Fluid flows and forces in development: functions, features and biophysical principles

Throughout morphogenesis, cells experience intracellular tensile and contractile forces on microscopic scales. Cells also experience extracellular forces, such as static forces mediated by the extracellular matrix and forces resulting from microscopic fluid flow. Although the biological ramifications of static forces have received much attention, little is known about the roles of fluid flows and forces during embryogenesis. Here, we focus on the microfluidic forces generated by cilia-driven fluid flow and heart-driven hemodynamics, as well as on the signaling pathways involved in flow sensing. We discuss recent studies that describe the functions and the biomechanical features of these fluid flows. These insights suggest that biological flow determines many aspects of cell behavior and identity through a specific set of physical stimuli and signaling pathways.     

Physics of Bacterial Morphogenesis

Summary: Bacterial cells utilize three-dimensional (3D) protein assemblies to perform important cellular functions such as growth, division, chemoreception, and motility. These assemblies are composed of mechanoproteins that can mechanically deform and exert force. Sometimes, small-nucleotide hydrolysis is coupled to mechanical deformations. In this review, we describe the general principle for an understanding of the coupling of mechanics with chemistry in mechanochemical systems. We apply this principle to understand bacterial cell shape and morphogenesis and how mechanical forces can influence peptidoglycan cell wall growth. We review a model that can potentially reconcile the growth dynamics of the cell wall with the role of cytoskeletal proteins such as MreB and crescentin. We also review the application of mechanochemical principles to understand the assembly and constriction of the FtsZ ring. A number of potential mechanisms are proposed, and important questions are discussed.     

Polymer motors: pushing out the front and pulling up the back

Mechanical work in cells is performed by specialized motor proteins that operate in a continuous mechanochemical cycle. Less complex, but still efficient, 'one-shot' motors evolved based on the assembly and disassembly of polymers. We review the mechanisms of pushing and pulling by actin and microtubule filaments and the organizational principles of actin networks. We show how these polymer force generators are used for the propulsion of intracellular pathogens, protrusion of lamellipodia and mitotic movements. We discuss several examples of cellular forces generated by the assembly and disassembly of polymer gels.     

Multi-scale mechanics from molecules to morphogenesis

Dynamic mechanical processes shape the embryo and organs during development. Little is understood about the basic physics of these processes, what forces are generated, or how tissues resist or guide those forces during morphogenesis. This review offers an outline of some of the basic principles of biomechanics, provides working examples of biomechanical analyses of developing embryos, and reviews the role of structural proteins in establishing and maintaining the mechanical properties of embryonic tissues. Drawing on examples we highlight the importance of investigating mechanics at multiple scales from milliseconds to hours and from individual molecules to whole embryos. Lastly, we pose a series of questions that will need to be addressed if we are to understand the larger integration of molecular and physical mechanical processes during morphogenesis and organogenesis.     

Mobility of Molecular Motors Regulates Contractile Behaviors of Actin Networks

Cells generate mechanical forces primarily from interactions between F-actin, cross-linking proteins, myosin motors, and other actin-binding proteins in the cytoskeleton. To understand how molecular interactions between the cytoskeletal elements generate forces, a number of in vitro experiments have been performed but are limited in their ability to accurately reproduce the diversity of motor mobility. In myosin motility assays, myosin heads are fixed on a surface and glide F-actin. By contrast, in reconstituted gels, the motion of both myosin and F-actin is unrestricted. Because only these two extreme conditions have been used, the importance of mobility of motors for network behaviors has remained unclear. In this study, to illuminate the impacts of motor mobility on the contractile behaviors of the actin cytoskeleton, we employed an agent-based computational model based on Brownian dynamics. We find that if motors can bind to only one F-actin like myosin I, networks are most contractile at intermediate mobility. In this case, less motor mobility helps motors stably pull F-actins to generate tensile forces, whereas higher motor mobility allows F-actins to aggregate into larger clustering structures. The optimal intermediate motor mobility depends on the stall force and affinity of motors that are regulated by mechanochemical rates. In addition, we find that the role of motor mobility can vary drastically if motors can bind to a pair of F-actins. A network can exhibit large contraction with high motor mobility because motors bound to antiparallel pairs of F-actins can exert similar forces regardless of their mobility. Results from this study imply that the mobility of molecular motors may critically regulate contractile behaviors of actin networks in cells.     

Providing Positional Information with Active Transport on Dynamic Microtubules

Microtubules (MTs) are dynamic protein polymers that change their length by switching between growing and shrinking states in a process termed dynamic instability. It has been suggested that the dynamic properties of MTs are central to the organization of the eukaryotic intracellular space, and that they are involved in the control of cell morphology, but the actual mechanisms are not well understood. Here, we present a theoretical analysis in which we explore the possibility that a system of dynamic MTs and MT end-tracking molecular motors is providing specific positional information inside cells. We compute the MT length distribution for the case of MT-length-dependent switching between growing and shrinking states, and analyze the accumulation of molecular motors at the tips of growing MTs. Using these results, we show that a transport system consisting of dynamic MTs and associated motor proteins can deliver cargo proteins preferentially to specific positions within the cell. Comparing our results with experimental data in the model organism fission yeast, we propose that the suggested mechanisms could play important roles in setting length scales during cellular morphogenesis.     

