Molecular-scale substrate anisotropy and crowding drive long-range nematic order of cell monolayers Yimin Luo12 Mengyang Gu3 Minwook Park4 Xinyi Fang3

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Molecular-scale substrate anisotropy and crowding

drive long-range nematic order of cell monolayers

Yimin Luo1,2, Mengyang Gu3, Minwook Park4, Xinyi Fang3,

Younghoon Kwon2, Juan Manuel Urue˜

na5, Javier Read de Alaniz4,

Matthew E. Helgeson1, M. Cristina Marchetti6and Megan T. Valentine2,∗

1Department of Chemical Engineering

2Department of Mechanical Engineering

3Department of Statistics and Applied Probability

4Department of Chemistry and Biochemistry

5BioPACIFIC MIP, California NanoSystems Institute

6Department of Physics, University of California, Santa Barbara, USA

∗To whom correspondence should be addressed; E-mail: valentine@engineering.ucsb.edu

The ability of cells to reorganize in response to external stimuli is important in

areas ranging from morphogenesis to tissue engineering. Elongated cells can

co-align due to steric effects, forming states with local order. We show that

molecular-scale substrate anisotropy can direct cell organization, resulting in

the emergence of nematic order on tissue scales. To quantitatively examine

the disorder-order transition, we developed a high-throughput imaging plat-

form to analyze velocity and orientational correlations for several thousand

cells over days. The establishment of global, seemingly long-ranged, order is

facilitated by enhanced cell division along the substrate’s nematic axis, and

associated extensile stresses that restructure the cells’ actomyosin networks.

arXiv:2210.13425v1 [physics.bio-ph] 24 Oct 2022

Our work, which connects to a class of systems known as active dry nemat-

ics, provides new understanding of the dynamics of cellular remodeling and

organization in weakly interacting cell collectives. This enables data-driven

discovery of cell-cell interactions and points to strategies for tissue engineer-

ing.

Introduction

Active matter comprises systems of agents or particles that individually consume energy from

the environment to generate motion and forces, and collectively organize in emergent structures

on scales much larger than the individual (1, 2). In particular, active nematics (3, 4) are collec-

tions of elongated, apolar active particles that organize in states of orientational order. Nematic

order has been observed ubiquitously in active and living systems, from reconstituted suspen-

sions of cytoskeletal ﬁlaments and associated motor proteins (5–7) to cell monolayers (8–11),

bacterial colonies (12), and even on the scale of entire organisms (13).

The nematic arrangement of cells in biological systems appears to serve key biological func-

tions, such as driving the expansion of bacterial colonies (14), controlling cell extrusions and

multilayer formation in conﬂuent tissue (10,11,15), and providing an underlying organizational

structure for morphogenetic processes (13). This realization has motivated efforts to develop

in vitro techniques to control cell organization, which are important both as platforms for con-

trolled fundamental studies as well as for tissue engineering. Established methods include pat-

terning of the topography (16), stiffness (17) and mechanical stretching (18) of the substrate.

These methods control the orientation at the level of individual cells such that even isolated

cells can be sufﬁciently polarized to follow a preferred direction. Thus, they do not allow the

study of the role of steric effects or other aligning mechanisms in tuning the onset of nematic

order in the cell collective.

As a complement to topographically modiﬁed substrates, recent work (19) showed that my-

oblasts cultured on uniform, ﬂat substrates made of liquid crystal elastomers (LCEs) developed

nematic order, but only at the collective level. Although this result hinted at the presence of a

density-driven isotropic-nematic transition in the orientational order of cells, the mechanisms

through which both the structure of the substrate and cell proliferation drive alignment remain

largely unclear. This is in part because of a lack of quantitative, time-resolved analysis of

dynamical trajectories for a statistically meaningful number of cells that would inform such

mechanistic insights.

In this work, we develop methods for the high-resolution tracking and quantitative analysis of

several thousand shape anisotropic cells over days, and demonstrate experimentally that elon-

gated apolar active units can order through steric effects. Speciﬁcally, we study the organization

and motility of human dermal ﬁbroblasts (hdFs), chosen because of their shape anisotropy. By

growing these weakly interacting cells on topographically ﬂat LCE substrates, we can examine

the interplay between cell crowding and molecular-level guidance from the substrate in con-

trolling the establishment of orientational order. Earlier work ﬁnds that when the substrate is

isotropic, steric effects alone establish domains of local orientational order on scales of 10-15

cells (9, 11, 20–22). These domains are randomly oriented and the orientational order does not

persist on the scale of the entire tissue. By contrast, we ﬁnd that a nematic substrate provides a

direction of broken symmetry and drives the establishment of nematic order over large (∼mil-

limeter) scales. In this study, we develop techniques to visualize and analyze cellular dynamics

at a high space and time resolution for thousands of cells by recording long trajectories over a

very large ﬁeld of view. Using this method, we show that the establishment of global nematic

order occurs in a three-step process. With increasing cell density, the system transitions from

(i) a disordered state where individual cell trajectories are unaffected by substrate alignment to

(ii) an intermediate state where chaotic bands of aligned cells coexist with disordered regions,

while the system remains isotropic at the global scale, and ﬁnally (iii) an ordered nematic state

where the tissue exhibits long-range order on millimeter scales.

