Modulation of the reaction rate of regulating protein induces large morphological and motional change of amoebic cell

Morphologies of moving amoebae are categorized into two types. One is the "neutrophil" type in which the long axis of cell roughly coincides with its moving direction. This type of cell extends a leading edge at the front and retracts a narrow tail at the rear, whose shape has been often drawn as a typical amoeba in textbooks. The other one is the "keratocyte" type with widespread lamellipodia along the front side arc. Short axis of cell in this type roughly coincides with its moving direction. In order to understand what kind of molecular feature causes conversion between two types of morphologies, and how two typical morphologies are maintained, a mathematical model of amoebic cells is developed. This model describes movement of cell and intracellular reactions of activator, inhibitor and actin filaments in a unified way. It is found that the producing rate of activator is a key factor of conversion between two types. This model also explains the observed data that the keratocyte type cells tend to rapidly move along a straight line. The neutrophil type cells move along a straight line when the moving velocity is small, but they show fluctuated motions deviating from a line when they move as fast as the keratocyte type cells. Efficient energy consumption in the neutrophil type cells is predicted.     

Representation of motion onset and offset in an augmented Barlow-Levick model of motion detection

Kinetic occlusion produces discontinuities in the optic flow field, whose perception requires the detection of an unexpected onset or offset of otherwise predictably moving or stationary contrast patches. Many cells in primate visual cortex are directionally selective for moving contrasts, and recent reports suggest that this selectivity arises through the inhibition of contrast signals moving in the cells’ null direction, as in the rabbit retina. This nulling inhibition circuit (Barlow-Levick) is here extended to also detect motion onsets and offsets. The selectivity of extended circuit units, measured as a peak evidence accumulation response to motion onset/offset compared to the peak response to constant motion, is analyzed as a function of stimulus speed. Model onset cells are quiet during constant motion, but model offset cells activate during constant motion at slow speeds. Consequently, model offset cell speed tuning is biased towards higher speeds than onset cell tuning, similarly to the speed tuning of cells in the middle temporal area when exposed to speed ramps. Given a population of neurons with different preferred speeds, this asymmetry addresses a behavioral paradox—why human subjects in a simple reaction time task respond more slowly to motion offsets than onsets for low speeds, even though monkey neuron firing rates react more quickly to the offset of a preferred stimulus than to its onset.     

Polarization and Movement of Keratocytes: A Multiscale Modelling Approach

Eukariotic cell motility is a complex phenomenon, in which the cytoskeleton and its major constituent, actin, play an essential role. Actin forms polymers of long, stiff filaments that are cross-linked into an anisotropic network inside a thin sheet-like cellular protrusion, the lamellipod. At the leading edge of this structure, polymerization of actin filaments creates the force that pushes out the membrane and leads to translocation of a motile cell. Dynamics of the actin network account for changes in cell shape, crawling motion and turning of the cell in response to external cues. Regulating the dynamics of the cytoskeleton, and playing a central role in signal transduction in the cell, are Cdc42, Rac and Rho (GTPases of the rho family, collectively known as the small G-proteins) and the actin nucleating complex, Arp2/3.In this paper, we use a multiscale modelling approach in a 2D model of a motile cell. We describe the mutual interactions of the small G-proteins, and their effects on capping and side-branching of actin filaments. We incorporate the pushing exerted by oriented actin filament ends on the cell edge, and a Rho-dependent contraction force. Combining these biochemical and mechanical aspects, we investigate the dynamics of a model epidermal fish keratocyte through in silico experiments. Our model gives insight into how, in response to some cue, a cell can polarize, form a leading edge, and move; concomitantly it explains how a keratocyte cell can maintain its shape and polarity, even after removal of the initial stimulus, and how it can change direction quickly in response to changes in its environment. We show that establishment of polarity stems from interactions of Cdc42, Rac and Rho, while maintenance and robustness of polarity is due to the rapid cytosolic diffusion of the inactive (GDI-bound) forms of the small G-proteins. Our model produces a cell shape that closely resembles the keratocytes and correct speeds for biologically reasonable parameter values. Movies of the simulations can be obtained from http://theory.bio.uu.nl/stan/keratocyte.     

Gap junctions increase the sensitivity of tissue cells to exogenous electric fields

Cells coupled by gap junctions will react as a single unit to an applied electric field. In a given field, the hyperpolarization and depolarization of cell membranes at the ends of an electrotonically coupled tissue are increases by a factor of 10-100 over single, uncoupled cells. Gap junctional coupling therefore increases the likelihood that cells are influenced by the weak electric fields which are commonly found in developing and regenerating tissues.     