The basic mechanism of ATP powered motor proteins

The ability of ATP powered motor proteins to convert chemical free energy into the mechanical work required to move intra-cellular organelles is discussed in terms of the molecular and dynamic fundamentals involved in producing such movements. This is carried out in detail for muscle contraction with the result that in order for a myosin head to act as a motor protein, it is necessary for it to be able to impose a unique series of impacts on an actin filament. It is further shown that these impacts can be generated when a single water molecule is transiently attached to the ADP formed during one step of an ATP cycle in the myosin head. This analysis leads to the conclusion that muscle must be a type of heat machine which has the capability of attaining mechanochemical efficiencies that approach 100%. An extension of ATP powered motor proteins in general is made with the finding that they must share the same motor mechanism of the transiently attached water molecule. A possible application of these considerations to the problem of the active transport of ions is also pointed out.     

Crosslinkers and motors organize dynamic microtubules to form stable bipolar arrays in fission yeast

Microtubule (MT) nucleation not only occurs from centrosomes, but also in large part from dispersed nucleation sites. The subsequent sorting of short MTs into networks like the mitotic spindle requires molecular motors that laterally slide overlapping MTs and bundling proteins that statically connect MTs. How bundling proteins interfere with MT sliding is unclear. In bipolar MT bundles in fission yeast, we found that the bundler ase1p localized all along the length of antiparallel MTs, whereas the motor klp2p (kinesin-14) accumulated only at MT plus ends. Consequently, sliding forces could only overcome resistant bundling forces for short, newly nucleated MTs, which were transported to their correct position within bundles. Ase1p thus regulated sliding forces based on polarity and overlap length, and computer simulations showed these mechanisms to be sufficient to generate stable bipolar bundles. By combining motor and bundling proteins, cells can thus dynamically organize stable regions of overlap between cytoskeletal filaments.     

Computational Tool for Ensemble Averaging of Single-Molecule Data

Molecular motors couple chemical transitions to conformational changes that perform mechanical work in a wide variety of biological processes. Disruption of this coupling can lead to diseases, and therefore there is a need to accurately measure mechanochemical coupling in motors in both health and disease. Optical tweezers with nanometer spatial and millisecond temporal resolution have provided valuable insights into these processes. However, fluctuations due to Brownian motion can make it difficult to precisely resolve these conformational changes. One powerful analysis technique that has improved our ability to accurately measure mechanochemical coupling in motor proteins is ensemble averaging of individual trajectories. Here, we present a user-friendly computational tool, Software for Precise Analysis of Single Molecules (SPASM), for generating ensemble averages of single-molecule data. This tool utilizes several conceptual advances, including optimized procedures for identifying single-molecule interactions and the implementation of a change-point algorithm, to more precisely resolve molecular transitions. Using both simulated and experimental data, we demonstrate that these advances allow for accurate determination of the mechanics and kinetics of the myosin working stroke with a smaller set of data. Importantly, we provide our open-source MATLAB-based program with a graphical user interface that enables others to readily apply these advances to the analysis of their own data.     

Optical tweezers in biology and medicine

Optical trapping techniques provide unique means to manipulate biological particles such as virus, living cells and subcellular organelles. Another area of interest is the measurement of mechanical (elastic) properties of cell membranes, long strands of single DNA molecule, and filamentous proteins. One of the most attractive applications is the study of single motor molecules. With optical tweezers traps, one can measure the forces generated by single motor molecules such as kinesin and myosin, in the piconewton range and, for the first time, resolve their detailed stepping motion.     

Brushes,cables, and anchors: Recent insights into multiscale assembly and mechanics of cellular structural networks

The remarkable ability of living cells to sense, process, and respond to mechanical stimuli in their environment depends on the rapid and efficient interconversion of mechanical and chemical energy at specific times and places within the cell. For example, application of force to cells leads to conformational changes in specific mechanosensitive molecules which then trigger cellular signaling cascades that may alter cellular structure, mechanics, and migration and profoundly influence gene expression. Similarly, the sensitivity of cells to mechanical stresses is governed by the composition, architecture, and mechanics of the cellular cytoskeleton and extracellular matrix (ECM), which are in turn driven by molecular-scale forces between the constituent biopolymers. Understanding how these mechanochemical systems coordinate over multiple length and time scales to produce orchestrated cell behaviors represents a fundamental challenge in cell biology. Here, we review recent advances in our understanding of these complex processes in three experimental systems: the assembly of axonal neurofilaments, generation of tensile forces by actomyosin stress fiber bundles, and mechanical control of adhesion assembly.     

