment values within ,1 week in molecule that is 21–23 nt in length with 2 nt long 3 overhangs rapidly dividing cell lines, but take longer than (9). These siRNA effector molecules can be introduced into 3 weeks to return to steady-state levels in nondividing cells directly as synthetic siRNAs or indirectly as precursor fibroblasts. Similar results are observed in vivo, with long dsRNAs or short-hairpin RNAs (shRNAs). RNA poly- knockdown lasting 10 days in subcutaneous tumors merase II- or III-driven expression cassettes can be used for in A/J mice and 3–4 weeks in the nondividing constitutive expression of shRNA molecules (10). Both the hepatocytes of BALB/c mice. These data indicate long dsRNAs and shRNAs are cleaved by Dicer (RNase III that dilution due to cell division, and not intracellular family of endonucleases) into the appropriately sized siRNA effectors. Although the presence of dsRNA >30 nt can elicit an siRNA half-life, governs the duration of gene silencing interferon response in mammalian cells (11), Elbashir and co- under these conditions. To demonstrate the practical workers demonstrated that synthetic 21mer siRNAs evaded use of the model in treatment design, model calcula- the interferon response and yet were still effective mediators tions are used to predict the dosing schedule required of sequence-speciﬁc gene silencing in mammalian cells (9). to maintain persistent silencing of target proteins with Here, we have chosen to focus on the use of synthetic 21mer different half-lives in rapidly dividing or nondividing siRNA duplex molecules in mammalian cells for transient cells. The approach of bioluminescent imaging com- gene silencing. bined with mathematical modeling provides useful Because synthetic siRNA molecules must be transported insights into siRNA function and may help expedite into the cells before they can function in RNAi, successful the translation of siRNA into clinically relevant thera- delivery of siRNA is of central importance. Delivery vehicles peutics for disease treatment and management. must protect the siRNA from nucleases in the serum or extra- cellular media, enhance siRNA transport across the cell membrane and guide the siRNA to its proper location through interactions with the intracellular trafﬁcking machinery. INTRODUCTION While naked siRNA molecules have been shown to enter RNA interference (RNAi) refers to the ability of double- cells, signiﬁcantly more siRNA can be delivered using car- stranded RNA (dsRNA) to cause sequence-speciﬁc degra- rier vehicles (12,13). Both viral and nonviral vectors deli- dation of complementary mRNA molecules. Since its ver siRNA into cells, although viral vectors are limited to *To whom correspondence should be addressed. Tel: +1 626 395 4251; Fax: +1 626 568 8743; Email: [email protected] The Author 2006. Published by Oxford University Press. All rights reserved. The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact [email protected] Nucleic Acids Research, 2006, Vol. 34, No. 1 323 delivering siRNA-expressing constructs such as shRNA. Com- MATERIALS AND METHODS mercially available cationic lipids such as Oligofectamine can Production of luciferase-expressing cell lines by effectively deliver siRNA molecules into cells in vitro with lentiviral transduction transfection efﬁciencies approaching 90% (9). However, the Cell lines were incubated with viral supernatant containing high toxicity of cationic lipids limits their use for systemic SMPU-R-MNCU3-LUC, a lentiviral vector based on HIV-1 delivery in vivo. Recent studies from our laboratory have that transduces the ﬁreﬂy luciferase gene. The backbone vector shown that cyclodextrin-containing polycations (CDPs) can SMPU-R has deletions of the enhancers and promoters of the achieve safe and effective systemic delivery of siRNA in HIV-1 long terminal repeat (SIN), has minimal HIV-1 gag mice (14). Here, we consider the nonviral delivery of sequences, contains the cPPT/CTS sequence from HIV-1, siRNA using cationic lipids or polymers. has three copies of the UES polyadenylation enhancement A challenge for the successful application of siRNA will element from SV40 and has a minimal HIV-1 RRE [gift be to determine the dosing schedule required for efﬁcacy, from Paula Cannon, Children’s Hospital Los Angeles, Los making insights into the kinetics of siRNA-mediated gene Angeles, CA (19)]. The vector has the U3 region from the silencing foundational for the future clinical use of siRNA. MND retroviral vector as an internal promoter driving expres- Without a proper understanding of the kinetics of the pro- sion of the ﬁreﬂy luciferase gene from SP-LUC+ [Promega, cess and the parameters that can affect the resulting gene Madison, WI (20)]. silencing, application of RNAi will be governed largely by trial and error. The ability to speciﬁcally tailor and optimize siRNA duplexes the treatment for each particular system would save signiﬁcant time and resources, especially given the high cost of synthetic All siRNA molecules were ordered puriﬁed and pre-annealed siRNA molecules and the amount of material required for (‘Option C’) from Dharmacon Research, Inc. (Lafayette, CO). 0 0 in vivo studies. Mathematical modeling using simple kinetic siGL3 (sense, 5 -CUUACGCUGAGUACUUCGAdTdT-3 ; 0 0 equations for each step in the RNAi process can shed light antisense, 5 -UCGAAGUACUCAGCGUAAGdTdT-3 )isan on many of these questions regarding the kinetic aspects of unmodiﬁed siRNA duplex that targets the luciferase gene, RNAi. To our knowledge, there are only a few published while siCONTROL non-targeting siRNA #1 (siCON1; sense, 0 0 0 examples of such studies looking at the kinetics of the intra- 5 -UAGCGACUAAACACAUCAAUU-3 ;antisense, 5 -UUG- cellular RNAi process (15–18). Of these studies, none has AUGUGUUUAGUCGCUAUU-3 ) is an unmodiﬁed siRNA combined the delivery process and the interaction with the duplex bioinformatically designed to minimize the potential RNAi machinery in mammalian cells. Bergstrom and for targeting any known human or mouse genes. co-workers (15) proposed a unidirectional ampliﬁcation method in their mathematical model of RNAi-mediated In vitro