Active cell-matrix coupling regulates cellular force landscapes
of cohesive epithelial monolayers
, Yao Zhang
, Qiong Wei
, Xuechen Shi
, Peng Zhao
, Long-Qing Chen
and Sulin Zhang
Epithelial cells can assemble into cohesive monolayers with rich morphologies on substrates due to competition between elastic,
edge, and interfacial effects. Here we present a molecularly based thermodynamic model, integrating monolayer and substrate
elasticity, and force-mediated focal adhesion formation, to elucidate the active biochemical regulation over the cellular force
landscapes in cohesive epithelial monolayers, corroborated by microscopy and immunoﬂuorescence studies. The predicted
extracellular traction and intercellular tension are both monolayer size and substrate stiffness dependent, suggestive of cross-talks
between intercellular and extracellular activities. Our model sets a ﬁrm ground toward a versatile computational framework to
uncover the molecular origins of morphogenesis and disease in multicellular epithelia.
npj Computational Materials (2018) 4:10 ; doi:10.1038/s41524-018-0069-8
Small self-assembled monolayers are common in chemistry,
condensed matter physics, and biology.
often exhibit rich morphologies, arising from a combination of
short-range inter-monomer interactions and long-range interac-
tions through elastic or electrical ﬁelds. For example, a graphene
monolayer on a substrate may form wrinkles with
different wavelengths due to the elastic, edge, and interfacial
These effects may also present in multicellular epithelial
ensembles. Yet, different from atomic monolayers or thin ﬁlms in
condensed matters, a multicellular monolayer is biochemically
active in that it probes and senses physical cues from its
surroundings and responds by a cascade of biochemical
The biochemical activities are accompanied by
mechanical force generation and transmission,
assembling of mechanical force responsive molecules,
morphogenesis of the entire multicellular monolayer.
address the cellular force landscapes of equilibrated multicellular
epithelial monolayers and its implications to cell fate and
We have examined the HCT-8 epithelial cell colonies (a colony
consists of hundreds of cells packed together through cell–cell
adhesion.), as an example of cohesive multicellular monolayers.
Upon seeding adherent HCT-8 cells onto polyacrylamide (PAA)
gels in vitro, they proliferate and aggregate to form cohesive
multicellular monolayers of different sizes and morphologies (Fig.
S1). The proliferation of the cells slows down and the colonies size
and shape nearly unchanged beyond 3 days of culture. In the
course of morphogenesis, mechanosensation of mechanical cues
from the substrate through cell surface integrin receptors
activates a complex biochemical-signaling network, leading to
increased actomyosin contractility.
The increased intracellular
contraction feeds back to the mechanotransduction pathway by
promoting integrin clustering,
focal adhesion assembling,
and cell–cell adhesion and cytoskeletal remodeling.
adhesion junctions and focal adhesions are both biochemically
and structurally linked, intracellular contraction invokes cross-talks
generating extracellular traction onto the
substrate and intercellular tension in a coordinated fashion that
are counter-balanced by cell body stress. We have therefore
developed an energy functional, combining monolayer and
substrate elasticity, integrin-mediated interfacial adhesion, and
chemical potential of adhesion molecules, to determine the
cellular force landscapes of the cohesive multicellular monolayers.
To a minimal setting, we consider an epithelial monolayer with a
total of N cells seeded on PAA gels coated with ﬁbronectin to
which integrins bind and form focal adhesion points (see Fig. 1).
The extracellular traction and intercellular tension originated from
actomyosin contraction displace both the substrate and the
monolayer. Adopting a continuum view within the framework of
elasticity, we denote the displacement ﬁelds of the monolayer and
the substrate by u and
u, and the respective conjugate stress
ﬁelds by σ and
σ. Focal adhesion points furnish the structural units
that transmit forces between the monolayer and the substrate.
The bridging role and spatially heterogeneous distribution of focal
adhesion points warrant a microstructure-based description. To
capture the molecular basis of focal adhesion formation through
integrin clustering, we categorize the integrin receptors on the cell
membrane into two distinct phases: a freely diffusive phase with a
density of ϕ
(number per unit area) and a bound phase to the
ligands on the substrate with a density of ϕ
for the i-th cell.
Conservation of the receptors expressed on the membrane of
each cell requires
ÞdΩ ¼ ϕ
Received: 17 July 2017 Revised: 12 January 2018 Accepted: 14 February 2018
Department of Engineering Science and Mechanics Pennsylvania State University, University Park Pennsylvania, PA 16802, USA;
Department of Biomedical Engineering
Pennsylvania State University, University Park, Pennsylvania, PA 16802, USA and
Department of Materials Science and Engineering, Pennsylvania State University, University
Park, Pennsylvania, PA 16802, USA
Correspondence: Sulin Zhang (firstname.lastname@example.org)
Tiankai Zhao, Yao Zhang and Qiong Wei contributed equally to this work.
Published in partnership with the Shanghai Institute of Ceramics of the Chinese Academy of Sciences