Life is intrinsically mechanical. Animals run, fly, and swim. Plants move daily to track the Sun. Even microscopic organisms, first observed more than three centuries ago when Antoni van Leeuwenhoek trained his microscope on pond water, swarm and tumble. A look at our own cells reveals that subcellular components are in constant motion, which allows living cells to grow, divide, change shape, and move.

In addition to producing motion, our bodies must also sense it. Living cells respond to a wide variety of mechanical stimuli, including stretch, fluid flow, osmotic potential, and the stiffness of their surroundings. Our senses of hearing and touch require nerve cells to detect minuscule mechanical forces. And our ability to regulate blood pressure across meters of height depends on mechanosensitive arteries and arterioles distributed throughout the body.

cells grown on soft surfaces are primed to differentiate and form correspondingly soft tissues such as fat or nervous tissue, whereas cells grown on harder surfaces differentiate to form bone cells. 1 et al. , Dev. Cell 6, 483 (2004); et al. , Cell 126, 677 (2006). 1. R. McBeath, Dev. Cell, 483 (2004); https://doi.org/10.1016/S1534-5807(04)00075-9 A. J. Engler, Cell, 677 (2006). https://doi.org/10.1016/j.cell.2006.06.044 growth and development of our organs require precise changes in shape, with tightly controlled tissue-level mechanical stresses and strains. The mechanosensory response is also apparent in everyday life: Consistent exercise, for instance, leads to increases in bone and muscle mass, and slacking off reverses the gains. More subtly, living tissues are remarkably sensitive to the mechanical cues provided by their surroundings. Stemon soft surfaces are primed to differentiate and form correspondingly soft tissues such as fat or nervous tissue, whereason harder surfaces differentiate to form boneOn longer length scales, theand development of our organs require precise changes in shape, with tightly controlled tissue-level mechanical stresses and strains. The mechanosensory response is also apparent in everyday life: Consistent exercise, for instance, leads to increases in bone andmass, and slacking off reverses the gains.

cells must constantly communicate with each other. Much of the intercellular communication is through chemical signals, but growing evidence suggests that physical mechanisms provide significant control as well. 2 et al. , Dev. Cell 27, 131 (2013); et al. , Nat. Commun. 4, 2821 (2013). 2. R. Hiramatsu, Dev. Cell, 131 (2013); https://doi.org/10.1016/j.devcel.2013.09.026 T. Brunet, Nat. Commun., 2821 (2013). https://doi.org/10.1038/ncomms3821 image above cells. Individual cells are squeezed, pushed, and pulled across significant distances to form different parts of the developing body. To make complex morphogenetic decisions, ourmust constantly communicate with each other. Much of the intercellular communication is through chemical signals, butevidence suggests that physical mechanisms provide significant control as well.The, a still from a video of the development of a fruit-fly embryo, exemplifies the complex orchestration among hundreds ofIndividualare squeezed, pushed, and pulled across significant distances to form different parts of the developing body.

Although motion is a pervasive aspect of life, until recently biologists had little understanding of how living things produce, detect, and respond to mechanical cues at the cellular level. Only in the past decade have researchers learned key aspects of how living cells pull that off and how those different functions are integrated among groups of cells within tissues. Although the molecular details of how a cell works are complex, some relatively simple physical models provide powerful hints.

