Active Regulation of Pressure and Volume Defines an Energetic Constraint on the Size of Cell Aggregates

M. S. Yousafzai, V. Yadav, S. Amiri, Y. Errami, S. Amiri, and M. Murrell

Phys. Rev. Lett. 128, 048103 – Published 28 January 2022

Abstract

We explore the relationship between the nonequilibrium generation of myosin-induced active stress within the $F$ -actin cytoskeleton and the pressure-volume relationship of cellular aggregates as models of simple tissues. We find that due to active stress, aggregate surface tension depends upon its size. As a result, both pressure and cell number density depend on size and violate equilibrium assumptions. However, the relationship between them resembles an equilibrium equation of state with an effective temperature. This suggests that bulk and surface properties of aggregates balance to yield a constant average work performed by each cell on their environment in regulating tissue size. These results describe basic physical principles that govern the size of cell aggregates.

Received 9 February 2021
Accepted 3 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.048103

Physics Subject Headings (PhySH)

Biomechanics Biomolecular self-assembly Cell aggregation Cell mechanics

Tissues

Physics of Living Systems

Authors & Affiliations

M. S. Yousafzai^1,2,5,*, V. Yadav ^1,2,*, S. Amiri^2,3, Y. Errami ^2,4,5, S. Amiri^1,2, and M. Murrell ^1,2,5,6,†

¹Department of Biomedical Engineering, Yale University, 55 Prospect Street, New Haven, Connecticut 06511, USA
²Systems Biology Institute, Yale University, 850 West Campus Drive, West Haven, Connecticut 06516, USA
³Department of Mechanical Engineering and Material Science, Yale University, 10 Hillhouse Avenue, New Haven, Connecticut 06511, USA
⁴Department of Genetics, Yale School of Medicine, Sterling Hall of Medicine, 333 Cedar Street, New Haven, Connecticut 06510, USA
⁵Center for Cancer Systems Biology, Yale University, 850 West Campus Drive, West Haven, Connecticut 06516, USA
⁶Department of Physics, Yale University, 217 Prospect Street, New Haven, Connecticut 06511, USA

^*These authors contributed equally to this work.
^†Corresponding author. michael.murrell@yale.edu

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Issue

Vol. 128, Iss. 4 — 28 January 2022

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Images

Figure 1
Aggregates exhibit size-dependent cytoskeletal organization. (a) Fluorescently labeled $F$ -actin and (b) fluorescently labeled nuclei at an equatorial plane of an aggregate. Red lines in (a) and (b) denote $F$ -actin alignment ( $\hat{n}$ ) and nuclei orientation respectively ( ${\hat{n}}_{i}$ ). (c) Radially averaged orthoradial ordering ( $ϕ$ ) as measured from $F$ -actin alignment (defined as $ϕ = ⟨ | {\hat{r}}_{i} \times {\hat{n}}_{i} | ⟩$ ) (red) and from nuclei deformation (black), as a function of distance from the aggregate center $r$ normalized by the radius of aggregate $R_{0}$ ( $n = 8$ ). (d) Mean orthoradial ordering for actin orientation and nucleus deformation is size dependent ( $n = 23$ ). Dashed red and black lines in panels (c) and (d) denote orthoradial ordering in actin and nuclei respectively, in Blebbistatin-treated aggregates. The scale bar is $50 μ m$ . Error bars are mean $\pm$ standard deviation. ^*** $P < 0.001$ , ^* $P < 0.05$ .
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Figure 2
Aggregate surface tension is size-dependent. (a) Brightfield image of micropipette aspiration which shows the aggregate entering the pipette over a length $L$ (indicated by dotted red line). (b) $L$ over time (black circles, dotted red line). A step increase in pressure is applied and then released at the apex of $L$ (blue dotted line). Solid gray lines represent the region where aspiration and retraction rates are measured. This region represents a fluid like regime. (c) Comparison between viscoelastic and experimental time scales. (d) Surface tension $γ$ as a function of aggregate size, $R_{0}$ , for control ( $n = 21$ , blue) and $50 μ M$ Blebbistatin-treated aggregates ( $n = 9$ , red). ^*** $P < 0.001 ns$ is nonsignificant. Scale bar is $50 μ m$ . Error bars are mean $\pm$ standard deviation.
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Figure 3
Pressure and cell number density are both size dependent yielding constant work. (a) Pressure-volume relationship for different aggregates of multiple sizes (blue, no treatment; red, treated with $50 μ M$ Blebbistatin). Inset: volume expansion of a nonadherent aggregate in $50 μ M$ Blebbistatin. (b) Cell number density ( $ρ$ ), as measured through nuclei counting, decreases with the increasing size of the aggregate. Inset: inverted fluorescence image of nuclei of an aggregate with red dots that identify their fluorescent centers. (c) Aggregate pressure and number density are linearly correlated and inversely proportional to the aggregate size. (a)–(c) Each point represents a single experiment. (d) Pressure and number density relationship for different levels of active stress. $R T^{*}$ for 0 and $50 μ M$ Blebbistatin (d, inset). ^*** $P < 0.001$ . ^** $P < 0.01 ns$ is nonsignificant. Scale bar is $100 μ m$ . Error bars are mean $\pm$ standard deviation.
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