transfections gene silencing. Because no RNA-dependent RNA polymerase Cells were seeded in 24-well plates 2–3 days prior to trans- has yet been found in mammalian cells, they acknowledged 4 5 fection at 2 · 10 –1 · 10 cells per well and grown in media that their model did not address the silencing mechanisms supplemented with 10% fetal bovine serum (FBS) and anti- observed in mammals. Groenenboom and co-workers (16) biotics (penicillin/streptomycin). siRNA was complexed recently proposed a mathematical model for RNAi that with Oligofectamine (Invitrogen, Carlsbad, CA) according contained several extensions to the core RNAi pathway, pro- to the manufacturer’s instructions and applied to each well viding for siRNA degradation by RNase as well as primed in a total volume of 200 ml OptiMEM (Invitrogen). Trans- ampliﬁcation. Their model aimed to explain transgene- fection medium was removed and replaced with complete or virus-induced gene silencing and avoidance of self- medium after 5 h. reactivity, but did not consider any steps in the delivery process. Similarly, Raab and Stephanopoulos (17) looked at Formation of subcutaneous tumors in mice the dynamics of gene silencing by siRNA given at different Luciferase-expressing Neuro2A (Neuro2A-Luc) cells were doses and at various times relative to plasmid transfection, but grown to conﬂuence in media supplemented with 10% FBS did not incorporate siRNA delivery. Arciero and co-workers and antibiotics (penicillin/streptomycin). Immediately prior to (18) created a mathematical model to investigate tumor- injection, cells were washed with phosphate-buffered saline immune evasion and siRNA treatment. Although this model (PBS), trypsinized and resuspended in serum-free media at provided insights into how siRNA can be used in cancer 2 · 10 cells/ml. Each mouse received 0.5 ml of the resulting treatment, it did not examine the delivery process and there cell suspension by subcutaneous injection. were no experimental data from in vitro or in vivo studies. Here, we use bioluminescent imaging and mathematical Low-pressure tail-vein (LPTV) injection of modeling to investigate the steps of RNAi from siRNA deliv- formulated siRNA polyplexes ery to intracellular function with the aim of enabling the practical application and design of siRNA-based treatment All complexes were made with siRNA and an imidazole- strategies both in vitro and in vivo. Because the imaging is modiﬁed CDP (CDP-Im) synthesized as described previously noninvasive and nondestructive, the same set of cells or ani- (21,22). Before addition to siRNA, CDP-Im was mixed with mals can be followed for the entire study. These results will an adamantane-PEG (AD-PEG) conjugate and an AD- complement investigations using more traditional analytical PEG-transferrin (Tf) conjugate such that the total moles of methods to monitor mRNA or protein knockdown and hope- AD-PEG or AD-PEG-Tf equaled the number of moles of fully serve to encourage the rational design of experimental b-CD. Tf-targeted polyplexes contained 1% AD-PEG-Tf rel- and clinical siRNA-based treatments. ative to AD-PEG. This mixture was added to an equal volume 324 Nucleic Acids Research, 2006, Vol. 34, No. 1 Figure 1. Simplified schematic of the key steps required for siRNA delivery to and function within mammalian cells. Steps 1–3 are unique to in vivo application of siRNA, whereas steps 4–9 represent the general processes on the level of an individual cell and are therefore common to both in vivo and in vitro application of siRNA. of siRNA at a charge ratio (positive charges from CDP-Im to light emission. Mice were anesthetized with an initial dose negative charges from siRNA backbone) of 3:1 (+:). An of 5% isoﬂurane followed by a maintenance dose of 2.5% equal volume of 10% (w/v) glucose in water was added to isoﬂurane. Bioluminescent signal intensities were quantiﬁed the resulting polyplexes to yield a 5% (w/v) glucose (D5W) using Living Image software (Xenogen). solution suitable for injection. Each mouse was injected with 200 ml of this polyplex solution containing 50 mg siRNA per Mathematical model 20 g mouse (2.5 mg/kg siRNA). The model presented here was designed to allow the user High-pressure tail-vein (HPTV) co-injection of to speciﬁcally study the impact of parameter values on plasmid and siRNA gene silencing by RNAi. When designing an siRNA-based treatment, the main controllable parameters are the Hydrodynamic, or HPTV, injection of nucleic acids can delivery method (naked siRNA, formulated with vector, achieve signiﬁcant levels of nucleic acid in the hepatocytes chemically modiﬁed) and dosing schedule. These choices of mice (23,24). A. McCaffrey and M. Kay kindly donated a must be governed by parameters such as the target mRNA plasmid (pApoEHCRLuc) containing the ﬁreﬂy luciferase half-life, target protein half-life, threshold for reduction gene under the control of the human a -antitrypsin promoter (in either target mRNA or protein), number of target cells and the apolipoprotein E locus control region. For HPTV and desired knockdown duration. The model’s design co-injection studies in BALB/c mice, each 20 g mouse criteria therefore included the ability to enable user-deﬁned received a 10% w/v injection of a D5W solution containing values for these parameters that characterize each experi- 0.25 mg/kg of the luciferase-containing plasmid and 2.5 mg/kg mental system. siRNA. A simpliﬁed schematic of the major processes included in the model is shown in Figure 1. Model variables (Table 1) and Bioluminescent imaging parameters (Table 2) were used to develop a set of ordinary Cell culture plates or mice containing the luciferase- differential equations for the steps involved in siRNA delivery expressing cells were imaged using the Xenogen IVIS 100 to and function within mammalian cells in vitro and in vivo. Imaging System (Xenogen, Alameda, CA). D-luciferin The differential equations governing each major process from (Xenogen) was dissolved in PBS at 15 g/l. For in vitro assays the delivery of siRNA to its intracellular interaction with the in 24-well plates, 50 ml of the 15 g/l luciferin solution was RNAi