The cellular perspective Section: Choose Top of page ABSTRACT The cellular perspective << Protein energetics Molecular machines Molecular mechanosensors Meet in the middle REFERENCES CITING ARTICLES Cells are rarely subject to inertia. The Reynold’s number, Re, which describes the ratio of inertial to viscous forces in a system, is given by ρvl/μ, where ρ is density, v is velocity, l is a relevant length scale, and μ is viscosity. With each human cell typically about 10 µm across and moving at speeds no greater than 10 µm/s, cells experience a Re of 10−4, meaning that viscous forces on a cell are 10 000 times as great as those of inertia. 3 45, 3 (1977). 3. E. M. Purcell, Am. J. Phys., 3 (1977). https://doi.org/10.1119/1.10903 are rarely subject to inertia. The Reynold’s number,, which describes the ratio of inertial toforces in a system, is given by, whereis density,is velocity,is a relevant length scale, andisWith each humantypically about 10 µm across and moving at speeds no greater than 10 µm/s,experience aof 10, meaning thatforces on aare 10 000 times as great as those of inertia. In the absence of inertia and without a constant input of directed force, cellular motion would essentially stop, save for diffusion and fluid currents. But cells possess a sophisticated internal structural network termed the cytoskeleton that can both resist external load and produce mechanical forces of its own. The cytoskeleton is made of several different proteins that assemble into ropes or tubes whose length ranges from about 100 nanometers to a few millimeters. The cytoskeleton’s stiff microtubules are thought to withstand compression and provide roadways along which other proteins move inside the cell. Loose, ropey strands known as intermediate filaments provide the cell with mechanical toughness and resist stretching. The protein actin assembles into thin strands that act like temporary struts that rapidly assemble and then disappear. And the component known as myosin organizes itself into protein assemblies that pull on actin. All of those cytoskeletal components are essential, but actin and myosin are particularly interesting because they allow the cell to move, change shape, and exert forces on its surroundings. Together, the different components form a cross-linked mesh that is anchored to the cell’s nucleus, membrane, organelles, and surroundings. cytoskeleton functions are complex, one way to think about its physical properties is in terms of a continuum, Kelvin–Voigt model—also known as the Voigt material—which lumps all of the biological complexity into a spring and a dashpot, shown in figure 1 cells flow and deform on the scale of minutes and hours but are solid-like on the scale of seconds or shorter. It also illustrates how important both the magnitude and the loading rate of a force can be for dictating the cellular response. Our sense of touch provides an elegant, though still debated, example of the principle. Fingertips contain nerves that are optimized to sense vibrations at about 200 Hz, which allows one to pick up subtle features such as roughness by running a finger across a surface. In that context, the loading rate, rather than the load itself, is the important stimulus. Although the details of how thefunctions are complex, one way to think about its physical properties is in terms of a continuum, Kelvin–Voigt model—also known as the Voigt material—which lumps all of the biological complexity into a spring and a dashpot, shown in figure. That model captures the property thatflow and deform on the scale of minutes and hours but are solid-like on the scale of seconds or shorter. It also illustrates how important both the magnitude and the loading rate of a force can be for dictating theresponse. Our sense of touch provides an elegant, though still debated, example of the principle. Fingertips contain nerves that are optimized to sense vibrations at about 200 Hz, which allows one to pick up subtle features such as roughness by running a finger across a surface. In that context, the loading rate, rather than the load itself, is the important stimulus. 4 et al. , Nat. Mater. 12, 253 (2013). 4. E. Moeendarbary, Nat. Mater., 253 (2013). https://doi.org/10.1038/nmat3517 viscous goo flowing through a cytoskeletal network of pores. Certain parameters set the time scale for the flow: the size ξ of hydraulic pores, through which liquids pass; an elastic modulus E, which incorporates elasticity of the cytoskeleton; and the effective viscosity μ, which describes the slow movement of embedded cytoplasmic elements. Those concepts come together in a poroelastic diffusion constant D p ~ Eξ2/μ, according to which the apparent diffusive motion of water depends not only on the viscosity of the flow but also on the stiffness and structure of the cytoskeleton. Recent work has modeled the cell’s cytoplasm as a poroelastic material.In that way of thinking, the cytoplasm is agoo flowing through a cytoskeletal network of pores. Certain parameters set the time scale for the flow: the sizeof hydraulic pores, through which liquids pass; an elastic modulus, which incorporates elasticity of theand the effective, which describes the slow movement of embedded cytoplasmic elements. Those concepts come together in a poroelastic diffusion constant, according to which the apparent diffusive motion of water depends not only on theof the flow but also on the stiffness and structure of the When and where the cytoskeleton has an important effect on diffusive transport is set by a poroelastic Péclet number Pe, the ratio of the advection to diffusion, or vl/D p , where v and l are characteristic velocity and length scales, respectively.4 If Pe ≫ 1, the pore size and elastic properties of the cytoskeleton dominate the movement of water through the cell. In a muscle cell, for instance, D p is likely about 50 µm2/s, l about 10 µm, and maximal contraction velocity v about 50 µm/s, which yields a Pe of about 10. That large a value suggests that cytoplasmic flow could be a source of interior, dissipative load in the muscle. The contraction of the muscle plausibly forces water through the relatively tiny holes in the cytoskeleton, which would consume some of the energy the muscle could otherwise produce. Whether that is, in fact, an important source of energetic inefficiency in the heart (or other muscles) has, so far as we’re aware, not been addressed. cell also suggests that a cell can potentially move simply by controlling the flow of water across its membrane. Recent experimental evidence suggests as much: Last year, cancer cells were found to crawl through thin channels by taking up water in the front and then pushing it out behind them. 5 et al. , Cell 157, 611 (2014). 5. K. M. Stroka, Cell, 611 (2014). https://doi.org/10.1016/j.cell.2014.02.052 The poroelastic view of thealso suggests that acan potentially move simply by controlling the flow of water across itsRecent experimental evidence suggests as much: Last year, cancerwere found to crawl through thin channels by taking up water in the front and then pushing it out behind them. In short, a surprising amount about cells can be learned simply by thinking about them as bags of viscous liquid (the cytoplasm) flowing in an elastic polymer network (the cytoskeleton). But more can be learned by shrinking the perspective several orders of magnitude—from the micron scale of single cells to the nanometer scale of single proteins inside them.

