Forces at the scale of the cell

TL;DR

This review analyzes forces at the scale of the cell as arising from non-equilibrium, energy-consuming processes and organizes these forces within a soft-condensed-matter framework. It integrates active-matter concepts with biophysical descriptions of polymers, membranes, hydrodynamics, and orientational order to explain how forces generate form and drive functions such as division, motility, and tissue morphogenesis. The authors survey experimental force-measurement techniques (AFM, optical/magnetic tweezers, traction force methods) and present mechanochemical transduction as a unifying principle for motor proteins, polymerization, and cortex dynamics. By bridging molecular mechanisms with continuum theories, the paper highlights how physical forces couple to information processing and may have shaped evolutionary trajectories toward complex cellular architectures.

Abstract

The importance of molecular-scale forces in sculpting biological form and function has been acknowledged for more than a century. Accounting for forces in biology is a problem that lies at the intersection of soft condensed matter physics, statistical mechanics, computer simulations and novel experimental methodologies, all adapted to a cellular context. This review surveys how forces arise within the cell. We provide a summary of the relevant background in basic biophysics, of soft-matter systems in and out of thermodynamic equilibrium, and of various force measurement methods in biology. We then show how these ideas can be incorporated into a description of cell-scale processes where forces are involved. Our examples include polymerization forces, motion of molecular motors, the properties of the actomyosin cortex, the mechanics of cell division, and shape changes in tissues. We show how new conceptual frameworks are required for understanding the consequences of cell-scale forces for biological function. We emphasize active matter descriptions, methodological tools that provide ways of incorporating non-equilibrium effects in a systematic manner into conceptual as well as quantitative descriptions. Understanding the functions of cells will necessarily require integrating the role of physical forces with the assimilation and processing of information. This integration is likely to have been a significant driver of evolutionary change.

Figures (23)

• Figure 1: Schematic representations of a prokaryotic and a eukaryotic cell (not to scale). The figure illustrates some of the well-studied organelles in these cells whose physics we discuss in this review. Typically, prokaryotic cells are small ($\sim 1-2 \, \mu$m) compared to eukaryotic cells ($\sim 10-20 \, \mu$m). Genetic information is stored in the form of DNA across most cellular forms of life. A typical prokaryote, such as an E. coli cell, lacks intracellular membrane compartments and has its DNA floating around in the bulk of the cell. It uses a rotary motor to turn flagellar filaments which aid in the propulsion of the cell. The internal structure of a eukaryotic cell is dynamically maintained in an organized manner. The DNA is packaged, at several hierarchical levels of organization, into chromosomes. These chromosomes are enclosed inside a double-walled lipid bilayer, reinforced by a supporting polymer mesh (lamins), forming the nucleus. Long polymeric filaments (microtubules) act as tracks on which molecular motors transport cargo across different parts of the cell. A meshwork of actin filaments, myosin motors, and crosslinkers forms the "cortex" found towards the periphery of the cell. Active mechanochemical processes in this actomyosin cortex generates cellular protrusions such as filopodia and lamellopodia that help the cell to anchor on substrates or to move.
• Figure 2: This figure illustrates the hierarchy of force scales at the level of a single cell and below. The appropriate force scale is the pico-Newton ($10^{-12}$ N). Forces from molecular motor translocation are in the regime $1-10$ pN while the forces involved in cell adhesion are typically $2-3$ orders of magnitude larger.
• Figure 3: (a) A schematic of the master equation \ref{['eq:master_equation']} indicating stochastic transitions between the states $C_i$ with transition rates $W_{i \to j}$. (b) Ion-channels are proteins embedded in the cell-membrane which transition between "open" and "closed" states in a stochastic manner. (c) The production (by transcription) and degradation of the mRNA molecules can be captured within a master equation approach where $P(n,t)$ represents the probability of finding $n$ mRNA molecules at time $t$. (d) The translocation of molecular motors transporting cargo on filaments is another example of a stochastic process with discrete states. Here the internal states of the system are the attachment configurations of the two heads of the motor. The coupling between these transitions and directional asymmetries in the filament leads to motion of the motor.
• Figure 4: Collections of interacting particles driven by stochastic forces arising from the thermal environment. (a) shows a few colloidal scale particles ($10^{-6} \,$m) immersed in a bath of smaller particles. The interactions of the colloidal particles with the heat bath leads to diffusive dynamics at long time. (b) and (c) show extended structures -- one a polymer filament and the other a membrane sheet. The strength of the stochastic forces are comparable to the energies required to cause significant shape change. The extended nature of these structures requires that their energetics be modeled through energy functionals that depend upon shape.
• Figure 5: Coarse-grained descriptions. (a) Shows a varying particle density leads to the construction of a density field $\rho(\mathbf{x},t)$ as shown. (b) The momentum flux tensor $\mathsf{\Pi}$ measures the flux of momentum through an infinitesimal area element with normal $\hat{\mathbf{n}}$. In particular, the force per unit-area acting on this area element is $\mathbf{F} = \mathsf{\Pi} \cdot \hat{\mathbf{n}}$.