machinery are grouped into modules that can be added to each well containing 1 ml of media. Light emission changed independently to modify the model complexity as was measured 2–3 min after addition of the luciferin. For desired. A detailed description of the mathematical model in vivo experiments, 0.2 ml of the 15 g/l luciferin solution and the rationale for its design are provided in the Supple- was injected intraperitoneally 10 min before measuring the mentary Data. Nucleic Acids Research, 2006, Vol. 34, No. 1 325 Table 1. Model variables Cell growth and target protein production dP Name Model Description (units) ¼ kf ormprot M kdegprot P compartment dt dZ Z Bcf Plasma Free complex in circulation (# vol ) 1 ¼ kgrowth Z 1 Bcb Plasma Bound complex in circulation (# vol ) dt max Ec Extracellular Extracellular complex in local vicinity (# vol ) Enc Intracellular Endosomal complex (# vol ) All of the equations for intracellular siRNA-associated species Enna Intracellular Endosomal free siRNA (# vol ) contain a term to account for dilution due to cell division, Cc Intracellular Cytoplasmic complex (# vol ) where dilution is equal to the ratio of new cells divided by Cna Intracellular Cytoplasmic free siRNA (# vol ) R Intracellular Activated RISC complex (# vol ) the total number of cells. For example, if the number of cells C Intracellular Activated RISC complex bound to doubles in 1 day, then dilution would equal 0.5 and the con- mRNA (# vol ) centration of the intracellular species would likewise be M Intracellular Target mRNA (# vol ) reduced by 50%. For the sake of calculation simplicity, P Intracellular Target protein (# vol ) only species involving the delivered siRNA molecules are Z Intracellular Number of cells (#) diluted by this factor; all other intracellular species (i.e. target mRNA and target protein) are assumed to not change after cell division because they are produced intracellularly by both of Circulation/extracellular transport the daughter cells. The net effect of this is that the siRNA- dBcf associated species are diluted equally between the two daugh- ¼ kblooddis Bcb kbloodbind Bcf dt ter cells after each cell division. The set of ODEs was solved with MATLAB (The Math- ktransblood partition Bcf kelimpl Bcf Works, Inc., Natick, MA) using the stiff ODE15s solver. The dBcb : ODE15s solver is a variable-order solver based on the numeri- ¼ kbloodbind Bcf kblooddis Bcb dt cal differentiation formulas. Parametric sensitivity analysis dEc Vp was performed using SENS_SYS written by V. M. Garcia ¼ ktransblood partition Bcf dt Ve Molla. This MATLAB routine is an extension to the ODE15s solver that calculates the derivatives of the solution kint Ec Z kelimec Ec with respect to the parameters. Cellular uptake and intracellular trafﬁcking dEnc Ve ¼ kint Ec kescendvec Enc RESULTS dt Vi kunpackend Enc dilution Enc In vitro and in vivo experiments were conducted to gain insights into the general kinetics of siRNA-mediated gene dEnna ¼ kunpackend Enc kescendna Enna silencing in cell lines that constitutively express the luciferase dt gene. Constitutively expressed genes, in contrast to genes kdegendna Enna dilution Enna expressed transiently by plasmids, provide a more realistic dCc model for clinical application in which an endogenous ¼ kescendvec Enc kunpackcyt Cc dilution Cc gene, such as an oncogene, is the target for a therapeutic dt siRNA. The Xenogen IVIS 100 Imaging System allowed us dCna ¼ kescendna Enna þ kunpackcyt Cc þ kdisRISC R to monitor luciferase activity in luciferase-expressing cells dt growing in 24-well plates or present in subcutaneous tumors kf ormRISC ðrtot R CÞ Cna or livers in live mice; because the imaging was noninvasive, kdeginna Cna dilution Cna luciferase activity was measured in the same plate of cells or the same animals over the entire duration of the study. Moni- toring the kinetics of siRNA-mediated gene silencing in the RNAi same population of cells helps to avoid variability introduced when using different cell populations for each time point as dR ¼ kf ormRISC ðrtot R CÞ Cna þ kdisRISCm C required in luminometer-based luciferase detection or ﬂow dt cytometry (for ﬂuorescent reporters). Additionally, ﬁreﬂy þ kcleavage C kdisRISC R kdegRISC ðR þ CÞ luciferase has a short half-life of 2 h, so that its level should kf ormRISCm R M dilution R change concomitantly with the level of mRNA (25,26). This enables the use of bioluminescent imaging of luciferase pro- dC ¼ kf ormRISCm R M kdisRISCm C : tein activity as an indicator of mRNA transcript degradation by dt the delivered siRNA molecules. kdegRISC ðR þ CÞ kcleavage Cdilution C dM Effect of siRNA dose on luciferase knockdown in vitro ¼ kf ormmRNA þ kdisRISCm C kdegmRNA M dt The amount of siRNA applied to the extracellular media has a kf ormRISCm R M signiﬁcant impact on the magnitude of the gene silencing but a 326 Nucleic Acids Research, 2006, Vol. 34, No. 1 Table 2. Model parameters Name Description (units) Determination Value max Maximum number of cells (#) Determined experimentally Fit to each system partition Effective fraction of dose available to target cells Estimated from experimental data 1 · 10 1 15 rtot Total available amount of RISC protein complexes (# L ) Literature (42–44) 1.9 · 10 Ve Extracellular volume (L) Specified experimentally in vitro, 2 · 10 Estimated from experimental 1 · 10 data and literature (45,46) Vi Intracellular volume (L) Literature (47) 4 · 10 Vp Plasma volume, mouse (L) Literature (48) 1.5 · 10 1 4 kbloodbind Complex binding to blood components (h ) Estimated from experimental data 1 · 10 1 2 kblooddis Complex dissociation from blood components (h ) Estimated from experimental data 1 · 10 kcleavage Cleavage of target mRNA by activated RISC complex (h ) Literature (44) 7.2 1 1 kdegendna Endosomal siRNA degradation (h ) Literature (32–34,49) 5 · 10 1 2 kdeginna Intracellular siRNA degradation (h ) Estimated from experimental 2.9 · 10 data and literature (33) kdegmRNA Target mRNA degradation (h ) Literature (50–53) 2 1 1 kdegprot Target protein degradation, Luciferase (h ) Literature (25) 3.5 · 10 1 2 kdegRISC Activated RISC complex degradation (h ) Estimated from experimental data 7.7 · 10 1 9 kdisRISC Dissociation of activated RISC complex (h ) Chosen to be negligible once 1 · 10 activated RISC is formed kdisRISCm Dissociation of activated RISC complex and target mRNA (h ) Literature (42–44) 1 1 2 kelimec Extracellular complex degradation (h ) Estimated from experimental data 8.7 · 10 2.9 · 10 1 2 kelimpl Plasma complex degradation (h ) Estimated from experimental data 5.8 · 10 1 2 kescendna Endosomal escape for siRNA (h ) Estimated from experimental 6 · 10 data and literature (54) 1 2 kescendvec Endosomal escape for complex (h ) Estimated from experimental 1 · 10 data and literature (54) 1 1 13 kformmRNA Formation of target mRNA (# L h ) Literature (50,51) 5.2 · 10 1 2 kformprot Formation of target protein (h ) Literature (50,51) 5.2 · 10 1 1 19 kformRISC Formation of activated RISC complex (L # h ) Estimated from experimental data 2 · 10 1 1 14 kformRISCm Formation of activated RISC/mRNA complex (L # h ) Literature (42–44) 1.1 · 10 kgrowth Cell growth rate (h ) Determined experimentally Fit to each system 1 5 kint Internalization (h ) Literature (12,13,55) 1 · 10 5 · 10 1 2 ktransblood Transport from plasma to extracellular fluid (h ) Estimated from experimental data 1 · 10 1 1 kunpackcyt Cytosolic complex unpackaging (h ) Estimated from experimental data 5 · 10 6 · 10 1 4 kunpackend Endosomal complex unpackaging (h ) Estimated from experimental data 1 · 10 1 · 10 For parameters common to both in vitro and in vivo applications, the in vivo parameter values are shown in italics below the in vitro parameter values. minimal impact on the overall duration (Figure 2A). Using the can alter the duration of gene silencing. Consistent with pre- baseline parameters given in Table 2, the mathematical model vious observations, the duration of gene silencing in rapidly predicts the trends observed experimentally (Figure 2B). growing cell lines is 1 week; however, cell lines with slower Similar trends are observed with these siRNA doses in doubling times show a corresponding increase in the duration other luciferase-expressing cell lines (data not shown). of silencing. Figure 3B shows the predicted effect of cell doubling time when the experimental transfection parameters are input into the mathematical model. The model predictions Effect of cell doubling time on luciferase conﬁrm that the dilution effect due to cell doubling time alone knockdown in vitro can account for the decreased duration of gene silencing in The majority of studies examining the kinetics of siRNA- dividing cells. It is interesting to note that the duration of gene mediated gene silencing in vitro have used rapidly dividing silencing in nondividing cells is 3 weeks. This duration is cell lines that typically have doubling times of 1 day. Using consistent with the kinetics observed in two previous reports these cell lines, the silencing effect generally lasts for 1 week looking at siRNA-mediated gene silencing in nondividing (27,28). To investigate whether this duration of silencing is mammalian neurons and primary macrophages (29,30). In intrinsic to siRNA or a result of dilution due to cell division, nondividing cells, the duration of gene silencing is not con- siRNA-mediated gene silencing was monitored in four trolled by dilution from cell division but by the intrinsic sta- luciferase-expressing cell lines with different observed dou- bility of siRNA within the cell. bling times: Neuro2A-Luc (0.8 days), LNCaP-Luc (1.4 days), HeLa-Luc (1.6 days) and CCD-1074Sk-Luc (nondividing). Kinetics of luciferase knockdown by The cells were plated in 24-well plates and transfected siRNA in subcutaneous tumors under identical conditions to enable direct observation of the effect of cell doubling time alone. The experimental results Many tumors exhibit rapid growth with doubling times on the in Figure 3A reveal that the dilution effect from cell division order of only a few days, and the duration of gene silencing Nucleic Acids Research, 2006, Vol. 34, No. 1 327 Figure 2. Effect of siRNA dose on the duration and magnitude of luciferase Figure 3. Effect of cell doubling time on the duration of luciferase knockdown knockdown by siRNA in nondividing cells. (A) Experimental results using by siRNA in vitro.(A) Experimental results using Oligofectamine to deliver Oligofectamine to deliver siRNA to luciferase-expressing, nondividing fibro- 100 nM siRNA to luciferase-expressing cells with a range of doubling times blasts with 1.5 · 10 cells per well in a 24-well plate. Data points represent the (dt). Data points represent the ratio of the average luciferase signal intensity ratio of the average luciferase signal intensity from triplicate wells receiving from triplicate wells receiving siGL3 and siCON1 on day 0. Squares, Neuro2A- siGL3 and siCON1 on day 0. Squares, 10 nM; diamonds, 25 nM; triangles, Luc (dt ¼ 0.8 d); diamonds, LNCaP-Luc (dt ¼ 1.4 d); triangles, HeLa-Luc 50 nM; circles, 100 nM. (B) Luciferase knockdown after siRNA transfection (dt ¼ 1.6 d); circles, CCD-1074Sk-Luc (nondividing). (B) Luciferase knock- predicted by the mathematical model using the baseline in vitro parameters down after siRNA transfection predicted by the mathematical model using the given in Table 2 with the number of cells held constant at 1.5 · 10 , a transfec- baseline in vitro parameters given in Table 2 with the initial number of dividing 4 5 tion time of 5 h, and a transfection efficiency of 90%. and nondividing cells equal to 5 · 10 and 1.5 · 10 , respectively, a transfec- tion time of 5 h, and a transfection efficiency of 90%. should be limited by this rapid cell division. To test this hypothesis, subcutaneous tumors were created in A/J mice By adjusting only the parameters for the circulation/ using luciferase-expressing Neuro2A-Luc cells. Since the extracellular transport of the siRNA polyplexes, very good goal was to observe the kinetics of gene silencing and not agreement was obtained between the model’s predictions and the experimental data. The observed knockdown duration an actual therapeutic effect on the growth rate of the cells, siRNA against the luciferase