Protein energetics Section: Choose Top of page ABSTRACT The cellular perspective Protein energetics << Molecular machines Molecular mechanosensors Meet in the middle REFERENCES CITING ARTICLES The world of proteins is small and noisy. Typically exerting piconewtons of force, a protein will perform just 10−21 N·m, or 6.2 meV, of work by moving 1 nm against 1 pN of resisting load. While moving through the cell, a protein also experiences Brownian motion because of its own thermal energy and collisions with surrounding water molecules. Boltzmann’s constant k B times the absolute temperature T—about 4.1 pN·nm, or 25 meV, at room temperature—describes the thermal energy of each of the protein’s degrees of freedom. cell. To see why, consider a protein that can occupy two conformations, one compact and one elongated as shown in the box G/k B T), where ΔG is the Gibbs free energy difference between the states. If ΔG = 1 k B T, the ratio is 1/3, a meaningful difference in the abundance of one state over the other. If ΔG = 0.5 k B T, the ratio is only 1/1.6, a smaller difference in populations that a cell may not easily discern. An applied force can dramatically tilt the balance between the conformations. That thermal noise sets a rough lower energy bound for processes at work in theTo see why, consider athat can occupy two conformations, one compact and one elongated as shown in thebelow. The ratio of the two conformations follows a Boltzmann distribution exp(−Δ), where Δis the Gibbs free energy difference between the states. If Δ= 1, the ratio is 1/3, a meaningful difference in the abundance of one state over the other. If Δ= 0.5, the ratio is only 1/1.6, a smaller difference in populations that amay not easily discern. An applied force can dramatically tilt the balance between the conformations. A rough upper bound to the energy scale relevant to single proteins is that provided by adenosine triphosphate (ATP), the energy currency of the cell. Our enzymes couple the release of energy stored in the bonds of ATP’s charged backbone to otherwise unfavorable processes, like motion and synthesis. Metabolic energy from our food is used to recharge the cell’s supply of ATP. Under the conditions in a typical cell, the available energy per ATP molecule is about 20 k B T. The molecular machinery of the cell thus operates at energies between 1 and 20 k B T. At first glance, it might seem impossible to do any useful work with devices that operate at just a few times the thermal background energy. However, as we’ll see, nature has evolved remarkable protein-based machines that do exactly that. Proteins are nanomachines par excellence. Those precisely manufactured amino-acid sequences have an exact length, exact composition, and high information content—all properties that are unusual among manmade polymers. Those characteristics allow proteins to fold into well-defined three- dimensional shapes that perform countless and diverse duties in a cell. (For a brief tutorial on how proteins fold, see figure 2 proteins that interconvert chemical and mechanical cues; that class includes both motor proteins, which convert chemical energy into mechanical work, and mechanosensitive proteins, which convert mechanical deformation into chemical signals. are nanomachines par excellence. Those precisely manufactured amino-acid sequences have an exact length, exact composition, and high information content—all properties that are unusual among manmade polymers. Those characteristics allowto fold into well-defined three- dimensional shapes that perform countless and diverse duties in a(For a brief tutorial on howfold, see figure.) In this article, the focus will be on the class ofthat interconvert chemical and mechanical cues; that class includes bothwhich convert chemical energy into mechanical work, and mechanosensitivewhich convert mechanical deformation into chemical signals. Although the details are still debated, a passable approximation is that the folded shape of a protein is dictated by the space-efficient packing of greasy, hydrophobic amino acids on the protein’s interior and by the exposure of charged, hydrophilic amino acids on its exterior. More directional interactions—for example, hydrogen bonds and electrostatic forces—additionally specify a protein’s conformation so that it corresponds to a local energy minimum in the complex conformational space that the protein inhabits. Note that proteins can inhabit more than one such energy minimum; transitions between energy minima, which correspond to changes in the protein’s shape, can convey information and, in some cases, couple the chemical energy of ATP hydrolysis to the production of useful work. Shielding the average hydrophobic amino acid from water yields about 4 k B T of energy, assuming perfect space filling; hydrogen bonds likewise contribute roughly 2 k B T each. The loss of configurational entropy upon folding yields a penalty of 2 k B T per amino acid. So the hydrogen bonds and configurational entropy cancel each other out and leave about 2–4 k B T per amino acid for protein stabilization upon folding. For a typical protein with 100 amino acids in its hydrophobic core, that corresponds to as much as 400 k B T. To appreciate whether that’s a lot or a little, recall that the relative probability for a protein to inhabit one of two possible states scales as exp(−ΔG/k B T). In this case the probability of the protein becoming unfolded would be 1 in 5 × 10173! proteins are usually far less stable. A typical protein’s folding free energy is only 12 k B T, or one-half an ATP’s worth of energy. Mammalian proteins unfold at temperatures of around 50 °C. In contrast, proteins from thermophilic bacteria can remain folded in boiling water, which suggests that life can evolve exceedingly stable proteins when doing so is necessary. Indeed, the difference in stabilities appears deliberate: Computer-aided redesign of proteins that operate around room temperature show that a few design changes can lead to dramatic increases in thermal stability. 