Spontaneous Mechanical Oscillations

3D single cell migration driven by temporal correlation between oscillating force dipoles

Directional cell locomotion requires symmetry breaking between the front and rear of the cell. In some cells, symmetry breaking manifests itself in a directional flow of actin from the front to the rear of the cell. Many cells, especially in physiological 3D matrices do not show such coherent actin dynamics and present seemingly competing protrusion/retraction dynamics at their front and back. How symmetry breaking manifests itself for such cells is therefore elusive. We take inspiration from the scallop theorem proposed by Purcell for micro-swimmers in Newtonian fluids: self-propelled objects undergoing persistent motion at low Reynolds number must follow a cycle of shape changes that breaks temporal symmetry. We report similar observations for cells crawling in 3D. We quantified cell motion using a combination of 3D live cell imaging, visualization of the matrix displacement and a minimal model with multipolar expansion. We show that our cells embedded in a 3D matrix form myosin-driven force dipoles at both sides of the nucleus, that locally and periodically pinch the matrix. The existence of a phase shift between the two dipoles is required for directed cell motion which manifests itself as cycles with finite area in the dipole-quadrupole diagram, a formal equivalence to the Purcell cycle. We confirm this mechanism by triggering local dipolar contractions with a laser. This leads to directed motion. Our study reveals that these cells control their motility by synchronizing dipolar forces distributed at front and back. This result opens new strategies to externally control cell motion as well as for the design of micro-crawlers.

Interplay between cell height variations and planar pulsations in epithelial monolayers

Biological tissues change their shapes through collective interactions of cells. This coordination sets length and time scales for dynamics where precision is essential, in particular during morphogenetic events. However, how these scales emerge remains unclear. Here, we address this question using the pulsatile domains observed in confluent epithelial MDCK monolayers where cells exhibit synchronous contraction and extension cycles of [Formula: see text] h duration and [Formula: see text] length scale. We report that the monolayer thickness changes gradually in space and time by more than twofold in order to counterbalance the contraction and extension of the incompressible cytoplasm. We recapitulate these pulsatile dynamics using a continuum model and show that incorporation of cell stiffness dependent height variations is critical both for generating temporal pulsations and establishing the domain size. We propose that this feedback between height and mechanics could be important in coordinating the length scales of tissue dynamics.

Motion magnification analysis of microscopy videos of biological cells

It is well recognized that isolated cardiac muscle cells beat in a periodic manner. Recently, evidence indicates that other, non-muscle cells, also perform periodic motions that are either imperceptible under conventional lab microscope lens or practically not easily amenable for analysis of oscillation amplitude, frequency, phase of movement and its direction. Here, we create a real-time video analysis tool to visually magnify and explore sub-micron rhythmic movements performed by biological cells and the induced movements in their surroundings. Using this tool, we suggest that fibroblast cells perform small fluctuating movements with a dominant frequency that is dependent on their surrounding substrate and its stiffness.

The Biophysics of Cell Migration: Biasing Cell Motion with Feynman Ratchets

The concepts and frameworks of soft matter physics and the laws of thermodynamics can be used to describe relevant developmental, physiologic, and pathologic events in which directed cell migration is involved, such as in cancer. Typically, this directionality has been associated with the presence of soluble long-range gradients of a chemoattractant, synergizing with many other guidance cues to direct the motion of cells. In particular, physical inputs have been shown to strongly influence cell locomotion. However, this type of cue has been less explored despite the importance in biology. In this paper, we describe recent in vitro works at the interface between physics and biology, showing how the motion of cells can be directed by using gradient-free environments with repeated local asymmetries. This rectification of cell migration, from random to directed, is a process reminiscent of the Feynman ratchet; therefore, this framework can be used to explain the mechanism behind directed cell motion.

Living Matter: Mesoscopic Active Materials

An introduction to the physical properties of living active matter at the mesoscopic scale (tens of nanometers to micrometers) and their unique features compared with "dead," nonactive matter is presented. This field of research is increasingly denoted as "biological physics" where physics includes chemical physics, soft matter physics, hydrodynamics, mechanics, and the related engineering sciences. The focus is on the emergent properties of these systems and their collective behavior, which results in active self-organization and how they relate to cellular-level biological function. These include locomotion (cell motility and migration) forces that give rise to cell division, the growth and form of cellular assemblies in development, the beating of heart cells, and the effects of mechanical perturbations such as shear flow (in the bloodstream) or adhesion to other cells or tissues. An introduction to the fundamental concepts and theory with selected experimental examples related to the authors' own research is presented, including red-blood-cell membrane fluctuations, motion of the nucleus within an egg cell, self-contracting acto-myosin gels, and structure and beating of heart cells (cardiomyocytes), including how they can be driven by an oscillating, mechanical probe.