gene (siGL3) and a control after three consecutive injections was around 10 days, con- siRNA (siCON1) were used to show the sequence- sistent with the in vitro data for cell lines with similar observed speciﬁcity of the luciferase knockdown. Each mouse received growth rates. three consecutive daily LPTV injections of transferrin- targeted polyplexes containing 2.5 mg/kg siRNA. After quan- Kinetics of luciferase knockdown by tifying the luciferase activity in each tumor using the Xenogen siRNA in hepatocytes camera, data were used to create a predicted logistic growth curve (Figure 4A). Because the siRNA targets only the While cells in subcutaneous tumors are dividing rapidly (e.g. luciferase gene, the growth rate of the cells should be unaf- once per day), most of the hepatocytes in a normal mouse liver fected; as a result, a decrease in luciferase signal intensity are in a state of growth arrest (31). Therefore, it was hypothe- indicates a change in the luciferase protein level. Normaliza- sized that gene silencing by siRNA would exhibit different tion to predicted growth curves allowed estimation of the kinetics in hepatocytes versus tumors. Each BALB/c mouse knockdown resulting from siRNA treatment (Figure 4B). received a single HPTV injection of 0.25 mg/kg plasmid and 328 Nucleic Acids Research, 2006, Vol. 34, No. 1 Figure 5. Kinetics of luciferase knockdown by siRNA in nondividing hepatocytes in BALB/c mice. Experimental and predicted results are shown for luciferase knockdown after hydrodynamic tail-vein co-injection of 5 mg pApoEHCRLuc and 50 mg siRNA per 20 g mouse on day 0. Circles represent the ratio of the average luciferase signal intensity from three mice receiving plasmid + siRNA to the luciferase signal intensity from three mice receiving plasmid alone. The predicted luciferase knockdown, given by the solid line, was calculated using the baseline in vivo parameters given in Table 2 with the following modifications to account for hydrodynamic injection of naked siRNA without a delivery vehicle: eliminate steps involving the complexes (kescend- vec, kunpackend, kunpackcyt), modify uptake and intracellular trafficking to match observed kinetics (partition ¼ 1 · 10 , ktransblood ¼ 1, kint ¼ 1 · 3 1 2 1 3 1 10 h , kescendna ¼ 1 · 10 h , kdegendna ¼ 5 · 10 h ), and modify extracellular volume (Ve ¼ 1.5 · 10 L). The kescendna and kdegendna may no longer represent endosomal processes as hydrodynamically injected naked siRNA may be internalized through different vesicles or parti- tioned into a separate intracellular compartment (e.g. nucleus) that exhibits different degradation and release kinetics than in standard or receptor-mediated endocytosis of siRNA-containing complexes. The total number of hepatocytes was chosen to be 5 · 10 , on the same order of magnitude as the number of hepatocytes in a mouse liver (40,41). Figure 4. Kinetics of luciferase knockdown by siRNA in Neuro2A-Luc sub- cutaneous tumors in A/J mice. (A) Experimental and predicted results for ﬁeld of nucleic acid-based therapeutics seek to enhance luciferase knockdown after three consecutive LPTV injections on days 6, 7 the stability of the nucleic acids with the goal of increasing and 8 of transferrin-targeted CDP-Im polyplexes containing 50 mg siRNA per the duration of gene silencing by boosting their bioavailability 20 g mouse. Experimental data points are shown for a mouse receiving siCON1 and possibly prolonging their persistence intracellularly (squares) and a mouse receiving siGL3 (circles). Solid lines represent the predicted luciferase signal with siRNA treatment and dashed lines represent (32–34). Layzer and co-workers studied the kinetics of gene the predicted luciferase signal in the absence of siRNA treatment. (B) Normal- silencing in HeLa cells using 2 -F-modiﬁed siRNA and ization of the observed luciferase signal in the siGL3-treated mouse to the 0 0 unmodiﬁed 2 -OH siRNA. Although the 2 -F-modiﬁed predicted luciferase signal in the absence of treatment. Circles indicate siRNA led to a signiﬁcant increase in serum stability, it the normalized experimental data points, while the solid line represents the response predicted by the mathematical model using the baseline in vivo appeared to have no effect on the duration of gene silencing parameters given in Table 2 and assuming that 50% of the total cells are reached after transfection. This suggests that the intracellular stability with each dose. of siRNA molecules is not the limiting factor controlling the duration of gene silencing in rapidly dividing cells; instead, 2.5 mg/kg siGL3 on day 0, and the Xenogen camera was used dilution due to cell division limits how long gene silencing can to follow the luciferase signal in each mouse liver. Normal- occur under these conditions. If the intracellular half-life of ization to the signal intensity in mice that received plasmid siRNA molecules is already around 24 h, then even modiﬁ- only (no siRNA) allowed quantiﬁcation of the percent knock- cations to increase the half-life to >72 h have an insigniﬁcant down by siRNA. Figure 5 shows the experimental data effect on the duration of gene silencing (Figure 6). These together with the model predictions. Similar to the in vitro model predictions corroborate the experimental results results for gene silencing in nondividing cells, the duration of obtained by Layzer and co-workers (33). On the other gene silencing lasts for 3–4 weeks in the hepatocytes after a hand, the outcome of using modiﬁed siRNA may be different single dose of siRNA. in slowly dividing or nondividing cells since the intracellular siRNA half-life will be shorter than the cell doubling time, meaning dilution due to cell division will no longer be the Effect of siRNA stability on luciferase dominant factor. Increasing the persistence of siRNA within knockdown by siRNA the cell might prolong the duration of gene silencing. Because both double-stranded and single-stranded nucleic Results from such studies in nondividing cells should be inter- acids are rapidly degraded in serum, current efforts in the preted carefully since the apparent intracellular stability of