Session Z40: Biomechanics - Organismic Motion

The mechanics of anisotropic cytoskeletal networks

At the leading edge of a crawling cell, the actin cytoskeleton extends itself via a branched, crosslinked network of filaments, otherwise known as the lamellipodium. The filaments in this network have an average preferred orientation of around $\pm$ 30 degrees with respect to the normal of the leading edge. This preferred orientation of filaments leads to a material that is structurally anisotropic. To better understand the forces generated by the lamellipodium, we analytically and numerically study the mechanical properties of a model branched and crosslinked filamentous network where the filaments are preferentially oriented along one direction. We investigate the interplay between geometry, elasticity and anisotropy in the network. In particular, we show how anisotropy modulates the onset of rigidity and non-linear mechanical response of the network.   

Self-Organized Cell Motility from Motor-Filament Interactions

Cell motility is driven primarily by the dynamics of the cell cytoskeleton, a system of filamentous proteins and molecular motors. It has been proposed that cell motility is a self-organized process; that is, local short-range interactions determine much of the necessary dynamics required for the whole-cell organization that leads to polarization and directional motion. Here we present a mesoscopic meanfield description of filaments, motors, and cell boundaries; this description gives rise to a dynamical system exhibiting multiple self-organized states. We discuss several qualitative aspects of the asymptotic states and compare them to those of living cells.   

Modeling of a crawling C. elegans in a micro-structured environment

A simple curvature-based model is used to study crawling C. elegans in a micro-structured environment of periodic pillars. In our model system, the shape of the worm is described by a simple sinusoidal expression in curvature representation. The gait of the worm is determined by a set of parameters including the amplitude, frequency, and phase of the curvature. The moving worm is subject to the friction with the underlying substrate, and the forces due to interaction of the worm body with pillars. If the friction is isotropic the worm has to interact with the pillars to move forward. We find that only a narrow range of worm gaits leads to efficient propulsion in this case. To investigate how the worm adjusts its gait to the environment microstructure, we implement a simple control system that chooses the right set of parameters based on the past interactions of the worm with its surroundings. Results of our simulations of the worm motion are compared with our experimental observations of C. elegans crawling in an agar environment containing an array of fabricated pillars.   

Fluctuations, Dynamics, and the Stretch-Coil Transition of Single Actin Filaments in Extensional Flows

Semi-flexible polymers (actin filaments) subject to hydrodynamic forcing play an important role in cytoskeletal dynamics in the cell. The non-equilibrium problem of semi-flexible polymer dynamics is highly challenging due to the coupling between the objects deformations and the flow. This leads to a free-boundary hydrodynamic problem, where the object's shape is not given {\it a priori}, but determined by an interplay between the fluid stresses, bending energy and the length constrain of the actin filaments. We have investigated experimentally and analytically dynamics of actin filaments in elongational flow. Near hyperbolic stagnation points of the flow filaments experience a competition between bending elasticity and tension induced by the flow, and are predicted to display suppressed thermal fluctuations in the steady regime and a buckling instability under sudden change of the velocity gradient. Using a microfluidic cross-flow geometry we verify these predictions in detail, including a fluctuation-rounded stretch-coil transition of actin filaments.   

Cell Shape Dynamics: From Waves to Migration

We observe and quantify wave-like characteristics of amoeboid migration. Using the amoeba Dictyostelium discoideum, a model system for the study of chemotaxis, we demonstrate that cell shape changes in a wave-like manner. Cells have regions of high boundary curvature that propagate from the leading edge toward the back, usually along alternating sides of the cell. Curvature waves are easily seen in cells that do not adhere to a surface, such as cells that are electrostatically repelled from surfaces or cells that extend over the edge of micro-fabricated cliffs. Without surface contact, curvature waves travel from the leading edge to the back of a cell at $\sim $35 $\mu $m/min. Non-adherent myosin II null cells do not exhibit these curvature waves. At the leading edge of adherent cells, curvature waves are associated with protrusive activity. Like regions of high curvature, protrusive activity travels along the boundary in a wave-like manner. Upon contact with a surface, the waves stop moving relative to the surface, and the boundary shape thus reflects the history of protrusive motion. The wave-like character of protrusions provides a plausible mechanism for the ability of cells to both swim in viscous fluids and to navigate complex 3-D topography.   

A curvature-based description for the kinematics of \textit{C. Elegans}

Caenorhabditis Elegans is a free-living soil nematode that propels itself in various complex environments by producing undulatory body motion. Such nematodes display a rich variety of body shapes and trajectories during their locomotion. Here we show that the complex shapes and trajectories of \textit{C. Elegans }have a simple analytical description in curvature representation. Our model is based on the assumption that the curvature wave is generated in the head segment of the worm body and propagates backwards. We have found that a simple sinusoidal function for the curvature can capture multiple worm shapes during the undulatory movement. The worm body trajectories can be well represented by piece-wise sinusoidal curvature with abrupt changes in amplitude, frequency, and phase.   

Paramecia Swim with a constant propulsion in Solutions of Varying Viscosity

Paramecia swim through the coordinated beating of the 1000's of cilia covering their body. We have measured the swimming speed of populations of Paramecium Caudatam in solutions of different viscosity, $\eta$, to see how their propulsion changes with increased drag. We have found the average instantaneous speed, V to decrease monotonically with increasing $\eta$. The product $\eta v$ is roughly constant over a factor of 7 change in viscosity suggesting that paramecia swim at constant propulsion force. The distribution of swimming speeds is Gaussian. The width appears proportional to the average speed implying that both fast and slow swimmers exert a constant propulsion. We discuss the possibility that this behavior implies that the body cilia beat at constant force with varying viscosity.   