Synchronized mechanical oscillations at the cell-matrix interface in the formation of tensile tissue

The formation of uniaxial fibrous tissues with defined viscoelastic properties implies the existence of an orchestrated mechanical interaction between the cytoskeleton and the extracellular matrix. This study addresses the nature of this interaction. The hypothesis is that this mechanical interplay underpins the mechanical development of the tissue. In embryonic tendon tissue, an early event in the development of a mechanically robust tissue is the interaction of the pointed tips of extracellular collagen fibrils with the fibroblast plasma membrane to form stable interface structures (fibripositors). Here, we used a fibroblast-generated tissue that is structurally and mechanically matched to embryonic tendon to demonstrate homeostasis of cell-derived and external strain-derived tension over repeated cycles of strain and relaxation. A cell-derived oscillatory tension component is evident in this matrix construct. This oscillatory tension involves synchronization of individual cell forces across the construct and is induced in each strain cycle by transient relaxation and transient tensioning of the tissue. The cell-derived tension along with the oscillatory component is absent in the presence of blebbistatin, which disrupts actinomyosin force generation of the cell. The time period of this oscillation (60-90 s) is well-defined in each tissue sample and matches a primary viscoelastic relaxation time. We hypothesize that this mechanical oscillation of fibroblasts with plasma membrane anchored collagen fibrils is a key factor in mechanical sensing and feedback regulation in the formation of tensile tissues.

Emergence of epithelial cell density waves

Epithelial cell monolayers exhibit traveling mechanical waves. We rationalize this observation thanks to a hydrodynamic description of the monolayer as a compressible, active and polar material. We show that propagating waves of the cell density, polarity, velocity and stress fields may be due to a Hopf bifurcation occurring above threshold values of active coupling coefficients.

Protrusion fluctuations direct cell motion

Many physiological phenomena involve directional cell migration. It is usually attributed to chemical gradients in vivo. Recently, other cues have been shown to guide cells in vitro, including stiffness/adhesion gradients or micropatterned adhesive motifs. However, the cellular mechanism leading to these biased migrations remains unknown, and, often, even the direction of motion is unpredictable. In this study, we show the key role of fluctuating protrusions on ratchet-like structures in driving NIH3T3 cell migration. We identified the concept of efficient protrusion and an associated direction index. Our analysis of the protrusion statistics facilitated the quantitative prediction of cell trajectories in all investigated conditions. We varied the external cues by changing the adhesive patterns. We also modified the internal cues using drug treatments, which modified the protrusion activity. Stochasticity affects the short- and long-term steps. We developed a theoretical model showing that an asymmetry in the protrusion fluctuations is sufficient for predicting all measures associated with the long-term motion, which can be described as a biased persistent random walk.

'Single molecule': theory and experiments, an introduction

At scales below micrometers, Brownian motion dictates most of the behaviors. The simple observation of a colloid is striking: a permanent and random motion is seen, whereas inertial forces play a negligible role. This Physics, where velocity is proportional to force, has opened new horizons in biology. The random feature is challenged in living systems where some proteins - molecular motors - have a directed motion whereas their passive behaviors of colloid should lead to a Brownian motion. Individual proteins, polymers of living matter such as DNA, RNA, actin or microtubules, molecular motors, all these objects can be viewed as chains of colloids. They are submitted to shocks from molecules of the solvent. Shapes taken by these biopolymers or dynamics imposed by motors can be measured and modeled from single molecules to their collective effects. Thanks to the development of experimental methods such as optical tweezers, Atomic Force Microscope (AFM), micropipettes, and quantitative fluorescence (such as Förster Resonance Energy Transfer, FRET), it is possible to manipulate these individual biomolecules in an unprecedented manner: experiments allow to probe the validity of models; and a new Physics has thereby emerged with original biological insights. Theories based on statistical mechanics are needed to explain behaviors of these systems. When force-extension curves of these molecules are extracted, the curves need to be fitted with models that predict the deformation of free objects or submitted to a force. When velocity of motors is altered, a quantitative analysis is required to explain the motions of individual molecules under external forces. This lecture will give some elements of introduction to the lectures of the session 'Nanophysics for Molecular Biology'.

Ion channels contribute to the regulation of cell sheet forces during Drosophila dorsal closure

We demonstrate that ion channels contribute to the regulation of dorsal closure in Drosophila, a model system for cell sheet morphogenesis. We find that Ca(2+) is sufficient to cause cell contraction in dorsal closure tissues, as UV-mediated release of caged Ca(2+) leads to cell contraction. Furthermore, endogenous Ca(2+) fluxes correlate with cell contraction in the amnioserosa during closure, whereas the chelation of Ca(2+) slows closure. Microinjection of high concentrations of the peptide GsMTx4, which is a specific modulator of mechanically gated ion channel function, causes increases in cytoplasmic free Ca(2+) and actomyosin contractility and, in the long term, blocks closure in a dose-dependent manner. We identify two channel subunits, ripped pocket and dtrpA1 (TrpA1), that play a role in closure and other morphogenetic events. Blocking channels leads to defects in force generation via failure of actomyosin structures, and impairs the ability of tissues to regulate forces in response to laser microsurgery. Our results point to a key role for ion channels in closure, and suggest a mechanism for the coordination of force-producing cell behaviors across the embryo.