Tracking retrograde flow in keratocytes: news from the front

Actin assembly at the leading edge of the cell is believed to drive protrusion, whereas membrane resistance and contractile forces result in retrograde flow of the assembled actin network away from the edge. Thus, cell motion and shape changes are expected to depend on the balance of actin assembly and retrograde flow. This idea, however, has been undermined by the reported absence of flow in one of the most spectacular models of cell locomotion, fish epidermal keratocytes. Here, we use enhanced phase contrast and fluorescent speckle microscopy and particle tracking to analyze the motion of the actin network in keratocyte lamellipodia. We have detected retrograde flow throughout the lamellipodium at velocities of 1-3 microm/min and analyzed its organization and relation to the cell motion during both unobstructed, persistent migration and events of cell collision. Freely moving cells exhibited a graded flow velocity increasing toward the sides of the lamellipodium. In colliding cells, the velocity decreased markedly at the site of collision, with striking alteration of flow in other lamellipodium regions. Our findings support the universality of the flow phenomenon and indicate that the maintenance of keratocyte shape during locomotion depends on the regulation of both retrograde flow and actin polymerization.     

The electrophoretic hemolytic plaque assay - theory

We use the mathematical theory of plaque growth to determine if there is merit in performing a hemolytic plaque assay in the presence of an external electric field. In particular, we study the effects of an electric field on the transport of anti-bodies secreted by a single lymphocyte and on the size and shape of the plaques they produce. Our results indicate that in the presence of an applied electric field: (1) The mobility of the antibodies produced by the antibody forming cell can be determined from the plaque shape. (In the electric field the plaques are no longer circular, but cigar shaped.) (2) By changing the magnitude or direction of the applied electric field more than one plaque can be generated by a single AFC. Thus changes in mobility or the rate of antibody secretion can be assayed. (3) Plaques will reach a steady state size; for good emitters (cells that secrete antibodies at a high rate or that secrete high affinity antibodies) this steady state will be achieved rapidly.Equations are given which describe both the temporal development and steady state plaque size and shape. From the equations, computer generated plots of plaques produced by typical antibody farming cells are presented. These plots are then used to show how pictures of plaques formed in an electric field can be analyzed to determine the antibody mobility.     

Input-output relationship in galvanotactic response of Dictyostelium cells

Under a direct current electric field, Dictyostelium cells exhibit migration towards the cathode. To determine the input-output relationship of the cell's galvanotactic response, we developed an experimental instrument in which electric signals applied to the cells are highly reproducible and the motile response are analyzed quantitatively. With no electric field, the cells moved randomly in all directions. Upon applying an electric field, cell migration speeds became about 1.3 times faster than those in the absence of an electric field. Such kinetic effects of electric fields on the migration were observed for cells stimulated between 0.25 and 10 V/cm of the field strength. The directions of cell migrations were biased toward the cathode in a positive manner with field strength, showing galvanotactic response in a dose-dependent manner. Quantitative analysis of the relationship between field strengths and directional movements revealed that the biased movements of the cells depend on the square of electric field strength, which can be described by one simple phenomenological equation. The threshold strength for the galvanotaxis was between 0.25 and 1 V/cm. Galvanotactic efficiency reached to half-maximum at 2.6 V/cm, which corresponds to an approximate 8 mV voltage difference between the cathode and anode direction of 10 microm wide, round cells. Based on these results, possible mechanisms of galvanotaxis in Dictyostelium cells were discussed. This development of experimental system, together with its good microscopic accessibility for intracellular signaling molecules, makes Dictyostelium cells attractive as a model organism for elucidating stochastic processes in the signaling systems responsible for cell motility and its regulations.     

Generation and escape of local waves from the boundary of uncoupled cardiac tissue

We aim to understand the formation of abnormal waves of activity from myocardial regions with diminished cell-to-cell coupling. En route to this goal, we studied the behavior of a heterogeneous myocyte network in which a sharp coupling gradient was placed under conditions of increasing network automaticity. Experiments were conducted in monolayers of neonatal rat cardiomyocytes using heptanol and isoproterenol as means of altering cell-to-cell coupling and automaticity, respectively. Experimental findings were explained and expanded using a modified Beeler-Reuter numerical model. The data suggest that the combination of a heterogeneous substrate, a gradient of coupling, and an increase in oscillatory activity of individual cells creates a rich set of behaviors associated with self-generated spiral waves and ectopic sources. Spiral waves feature a flattened shape and a pin-unpin drift type of tip motion. These intercellular waves are action-potential based and can be visualized with either voltage or calcium transient measurements. A source/load mismatch on the interface between the boundary and well-coupled layers can lock wavefronts emanating from both ectopic sources and rotating waves within the inner layers of the coupling gradient. A numerical approach allowed us to explore how 1), the spatial distribution of cells, 2), the amplitude and dispersion of cell automaticity, and 3), the speed at which the coupling gradient moves in space affect wave behavior, including its escape into well-coupled tissue.     

Coherent Motions in Confluent Cell Monolayer Sheets

Cell migration plays a pivotal role in many physiologically important processes such as embryogenesis, wound-healing, immune defense, and cancer metastasis. Although much effort has been directed toward motility of individual cells, the mechanisms underpinning collective cell migration remain poorly understood. Here we develop a collective motility model that incorporates cell mechanics and persistent random motions of individual cells to study coherent migratory motions in epithelial-like monolayers. This model, in absence of any external chemical signals, is able to explain coordinate rotational motion seen in systems ranging from two adherent cells to multicellular assemblies. We show that the competition between the active persistent force and random polarization fluctuation is responsible for the robust rotation. Passive mechanical coupling between cells is necessary but active chemical signaling between cells is not. The predicted angular motions also depend on the geometrical shape of the underlying substrate: cells exhibit collective rotation on circular substrates, but display linear back-and-forth motion on long and narrow substrates.     