Response of Swimming Paramecia to {\it in situ} changes in their apparent weight

There is a class of marine micro-organisms that are small enough that low Reynold's number hydrodynamics dictates their swimming mechanics and large enough that the force of gravity exerts a noticeable influence on their motion. Experiments on populations of paramecia suggest that they exert a greater propulsion when swimming against gravity. This negative gravi-kinesis is surprising because it suggests that they sense their tiny apparent weight of about 80 pN. To understand this response in more detail, we are investigating how individual paramecia caudatum change their swimming speed and helical trajectories in response to changes in their apparent weight. We vary the apparent weight with the technique of Magnetic Force Buoyancy Variation employing a high field resistive magnet at the National High Magnetic Field Laboratory. We will present analysis of the swimming for apparent weight changes as large as a factor of 8.   

Capillary Action may act as a cooling method in Plants and Animals

A capillary tube in a plant may lead from its roots to the leaves. It takes no work for the column of water to rise from the roots to the leaves, and if there is capillarity in the soil, it takes no work for the water to flow through the ground to the roots. It does take work for a molecule of water to evaporate from the tube into the atmosphere. When a molecule of water evaporates another molecule travels through the soil and up the plant to replace it. The lost molecule creates a ``hole'' in the water column which like a signal is sent to the root and the sea of water in the soil replaces it. Since the water molecules are not unique this is the same situation as if the water vapor where condensed back to a liquid in a refrigeration cycle. Another interesting aspect of this sort of refrigeration is that the ``hole'' itself may be used to do work along the wall of the capillary tube, which may have Fermi Levels in it. An Hydraulic Semi Conductor, and in it is a method of cooling the Semi Conductor. This may be applicable to other similar systems using other liquids, or substances such as nanotube systems, where the hole signals,cools and performs chemical reactions involving not only obitals but Fermi Levels, a transition between Quantum and Classical Mechanics, with surprises.   

Data-Driven Classification of Animal Behavior

The last decades have seen an explosion in our ability to characterize the molecular, cellular and genetic building blocks of life; the ingredients out of which we try to explain the rich and compelling behavior of living organisms. Our characterization of behavior itself, however, has advanced more slowly. Since modern ethology was founded over a century ago, behavioral experiments have focused largely on a restricted set of behaviors within the scope of a limited environment. Moreover, the set of behaviors to be examined is often user-defined, creating the potential for human bias and anthropomorphism. The research presented here describes a data-driven methodology for analyzing animal behavior, focusing on the fruit fly, Drosophila melanogaster, as a model system. Towards this end, we have built an imaging system that can track single flies as they move about a relatively unencumbered environment. Utilizing this capacity to generate large data sets of animal behavior, we have developed a method for automatically identifying behavioral states using techniques from image analysis, machine learning, and nonlinear dynamics. Identifying these states provides the starting point for many analyses and creates the possibility for automatic phenotyping of subtle behavioral traits.   

Multiscale Analysis of Head Impacts in Contact Sports

Traumatic brain injury (TBI) is one of the world's major causes of death and disability. To aid companies in designing safer and improved protective gear and to aid the medical community in producing improved quantitative TBI diagnosis and assessment tools, a multiscale finite element model of the human brain, head and neck is being developed. Recorded impact data from football and hockey helmets instrumented with accelerometers are compared to simulated impact data in the laboratory. Using data from these carefully constructed laboratory experiments, we can quantify impact location, magnitude, and linear and angular accelerations of the head. The resultant forces and accelerations are applied to a fully meshed head-form created from MRI data by Simpleware. With appropriate material properties for each region of the head-form, the Abaqus finite element model can determine the stresses, strains, and deformations in the brain. Simultaneously, an in-vitro cellular TBI criterion is being developed to be incorporated into Abaqus models for the brain. The cell-based injury criterion functions the same way that damage criteria for metals and other materials are used to predict failure in structural materials.   

The fern sporangium: an ultrafast natural catapult

Plants have developed fascinating mechanisms to create ultra fast movements that often reach the upper limit allowed by physical laws. Inspiration for new technologies is one of the reasons for the strong interest for these mechanisms, along with the deep interest of understanding complex, natural systems. The fern sporangium is a capsule that contains the spores, it is surrounded by a row of cells called the annulus which acts as a beam. Due to the water evaporation from its cells, the annulus bends strongly and induces elastic energy storage during an opening phase. The tension in the cells breaks when cavitation bubbles appear in the cells, leading to a fast release of the elastic energy. The fern sporangium then acts as a catapult which ejects rapidly its spores by closing back to the initial closed shape. We have analyzed the slow opening motion and the fast catapulting mechanism. We found that the catapult motion involves two time scales, showing a very original behavior. In man-made catapults, the recoil motion needs to be arrested by a cross bar so that the projectile is released from the arm. We show here that the fern sporangium replaces the essential cross bar by an elegant poroelastic damping, leading to a completely autonomous, efficient device.   

Hydrodynamics of Active Permeating Gels

We present a hydrodynamic theory of active viscoelastic gels in which a polymer network is embedded in a background fluid. This work is motivated by active processes in the cell cytoskeleton in which motor molecules generate elastic stresses in the network which can drive permeation flows of the cytosol. Our approach differs from earlier ones by considering the elastic strain in the polymer network as a slowly relaxing dynamical variable. We discuss a specific case that illustrates the role of permeation in active gels: the self-propulsion of a thin slab of gel relative to a substrate driven by filament polymerization and depolymerization.