Bazooka inhibits aPKC to limit antagonism of actomyosin networks during amnioserosa apical constriction

Cell shape changes drive tissue morphogenesis during animal development. An important example is the apical cell constriction that initiates tissue internalisation. Apical constriction can occur through a phase of cyclic assembly and disassembly of apicomedial actomyosin networks, followed by stabilisation of these networks. Delayed negative-feedback mechanisms typically underlie cyclic behaviour, but the mechanisms regulating cyclic actomyosin networks remain obscure, as do mechanisms that transform overall network behaviour. Here, we show that a known inhibitor of apicomedial actomyosin networks in Drosophila amnioserosa cells, the Par-6-aPKC complex, is recruited to the apicomedial domain by actomyosin networks during dorsal closure of the embryo. This finding establishes an actomyosin-aPKC negative-feedback loop in the system. Additionally, we find that aPKC recruits Bazooka to the apicomedial domain, and phosphorylates Bazooka for a dynamic interaction. Remarkably, stabilising aPKC-Bazooka interactions can inhibit the antagonism of actomyosin by aPKC, suggesting that Bazooka acts as an aPKC inhibitor, and providing a possible mechanism for delaying the actomyosin-aPKC negative-feedback loop. Our data also implicate an increasing degree of Par-6-aPKC-Bazooka interactions as dorsal closure progresses, potentially explaining a developmental transition in actomyosin behaviour from cyclic to persistent networks. This later impact of aPKC inhibition is supported by mathematical modelling of the system. Overall, this work illustrates how shifting chemical signals can tune actomyosin network behaviour during development.

Signalling through mechanical inputs: a coordinated process

There is growing awareness that mechanical forces - in parallel to electrical or chemical inputs - have a central role in driving development and influencing the outcome of many diseases. However, we still have an incomplete understanding of how such forces function in coordination with each other and with other signalling inputs in vivo. Mechanical forces, which are generated throughout the organism, can produce signals through force-sensitive processes. Here, we first explore the mechanisms through which forces can be generated and the cellular responses to forces by discussing several examples from animal development. We then go on to examine the mechanotransduction-induced signalling processes that have been identified in vivo. Finally, we discuss what is known about the specificity of the responses to different forces, the mechanisms that might stabilize cells in response to such forces, and the crosstalk between mechanical forces and chemical signalling. Where known, we mention kinetic parameters that characterize forces and their responses. The multi-layered regulatory control of force generation, force response and force adaptation should be viewed as a well-integrated aspect in the greater biological signalling systems.

Mechano-electrical vibrations of microtubules--link to subcellular morphology

Spontaneous mechanical oscillations were predicted and experimentally proven on almost every level of cellular structure. Besides morphogenetic potential of oscillatory mechanical force, oscillations may drive vibrations of electrically polar structures or these structures themselves may oscillate on their own natural frequencies. Vibrations of electric charge will generate oscillating electric field, role of which in morphogenesis is discussed in this paper. This idea is demonstrated in silico on the conformation of two growing microtubules.

Duty ratio of cooperative molecular motors

Molecular motors are found throughout the cells of the human body and have many different and important roles. These micromachines move along filament tracks and have the ability to convert chemical energy into mechanical work that powers cellular motility. Different types of motors are characterized by different duty ratios, which is the fraction of time that a motor is attached to its filament. In the case of myosin II (a nonprocessive molecular machine with a low duty ratio), cooperativity between several motors is essential to induce motion along its actin filament track. In this work we use statistical mechanical tools to calculate the duty ratio of cooperative molecular motors. The model suggests that the effective duty ratio of nonprocessive motors that work in cooperation is lower than the duty ratio of the individual motors. The origin of this effect is the elastic tension that develops in the filament which is relieved when motors detach from the track.

Mechanosensitive shivering of model tissues under controlled aspiration

During embryonic development and wound healing, the mechanical signals transmitted from cells to their neighbors induce tissue rearrangement and directional movements. It has been observed that forces exerted between cells in a developing tissue under stress are not always monotonically varying, but they can be pulsatile. Here we investigate the response of model tissues to controlled external stresses. Spherical cellular aggregates are subjected to one-dimensional stretching forces using micropipette aspiration. At large enough pressures, the aggregate flows smoothly inside the pipette. However, in a narrow range of moderate aspiration pressures, the aggregate responds by pulsed contractions or "shivering." We explain the emergence of this shivering behavior by means of a simple analytical model where the uniaxially stretched cells are represented by a string of Kelvin-Voigt elements. Beyond a deformation threshold, cells contract and pull on neighboring cells after a time delay for cell response. Such an active behavior has previously been found to cause tissue pulsation during dorsal closure of Drosophila embryo.