Diffusion approximation of the stochastic process of microtubule assemblyMaly, Ivan
doi: 10.1006/bulm.2001.0265pmid: 11926115
Microtubules are protein polymers that guide intracellular motility. Stochastic switching of a microtubule between states of elongation, shortening, and pause is described in detail by the dynamic instability (DI) model. Recently we have described the dynamics of microtubules phenomenologically as generalized diffusion of their ends. Genesis of the diffusion dynamics and accuracy of diffusion model are studied in this work. It is shown that wandering of the end of a microtubule undergoing DI asymptotically approaches the Wiener diffusion process. Accuracy of the diffusion approximation is evaluated by comparing its predictions with results of simulation of DI. Stationary distributions of microtubule length and lifetime that are predicted by both models differ qualitatively between two cell types considered. However, predictions of the diffusion model are in each case practically identical to predictions of the DI model being also consistent with experimental data. The peculiar stochastic process of microtubule assembly thus converges at cell scale to a kind of widespread-in-nature diffusion process. This result is considered an example of qualitative change in dynamical properties in transition from the molecular to cellular level of biological organization. Additionally, it suggests employment of diffusion process theory in studying functions of microtubules in the cell.
Home range formation in wolves due to scent markingBriscoe, Brian; Lewis, Mark; Parrish, Stephen
doi: 10.1006/bulm.2001.0273pmid: 11926117
Social carnivores, such as wolves and coyotes, have distinct and well-defined home ranges. During the formation of these home ranges scent marks provide important cues regarding the use of space by familiar and foreign packs. Previous models for territorial pattern formation have required a den site as the organizational center around which the territory is formed. However, well-defined wolf home ranges have been known to form in the absence of a den site, and even in the absence of surrounding packs. To date, the quantitative models have failed to describe a mechanism for such a process. In this paper we propose a mechanism. It involves interaction between scent marking and movement behavior in response to familiar scent marks. We show that the model yields distinct home ranges by this new means, and that the spatial profile of these home ranges is different from those arising from the territorial interactions with den sites.
A dual-mode dynamic model of the human accommodation systemKhosroyani, Madjid; Hung, George
doi: 10.1006/bulm.2001.0274pmid: 11926118
The function of the accommodation system is to provide a clear retinal image of objects in the visual scene. The system was previously thought to be under simple continuous (i.e., single mode of operation) feedback control, but recent research has shown that it is under discontinuous (i.e., two stimulus-dependent modes of operation) feedback control by means of fast and slow processes. A model using MATLAB/SIMULINK was developed to simulate this dual-mode behavior. It consists of fast and slow components in a feedback loop. The fast component responds to step target disparity with an open-loop movement to nearly reach the desired level, and then the slow component uses closed-loop feedback to reduce the residual error to an acceptable small level. For slow ramps, the slow component provides smooth tracking of the stimulus, whereas for fast ramps, the fast component provides accurate staircase-like step responses. Simulation of this model using a variety of stimuli, including pulse, step, ramp, and sinusoid, showed good agreement with experimental results. Thus, this represents the first dynamic model of accommodation that can accurately simulate the complex dual-mode behavior seen experimentally. The biological significance of this model is that it can be used to quantitatively analyze clinical deficits such as amblyopia and accommodative insufficiency.
Modelling Dictyostelium discoideum morphogenesis: The culminationMarée, Athanasius; Hogeweg, Paulien
doi: 10.1006/bulm.2001.0277pmid: 11926120
The culmination of the morphogenesis of the cellular slime mould Dictyostelium discoideum involves complex cell movements which transform a mound of cells into a globule of spores on a slender stalk. We show that cyclic AMP signalling and differential adhesion, combined with cell differentiation and slime production, are sufficient to produce the morphogenetic cell movements which lead to culmination. We have simulated the process of culmination using a hybrid cellular automata/partial differential equation model. With our model we have been able to reproduce the main features that occur during culmination, namely the straight downward elongation of the stalk, its anchoring to the substratum and the formation of the long thin stalk topped by the spore head.
Kinetic heterogeneity of an experimental tumour revealed by BrdUrd incorporation and mathematical modellingBertuzzi, Alessandro; Faretta, Mario; Gandolfi, Alberto; Sinisgalli, Carmela; Starace, Giuseppe; Valoti, Giorgio; Ubezio, Paolo
doi: 10.1006/bulm.2001.0280pmid: 11926121
In the present paper we propose a method of analysis of the cell kinetic characteristics of in vivo experimental tumours, that uses DNA-BrdUrd flow cytometry data at various times after the bromodeoxyuridine (BrdUrd) injection and mathematical modelling. The model of the cell population takes into account the cell-cell heterogeneity of the progression rate across cell cycle phases within the tumour, and assumes a strict correlation between the durations of S and G2M phases. The model also allows for a nonconstant DNA synthesis rate across S phase. In addition, the measurement process is modelled, considering the possibility of nonimpulsive labelling and providing a representation of the time course of the bivariate DNA-BrdUrd fluorescence distribution. Sequential DNA-BrdUrd distributions were obtained in vivo from a human ovarian carcinoma transplanted in mice and, for comparison, in vitro from a cell line of the same origin. From these data, that included the fractional density and the mean BrdUrd-fluorescence of BrdUrd-positive cells as a function of the DNA-fluorescence, kinetic parameters such as the potential doubling time (T
pot) and the mean and variance of the transit times in S and G2M phases, were estimated. This study revealed the presence of a substantial heterogeneity in S and G2M phases within the in vivo cell population and of a lower heterogeneity in the in vitro population. Moreover, our analysis suggests a nonnegligible effect of the BrdUrd pharmacokinetics in the in vivo cell labelling.
Modeling deuterated glucose labeling of T-lymphocytesRibeiro, Ruy; Mohri, Hiroshi; Ho, David; Perelson, Alan
doi: 10.1006/bulm.2001.0282pmid: 11926122
Human immunodeficiency virus type 1 (HIV-1) infects cells of the immune system and leads to depletion of CD4+ T cells, and to an increase of CD8+ T-lymphocytes. However, not much is known about the dynamics of turnover (proliferation and death) of the CD4+ and CD8+ T cell populations in HIV-infected and healthy individuals. A new experimental technique has been developed using deuterated-glucose labeling that provides information on cell turnover in vivo. However, the quantitative interpretation of the data requires the development of specific dynamic models. In this paper we derive two models, a simple one-compartment model and a more complex two-compartment model. These models allow for robust quantification of death and proliferation rates, but careful consideration of the system is necessary to understand what is being measured in each case. We demonstrate that more realistic models can account not only for differences in the turnover rates between HIV-infected and healthy individuals, but also take into consideration the elevated state of activation in HIV infection. The use of these models in the interpretation of the experimental data will increase our knowledge of T cell dynamics in the context of HIV infection.
Stochasticity of the step size in the force generating process due to a single myosin moleculeKagawa, Yuki; Tsuchiya, Yoshimi
doi: 10.1006/bulm.2002.0285pmid: 11926123
We formulate a motional model on the basis of an experimental optical trapping system which reveals the single molecular events of the force generation due to actin and myosin, and we discuss the origin of the dispersion of the displacements of the beads bound to the actin filament. In some experimental data sets, this dispersion is larger than that presumed from the model under the condition that the thermal agitation is the only source of the fluctuation. Thus, other fluctuating elements besides that due to thermal agitation are supposed to cause the dispersion. A possible fluctuating element is the step size itself. We discuss this possibility and estimate the fluctuation in step size using two reported experimental data sets.