Reverse engineering a protein: the mechanochemistry of ATP synthase

ATP synthase comprises two rotary motors in one. The F(1) motor can generate a mechanical torque using the hydrolysis energy of ATP. The F(o) motor generates a rotary torque in the opposite direction, but it employs a transmembrane proton motive force. Each motor can be reversed: The F(o) motor can drive the F(1) motor in reverse to synthesize ATP, and the F(1) motor can drive the F(o) motor in reverse to pump protons. Thus ATP synthase exhibits two of the major energy transduction pathways employed by the cell to convert chemical energy into mechanical force. Here we show how a physical analysis of the F(1) and F(o) motors can provide a unified view of the mechanochemical principles underlying these energy transducers.     

Maximum force production: why are crabs so strong?

Durophagous crabs successfully hunt hard-shelled prey by subjecting them to extremely strong biting forces using their claws. Here I show that, for a given body mass, six species of Cancer crabs (Cancer antennarius, Cancer branneri, Cancer gracilis, Cancer magister, Cancer oregonensis and Cancer productus) were able to exert mean maximum biting forces greater than the forces exerted in any other activity by most other animals. These strong biting forces were in part a result of the high stresses (740-1350 kN m(-2)) generated by the claw closer muscle. Furthermore, the maximum muscle stress increased with increasing mean resting sarcomere length (10-18 microm) for the closer muscle of the claws of these six Cancer species. A more extensive analysis incorporating published data on muscle stresses in other animal groups revealed that stress scales isometrically with the resting sarcomere length among species, as predicted by the sliding filament model of muscle contraction. Therefore, muscle or filament traits other than a very long mean sarcomere length need not be invoked in explaining the high stresses generated by crustacean claws.     

Statistical kinetics of macromolecular dynamics

Fluctuations in biochemical processes can provide insights into the underlying kinetics beyond what can be gleaned from studies of average rates alone. Historically, analysis of fluctuating transmembrane currents supplied information about ion channel conductance states and lifetimes before single-channel recording techniques emerged. More recently, fluctuation analysis has helped to define mechanochemical pathways and coupling ratios for the motor protein kinesin as well as to probe the contributions of static and dynamic disorder to the kinetics of single enzymes. As growing numbers of assays are developed for enzymatic or folding behaviors of single macromolecules, the range of applications for fluctuation analysis increases. To evaluate specific biochemical models against experimental data, one needs to predict analytically the distribution of times required for completion of each reaction pathway. Unfortunately, using traditional methods, such calculations can be challenging for pathways of even modest complexity. Here, we derive an exact expression for the distribution of completion times for an arbitrary pathway with a finite number of states, using a recursive method to solve algebraically for the appropriate moment-generating function. To facilitate comparisons with experiments on processive motor proteins, we develop a theoretical formalism for the randomness parameter, a dimensionless measure of the variance in motor output. We derive the randomness for motors that take steps of variable sizes or that move on heterogeneous substrates, and then discuss possible applications to enzymes such as RNA polymerase, which transcribes varying DNA sequences, and to myosin V and cytoplasmic dynein, which may advance by variable increments.     

Pure thoughts with impure proteins: Permeabilized cell models of organelle motility

Permeabilized cell models provide an experimental middle ground wherein the in vitro properties of mechanochemical proteins can be reconciled with the physical and topological constraints of the intact cell. Several well-studied examples of organelle motility are described here, including the actin-based cytoplasmic streaming of Characean algae, the microtubule-based aggregation and dispersion of pigment granules in chromatophores and the saltatory movements of vesicles along microtubules in fibroblasts and macrophages. The permeabilized models developed for these systems have helped to integrate observations in vivo with in vitro assays of motor proteins.     

Direct evidence that stomatogastric (Panulirus interruptus) muscle passive responses are not due to background actomyosin cross-bridges

Muscles respond to imposed length changes with rapid, large force changes followed by slow relaxations to new steady-state forces. These responses were originally believed to arise from background levels of actomyosin binding. Discovery of giant sarcomere-spanning proteins suggested muscle passive responses could arise from length changes of elastic domains present in these proteins. However, direct evidence that actomyosin plays little role in passive muscle force responses to imposed length changes has not been provided. We show here that a poison of actomyosin interaction, thiourea, does not alter initial force changes or subsequent relaxations of lobster stomatogastric muscles. These data provide direct evidence that background actomyosin cross-bridge formation likely plays, at most, a small role in muscle passive responses to length changes. Thiourea does not alter lobster muscle electrical responses to motor nerve stimulation, although in this species it does cause tonic motor nerve firing. This firing limits the utility of thiourea to study lobster muscle electrical responses to motor nerve stimulation. However, it is unclear whether thiourea induces such motor nerve firing in other animals. Thiourea may therefore provide a convenient technique to measure muscle electrical responses to motor nerve input without the confounding difficulties caused by muscle contraction.     

The role of cellular active stresses in shaping the zebrafish body axis

Tissue remodelling and organ shaping during morphogenesis are products of mechanical forces generated at the cellular level. These cell-scale forces can be coordinated across the tissue via information provided by biochemical and mechanical cues. Such coordination leads to the generation of complex tissue shape during morphogenesis. In this short review, we elaborate the role of cellular active stresses in vertebrate axis morphogenesis, primarily using examples from postgastrulation development of the zebrafish embryo.