Nematic order has been studied extensively in conﬂuent monolayers of epithelial cells in previ-

ous works (10, 21), where the anisotropy of individual cells is very small and nematic order is

believed to arise not from steric effects, but from the anisotropy of forces transmitted through

strong cell-cell interactions (23–25). In our system, by contrast, cells are highly anisotropic

even when isolated and weakly interacting, and alignment is driven by crowding and steric re-

pulsion. On nematic substrates, we identify a strong correlation between the axis of cell division

and the direction of substrate alignment, which suggests that directed cell division may play a

role in the establishment of order on the tissue scale.

Our system can be considered an experimental realization of a dry active nematic (26,27), which

has been studied extensively via large scale simulations (28). Here “dry” refers to the situation

where the dominant dissipation mechanism is frictional coupling to a substrate, while viscous

dissipation from cell-cell interaction and hydrodynamic couplings mediated by the surrounding

medium are negligible (2). An important distinction, however, is that while in the numerical

models nematic order appears spontaneously, here order is externally biased by the direction of

substrate alignment, which is essential for the establishment of global order. Finally, the large

experimental datasets and statistical analyses we develop not only shed light on the mechanisms

driving cellular reorganization, but provide dynamical information at the single cell level that

is required for the calibration and reﬁnement of physical and machine learning models by data

inversion in future works.

Results

Nematic order within the LCE directs cell alignment

Leveraging our ability to visualize and analyze the dynamics of thousands of cells at a high

space and time resolution (Fig. 1), we observed a markedly different organization of cells on

isotropic and nematic LCE substrates, indicating that hdF cells are sensitive to the molecular

alignment of the polymer ﬁlm at the nanoscale, and that they use this molecular information to

control their orientation within the cell monolayer. Snapshots of cell orientation on isotropic

(Fig. 2a) and nematic (Fig. 2b,c) substrates illustrate the role of both substrate alignment and

cell density in controlling cell ordering. Cell nuclei are elongated and their orientation is corre-

lated with cell elongation (Fig. S2). The cell orientation is then deﬁned by the angle θibetween

the long axis of the nucleus of cell iand a ﬁxed direction ˆex. For nematic substrates, ˆexco-

incides with the direction of LCE alignment, whereas for isotropic substrates ˆexrepresents an

arbitrary direction. The angles θi’s are color-coded in the images. The corresponding angular

distributions are shown as polar histograms in Fig. 2d-f. At a high enough density, cells cul-

tured on an isotropic substrate form locally aligned domains (Fig. 2a), with a nearly uniform

distribution of θiacross the entire monolayer (Fig. 2d). In contrast, cells cultured on nematic

substrates at similar density preferentially align with the substrate nematic orientation ˆ

ex(Fig.

2b), with a strongly anisotropic distribution of θipeaked at 0 or π(Fig. 2e). At higher cell den-

sity on isotropic substrates, the angle distributions become more asymmetric and the domain

size increases (Fig. 2c).

To quantify the spontaneous nematic order of the cells and nematic order induced by the sub-

strate, we introduce two order parameters: the cell-substrate order parameter, Scs, generalized

from the Landau-de Gennes theory of liquid crystals (16, 19, 29), and the cell-cell order param-

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Molecular-scalesubstrateanisotropyandcrowdingdrivelong-rangenematicorderofcellmonolayersYiminLuo1;2,MengyangGu3,MinwookPark4,XinyiFang3,YounghoonKwon2,JuanManuelUruena5,JavierReaddeAlaniz4,MatthewE.Helgeson1,M.CristinaMarchetti6andMeganT.Valentine2;1DepartmentofChemicalEngineering2DepartmentofMech...

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Molecular-scale substrate anisotropy and crowding drive long-range nematic order of cell monolayers Yimin Luo12 Mengyang Gu3 Minwook Park4 Xinyi Fang3.pdf

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Molecular-scale substrate anisotropy and crowding drive long-range nematic order of cell monolayers Yimin Luo12 Mengyang Gu3 Minwook Park4 Xinyi Fang3

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