6 et al. , Science 308, 857 (2005). 6. A. Korkegian, Science, 857 (2005). https://doi.org/10.1126/science.1107387 In reality,are usually far less stable. A typicalfolding free energy is only 12, or one-half an ATP’s worth of energy. Mammalianunfold at temperatures of around 50 °C. In contrast,from thermophilic bacteria can remain folded in boiling water, which suggests that life can evolve exceedingly stablewhen doing so is necessary. Indeed, the difference in stabilities appears deliberate: Computer-aided redesign ofthat operate around room temperature show that a few design changes can lead to dramatic increases in thermal stability. protein evolve for marginal stability? One hypothesis is that it does not matter how stable a protein is, as long as it lies above a necessary stability threshold. Once the minimum threshold is met, random evolutionary drift would then generally leave the stability of a protein near that threshold. 7 175, 255 (2006); 46, 105 (2002). 7. J. D. Bloom, A. Raval, C. O. Wilke, Genetics, 255 (2006); https://doi.org/10.1534/genetics.106.061754 D. M. Taverna, R. A. Goldstein, Proteins, 105 (2002). https://doi.org/10.1002/prot.10016 Proteins that can’t be broken down accumulate and form plaques like the amyloid aggregates of Alzheimer’s or Parkinson’s disease (see Physics Today, Why would aevolve for marginal stability? One hypothesis is that it does not matter how stable ais, as long as it lies above a necessary stability threshold. Once the minimum threshold is met, random evolutionary drift would then generally leave the stability of anear that threshold.Another possibility is that excessive stability prevents regular metabolic turnover:that can’t be broken down accumulate and form plaques like the amyloid aggregates of Alzheimer’s or Parkinson’s disease (see June 2013, page 16 ). proteins may be intimately related to their role as chemical catalysts. Enzymes with complicated catalytic mechanisms adopt multiple conformations corresponding to distinct steps in their catalytic cycle. 8 et al. , Nature 450, 913 (2007). 8. K. A. Henzler-Wildman, Nature, 913 (2007). https://doi.org/10.1038/nature06407 protein inhabits an energy well that is too deep, it becomes stuck, uselessly frozen in place. More fundamentally, the marginal stability ofmay be intimately related to their role as chemical catalysts. Enzymes with complicated catalytic mechanisms adopt multiple conformations corresponding to distinct steps in their catalytic cycle.Consistent with that model, many thermophilic enzymes lose their catalytic activity at room temperature. If ainhabits an energy well that is too deep, it becomes stuck, uselessly frozen in place.

Molecular machines Section: Choose Top of page ABSTRACT The cellular perspective Protein energetics Molecular machines << Molecular mechanosensors Meet in the middle REFERENCES CITING ARTICLES protein dynamics to chemical catalysis is beautifully illustrated by the motor protein myosin, which works in muscle to convert chemical energy from ATP into force and directed motion. 9 288, 88 (2000); 2, 387 (2001). 9. R. D. Vale, R. A. Milligan, Science, 88 (2000); https://doi.org/10.1126/science.288.5463.88 J. A. Spudich, Nat. Rev. Mol. Cell Biol., 387 (2001). https://doi.org/10.1038/35073086 cellular actin. (See the article by Rob Phillips and Steve Quake, Physics Today, 3 The coupling ofdynamics to chemical catalysis is beautifully illustrated by themyosin, which works into convert chemical energy from ATP into force and directed motion.More specifically, it couples ATP hydrolysis to the swing of a lever arm by pulling on filaments ofactin. (See the article by Rob Phillips and Steve Quake, May 2006, page 38 .) ATP turns out to be hydrolyzed while myosin is detached from the actin filament. Elegant experiments demonstrate that ATP hydrolysis is reversible within myosin’s active site, meaning that very little change in energy occurs while both adenosine diphosphate and a phosphate group, the products of the hydrolysis, remain bound at the active site. The stored energy is ultimately used in a power stroke—the pulling of the lever arm about 10 nm—that is triggered when myosin binds to actin and frees the phosphate, as outlined in figure To maintain the traction necessary to pull on a tensed filament, the myosin head must bind to actin tightly. The strong binding is broken only by the affinity of myosin for ATP; thus the strong interaction between myosin and actin is traded for an even stronger interaction between myosin and ATP. The net effect is that myosin efficiently couples chemical energy to directed force.