Nucleic Acids Research, 2006, Vol. 34, No. 1 329 Figure 6. Effect of intracellular siRNA half-life on the duration of siRNA-mediated gene silencing in vitro. Curves represent model predictions for luciferase knockdown after transfection with 100 nM siRNA against luciferase on day 0 with a cell doubling time of 1 day (kgrowth ¼ 0.0.029 h ) and intracellular siRNA half-lives of 24, 48 and 72 h (kdeginna ¼ 0.029, 1 4 0.014 and 0.01 h ). The initial number of cells was 5 · 10 , transfection time was 5 h, transfection efficiency was 90%, and all other parameters were kept at their baseline in vitro values given in Table 2. siRNA molecules may be caused by association with other intracellular components or localization to speciﬁc compart- ments, both of which could lead to degradation kinetics inde- pendent of the properties of the siRNA molecules alone. In that case, modiﬁed siRNA would not necessarily increase the dura- tion of gene silencing relative to unmodiﬁed siRNA even in nondividing cells. Multiple doses to prolong luciferase knockdown by Figure 7. Effect of siRNA dose frequency on the duration of luciferase knock- siRNA in nondividing cells down by siRNA in nondividing cells. (A) Experimental results using Oligofectamine to deliver siRNA to luciferase-expressing nondividing fibro- The previous studies have looked at the transient knockdown blasts in vitro. Data points represent the ratio of the average luciferase signal of the luciferase reporter gene by 1–3 injections of siRNA intensity from triplicate wells receiving siGL3 and siCON1. To facilitate com- over a short-term period; even in nondividing cells, the parison of the knockdown kinetics, the data points are normalized such that all three curves exhibit the same magnitude of knockdown for the first four days maximum duration of silencing using typical siRNA doses since all three received the same treatment over this period. This normalization is 3–4 weeks. However, a clinically relevant treatment regi- permits comparison of the kinetics of gene silencing observed with different men using siRNA may require that a gene be silenced for a treatments even though the absolute magnitude of the knockdown varied prolonged period of time. Some have attempted to solve this slightly in each experiment. Squares, 100 nM (day 0); diamonds, 100 nM problem by using lentiviral delivery of expressed short-hairpin (day 0) + 10 nM (day 4); triangles, 100 nM (day 0) + 100 nM (day 4). (B) Luciferase knockdown after siRNA transfection predicted by the siRNAs (shRNAs) to achieve sustained gene silencing in vitro mathematical model using the baseline in vitro parameters given in Table 2 and in vivo (35,36). Precise control of the intracellular level of with the number of cells equal to 1.5 · 10 , a transfection time of 5 h, and a siRNA and having a means to turn off its production when transfection efficiency of 90%. treatment is no longer necessary represent two major chal- lenges to this use of shRNA. On the other hand, the intrinsi- Considerations for siRNA-based treatments that cally transient nature of siRNAs makes them more amenable require a threshold knockdown for efficacy to disease treatments in which the treatment is given over a period of time and then stopped once the desired therapeutic Because siRNA treatment of rapidly dividing cells requires outcome (e.g. regression of a tumor or inhibition of viral treating more cells over time while also having to deal with growth) is achieved. To illustrate how properly timed doses dilution effects, the amount of target gene or protein knock- of siRNA can prolong gene silencing by siRNA, nondividing down will be less than that observed in slowly dividing or CCD-1074Sk-Luc cells were transfected with a second dose of nondividing cells. More frequent dosing is required to over- siRNA 4 days after the initial dose (Figure 7A). With a second come these barriers. Cancer is one example of a disease often dose of 100 nM siRNA, the luciferase protein levels remained characterized by rapid cell division that may require target at <40% of the steady-state value for an additional 4 days. If gene knockdown lasting longer than that which can be the trends continue in such a fashion, a 100 nM dose every achieved with a single dose of siRNA. To address this situ- 4 days could lead to persistent gene silencing as shown by ation, the mathematical model was used to estimate siRNA dosing schedules needed to maintain a given gene below a model calculations in Figure 7B. 330 Nucleic Acids Research, 2006, Vol. 34, No. 1 threshold value for an extended period of time in dividing using mathematical modeling to give insights that help direct cells. While the magnitude of target gene (or protein) reduc- experimental studies. Here, we employed bioluminescent tion or the duration of knockdown relative to the steady-state imaging and mathematical modeling to investigate the effects value in the absence of treatment can be relatively good indi- of target-speciﬁc and treatment-speciﬁc parameters on siRNA- cators of the success of an siRNA treatment, the therapeutic mediated gene silencing in vitro and in vivo. efﬁcacy of an siRNA treatment regimen should perhaps be The experimental data presented here show the effects of judged by the length of time it is able to maintain the target cell doubling time, siRNA dosing schedule, and siRNA deliv- gene or protein level below a given threshold. Although a ery method on luciferase reporter-protein knockdown and aid short, substantial knockdown of certain targets may be sufﬁ- in developing mathematical models of siRNA delivery to and cient to trigger a cascade of downstream effects, other situa- function within mammalian cells. Luciferase knockdown in tions may require considerably longer knockdown to achieve cell lines engineered to constitutively express luciferase was the desired therapeutic effect. Additionally, this therapeutic used to mimic the knockdown of an endogenously expressed effect may only be seen when the target protein is reduced gene, analogous to an oncogene whose presence in a cell can below a threshold, or some fraction of its pre-treatment