Molecular mechanosensors Section: Choose Top of page ABSTRACT The cellular perspective Protein energetics Molecular machines Molecular mechanosensors << Meet in the middle REFERENCES CITING ARTICLES cells also contain numerous molecular force sensors that can detect mechanical stretch, substrate stiffness, fluid flow, vibration, compression, and, more broadly, heat and light. 10 et al. , PLoS Biol. 12, e1001996 (2014). 10. B. L. Pruitt, PLoS Biol., e1001996 (2014). https://doi.org/10.1371/journal.pbio.1001996 In addition to possessing molecular-scale machines such as myosin, variousalso contain numerous molecular force sensors that can detect mechanical stretch, substrate stiffness, fluid flow, vibration, compression, and, more broadly, heat and light.Because so many sensors stud a cell’s surface, understanding how each sensor functions is a major intellectual enterprise. Perhaps the most-studied molecular mechanosensor complex consists of the protein assemblies that link the cell to the surrounding extracellular matrix. Those assemblies, termed focal adhesions, are breathtakingly intricate, composed of thousands of protein molecules and hundreds of different protein types. Despite the compositional complexity, the way in which focal-adhesion proteins sense force can be described by fairly simple physics. proteins are likely present in focal adhesions, but the best understood are the proteins talin and vinculin, which link adhesion proteins to the cellular actin network. Biological and biophysical measurements support the model shown in figure 4 cytoskeleton and focal adhesion. 11 et al. , Science 323, 638 (2009). 11. A. del Rio, Science, 638 (2009). https://doi.org/10.1126/science.1162912 protein (see the box proteins. In essence, a mechanically driven physical transformation (unfolding) is converted into a protein-binding interaction, which acts as a form of information processing and storage. Many force-sensingare likely present in focalbut the best understood are thetalin and vinculin, which linkto theactin network. Biological and biophysical measurements support the model shown in figure: Mechanical stretch unfolds domains within talin, to which vinculin can bind to reinforce the connection between theand focalThe stretch tilts the energy balance between the folded and unfolded states for specific portions of the talin(see the). The unfolded domains recruit vinculin, which both binds to actin and recruits additionalIn essence, a mechanically driven physical transformation (unfolding) is converted into ainteraction, which acts as a form of information processing and storage. A single myosin molecule exerts about 2 pN, and the exposure of each new vinculin binding site adds at least 5 nm to the stretched talin molecule. As a result, the force produced by just one myosin motor is sufficient to bias a vinculin binding site in talin toward its open state by 5 nm × 2 pN, or 2.4 k B T. That results in a 10-fold shift in the equilibrium constant K toward the elongated, unfolded conformation. Four myosin molecules bound to an actin filament would lead to a 15 000-fold shift in K toward the elongated, unfolded state. 4 cell and its environment. Although the details still need to be worked out, it seems likely that this model and similar strategies allow the cell to automatically adjust the strength with which it adheres to its substrate, and likely to its neighbors, in response to variations in mechanical load. Force sensing also has mechanical consequences. Once it binds to talin, vinculin also changes conformation, such that it, too, can bind to actin, as pictured in figure. In that way, force sensing is automatically connected to reinforcement of a mechanical connection between theand its environment. Although the details still need to be worked out, it seems likely that this model and similar strategies allow theto automatically adjust the strength with which it adheres to its substrate, and likely to its neighbors, in response to variations in mechanical load. The talin–vinculin example is just one particularly well-studied case of a myriad of protein sensors at work in living cells. In most cases, biophysicists know next to nothing about how a cell converts the effects of membrane bending, fluid flow, or the vibrations from sound or touch, say, into chemical information it can process. Fortunately, techniques for measuring molecular-scale forces in living cells and even intact animals are improving rapidly. The example of talin indicates that proteins that undergo nanometer changes in length can sense the piconewton-scale forces inside cells. As techniques improve, it will be fascinating to discover how the cell’s many other mechanosensors function at the molecular level.