value. lead to tumorigenicity. The luciferase-expressing cell lines The data in Figure 8 show how the mathematical model can were used in cell culture experiments or injected into mice be used to simulate the effects of cell doubling time and target and then monitored for luciferase expression using noninva- protein half-life during treatment with siRNA. To avoid sive bioluminescent imaging with the Xenogen Imaging unnecessary complications, the calculations ignore the circu- System. The duration of gene silencing lasted for 1 week lation/extracellular transport and consider each siRNA dose in rapidly dividing cells but longer than 3 weeks in nondivid- already in the local extracellular environment of the cells ing cells both in vitro and in vivo, supporting the hypothesis (analogous to the in vitro situation). Figure 8A–D gives results that dilution due to cell division is the major factor controlling the duration of luciferase knockdown in rapidly dividing cells. that demonstrate how target protein half-life can impact the The duration of gene silencing by siRNA can be longer than observed dynamics of protein knockdown with once- or twice- weekly dosing in rapidly dividing or nondividing cells. For a that achieved with other nucleic acid-based gene inhibition target protein with a short half-life in rapidly dividing cells, strategies, such as antisense, whose knockdown typically lasts even twice-weekly dosing still can result in signiﬁcant oscil- only on the order of 1–2 days. Bertrand and co-workers (37) lations which may hinder the ability to cause a phenotypic studied antisense- and siRNA-mediated inhibition of GFP in change in the target cells (Figure 8A). If the target protein has a HeLa cells and showed that while antisense-mediated inhibi- long half-life, then twice-weekly dosing is able to maintain tion diminished after only 1 day, the siRNA-mediated inhibi- steady knockdown at 50% of the steady-state level, but this tion was still increasing. This signiﬁcant difference in the magnitude of protein knockdown is not achieved until about a duration of gene silencing could become important when try- week after the ﬁrst dose of siRNA (Figure 8B). In nondividing ing to use either antisense or siRNA molecules as therapeutic cells, once-weekly dosing is adequate to maintain persistent agents. In fact, the short duration of gene silencing by certain silencing at 20% of the steady-state value (Figure 8C and D). nucleic acid-based gene inhibition strategies could preclude Again, this protein knockdown can only be achieved after their ability to alter cellular behavior if the target gene is not more than a week from the initial siRNA dose if the target silenced for an adequate amount of time. This would be par- protein half-life is very long (Figure 8D). The fraction of the ticularly apparent if the target protein has a long intracellular total treatment time during which a target protein is below a half-life; then, knockdown of the target mRNA may not result threshold (e.g. 50% steady-state value) can be used as a metric in target protein knockdown if the mRNA levels can be res- to compare the efﬁcacy of different treatment regimens. The tored before a signiﬁcant amount of protein has degraded. data illustrated in Figure 8E reveal how cell growth rate and The ﬁndings presented here highlight several key consid- target protein half-life can affect protein knockdown when erations for experimental design when evaluating the efﬁcacy siRNA is administered once on day 0, once-weekly or of siRNA against certain genes that produce proteins with long twice-weekly over the 25-day treatment. As expected, cell half-lives. If the knockdown phenotype does not become apparent until the protein is below a certain threshold, then growth rate has a large impact on the duration of knockdown, observation at early time points may not reveal any effect. This directly affecting the fraction of the total time that the target is crucial for in vitro studies aimed at testing the ability of a protein level can be reduced below the threshold of 50%. therapeutic siRNA to induce apoptosis or growth arrest in certain cell lines. Common practice is to look at time points DISCUSSION within 48 and 72 h; here, model predictions suggest that these A more thorough understanding of the factors affecting the time points may be too early if the target protein half-life is any kinetics of siRNA-mediated gene silencing should prove to be longer than a couple of days. Similar considerations should be invaluable for experimental and clinical applications of made when deciding dosing schedules for in vivo studies using siRNA. Given the relatively recent discovery of RNAi, details siRNA for protein knockdown in tumors (e.g. an oncogenic of its action are still being elucidated, and many of the current fusion protein), since proteins with longer half-lives will show siRNA dosing schedules used in literature are based on prece- a slower initial response to the therapy but will require less dence rather than being optimized for each system. The high frequent dosing for persistent silencing. An important area for cost of siRNA molecules, especially for in vivo studies, limits future research will be to determine to what extent a gene or systematic exploration of the parameter space needed to protein needs to be knocked down before the intended thera- achieve the most effective siRNA dosing schedule for each peutic effect is realized. Such information can be combined model system. This situation can be partially rectiﬁed by with mathematical models like the one presented here to more Nucleic Acids Research, 2006, Vol. 34, No. 1 331 Figure 8. Effect of cell doubling time and target protein half-life on the ability to maintain persistent gene silencing. All plots represent predicted mRNA (dashed lines) and protein (solid lines) knockdown in transfected cells using the baseline in vitro parameters given in Table 2, a transfection time of 5 h, and an initial number 4 5 of dividing and nondividing cells equal to 5 · 10 and 1.5 · 10 , respectively. (A) Dose of 100 nM siRNA every 3 days with a target protein half-life of 1 1 2h (kdegprot ¼ 0.35 h ) in cells with a doubling time of 1 day (kgrowth ¼ 0.029 h ). (B) Dose of 100 nM siRNA every 3 days with a target protein 1 1 half-life of 48 h (kdegprot ¼ 0.014 h ) in cells with a doubling time of 1 day (kgrowth ¼ 0.029 h ). (C) Dose of 100 nM siRNA every 7 days with a target protein half-life of 2 h (kdegprot ¼ 0.35 h ) in nondividing cells. (D) Dose of 100 nM siRNA every 7 days with a target protein half-life of 48 h (kdegprot ¼ 0.014 h ) in nondividing cells. (E) Effect of variations in cell doubling time and target protein half-life on the ability to maintain a target protein level below a threshold of 50% its pre-treatment value over the 25-day period. I, 100 nM (day 0); II, 100 nM (days 0, 7, 14); III, 100 nM (days 0, 3, 7, 10, 14, 17, 21, 24). Surface vertices represent the fraction of the total time during which the relative protein level is below the 50% threshold. 332 Nucleic Acids Research, 2006, Vol. 34, No. 1 accurately determine the required treatment regimen needed to stability enables knockdown that can last for weeks in nondi- achieve efﬁcacy. Although the model in its current form does viding cells. It is shown here that an optimized siRNA-based not allow for treatment effects other than target gene knock- treatment schedule can be designed to achieve prolonged gene down, the simple addition of a death parameter to the cell silencing by properly timed injections of siRNA. Mathemati- growth equation could provide a target cell death rate that cal modeling can help to realize these optimized treatments at depends on the reduction of the target protein level below a a fraction of the time and cost that would be required by certain threshold. Other slightly more complicated modiﬁca- experimentation alone. Although there is no substitute for tions to the current set of equations could incorporate recruit- experimental data, especially for highly variable and not com- ment of immune effector cells, effects on angiogenesis or even pletely deﬁnable biological systems, model calculations can sensitization to other treatments including chemotherapy. help to guide effective experimental design and aid in data While the mathematical model can predict many of the interpretation. With the burgeoning interest in nucleic acid- trends observed experimentally for the systems used here, based therapeutics such as siRNA, development of mathemati- conﬁdence in the actual magnitude and duration of the pre- cal models such as the one presented here may expedite their dicted gene silencing in hypothetical situations can still be translation into clinically relevant therapeutics for disease greatly increased as more accurate parameter values become treatment and management. available. Parametric sensitivity analysis was performed using the SENS_SYS modiﬁcation of the ODE15s solver in MAT- SUPPLEMENTARY DATA LAB. Parameters governing RISC formation (kformRISC) and binding to target mRNA (kformRISCm) have a signiﬁcant Supplementary Data are available at NAR Online. impact on target mRNA or protein levels. Although studies of the RISC complex are rapidly elucidating details of its ACKNOWLEDGEMENTS mechanism and kinetics, these parameters will need to be reﬁned as more data become available. Additional equations The authors are especially grateful to D. Petersen and D. Kohn will be needed to model a multi-step RISC formation process, (Children’s Hospital Los Angeles) for performing the lentiviral or the lumped rate constants currently used can be modiﬁed to transductions of the luciferase-expressing cell lines; A. provide reasonable estimates of the overall kinetics. As McCaffrey and M. Kay (Stanford University) for donating expected, target mRNA and protein levels are also sensitive the luciferase-containing plasmid; and J. Heidel (Calando to parameters governing the siRNA delivery process, such as Pharmaceuticals, Inc.) for performing bioluminescent imaging cellular uptake, endosomal escape and vector unpackaging. It of the mice used in the HPTV studies looking at hepatocyte- will be important to determine these parameters for each indi- specific luciferase expression. This material is based upon work vidual delivery vehicle since such rates will vary from system supported under a National Science Foundation Graduate to system. With knowledge of these different parameters, the Research Fellowship. This publication was made possible by model can be used to mimic delivery by a variety of methods Grant Number 1 R01 EB004657-01 from the National including naked siRNA (by high-pressure or low-pressure tail- Institutes of Health (NIH). Its contents are solely the respon- vein injection) or formulation into liposomes, lipoplexes or sibility of the authors and do not necessarily represent the polyplexes. Such comparisons may reveal how the character- official views of the NIH. Funding to pay the Open Access istics of each delivery method speciﬁcally affect the kinetics of publication charges for this article was provided by the gene silencing. This information may help to focus design California Institute of Technology. improvements for delivery vehicles or improve the efﬁcacy Conflict of interest statement. None declared. of treatment regimens employing them, as suggested in gen- eral for gene delivery by Varga and co-workers (38). Of the parameters intrinsic to the target cells, the most important are REFERENCES the cell growth rate (dilution effect), compartment volumes 1. Fire,A., Xu,S., Montgomery,M.K., Kostas,S.A., Driver,S.E. and (that control the concentration of siRNA available to drive Mello,C.C. 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Nucleic Acids Research – Oxford University Press

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Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging

Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging

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Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging

Insights into the kinetics of siRNA-mediated gene silencing from live-cell and live-animal bioluminescent imaging

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