Coherent Motions in Confluent Cell Monolayer Sheets

Cell migration plays a pivotal role in many physiologically important processes such as embryogenesis, wound-healing, immune defense, and cancer metastasis. Although much effort has been directed toward motility of individual cells, the mechanisms underpinning collective cell migration remain poorly understood. Here we develop a collective motility model that incorporates cell mechanics and persistent random motions of individual cells to study coherent migratory motions in epithelial-like monolayers. This model, in absence of any external chemical signals, is able to explain coordinate rotational motion seen in systems ranging from two adherent cells to multicellular assemblies. We show that the competition between the active persistent force and random polarization fluctuation is responsible for the robust rotation. Passive mechanical coupling between cells is necessary but active chemical signaling between cells is not. The predicted angular motions also depend on the geometrical shape of the underlying substrate: cells exhibit collective rotation on circular substrates, but display linear back-and-forth motion on long and narrow substrates.     

Stochastic models for cell motion and taxis

Certain biological experiments investigating cell motion result in time lapse video microscopy data which may be modeled using stochastic differential equations. These models suggest statistics for quantifying experimental results and testing relevant hypotheses, and carry implications for the qualitative behavior of cells and for underlying biophysical mechanisms. Directional cell motion in response to a stimulus, termed taxis, has previously been modeled at a phenomenological level using the Keller-Segel diffusion equation. The Keller-Segel model cannot distinguish certain modes of taxis, and this motivates the introduction of a richer class of models which is nevertheless still amenable to statistical analysis. A state space model formulation is used to link models proposed for cell velocity to observed data. Sequential Monte Carlo methods enable parameter estimation via maximum likelihood for a range of applicable models. One particular experimental situation, involving the effect of an electric field on cell behavior, is considered in detail. In this case, an Ornstein- Uhlenbeck model for cell velocity is found to compare favorably with a nonlinear diffusion model.     

Effect of electric field induced transmembrane potential on spheroidal cells: theory and experiment

The transmembrane potential on a cell exposed to an electric field is a critical parameter for successful cell permeabilization. In this study, the effect of cell shape and orientation on the induced transmembrane potential was analyzed. The transmembrane potential was calculated on prolate and oblate spheroidal cells for various orientations with respect to the electric field direction, both numerically and analytically. Changing the orientation of the cells decreases the induced transmembrane potential from its maximum value when the longest axis of the cell is parallel to the electric field, to its minimum value when the longest axis of the cell is perpendicular to the electric field. The dependency on orientation is more pronounced for elongated cells while it is negligible for spherical cells. The part of the cell membrane where a threshold transmembrane potential is exceeded represents the area of electropermeabilization, i.e. the membrane area through which the transport of molecules is established. Therefore the surface exposed to the transmembrane potential above the threshold value was calculated. The biological relevance of these theoretical results was confirmed with experimental results of the electropermeabilization of plated Chinese hamster ovary cells, which are elongated. Theoretical and experimental results show that permeabilization is not only a function of electric field intensity and cell size but also of cell shape and orientation.     

Short-Range Guiding Can Result in the Formation of Circular Aggregates in Myxobacteria Populations

Myxobacteria are social bacteria that upon starvation form multicellular fruiting bodies whose shape in different species can range from simple mounds to elaborate tree-like structures. The formation of fruiting bodies is a result of collective cell movement on a solid surface. In the course of development, groups of flexible rod-shaped cells form streams and move in circular or spiral patterns to form aggregation centers that can become sites of fruiting body formation. The mechanisms of such cell movement patterns are not well understood. It has been suggested that myxobacterial development depends on short-range contact-mediated interactions between individual cells, i.e. cell aggregation does not require long-range signaling in the population. In this study, by means of a computational mass-spring model, we investigate what types of short-range interactions between cells can result in the formation of streams and circular aggregates during myxobacterial development. We consider short-range head-to-tail guiding between individual cells, whereby movement direction of the head of one cell is affected by the nearby presence of the tail of another cell. We demonstrate that stable streams and circular aggregates can arise only when the trailing cell, in addition to being steered by the tail of the leading cell, is able to speed up to catch up with it. It is suggested that necessary head-to-tail interactions between cells can arise from physical adhesion, response to a diffusible substance or slime extruded by cells, or pulling by motility engine pili. Finally, we consider a case of long-range guiding between cells and show that circular aggregates are able to form without cells increasing speed. These findings present a possibility to discriminate between short-range and long-range guiding mechanisms in myxobacteria by experimentally measuring distribution of cell speeds in circular aggregates.     

Possible role of contact following in the generation of coherent motion of Dictyostelium cells

After aggregation by chemotaxis, cells of the cellular slime mold Dictyostelium discoideum form a multicellular structure and show coherent motion such as vortices. Here, we present a mathematical model to explain both aggregation and coherent motion of cells in two-dimensional space. The model incorporates chemotactic response of cells and the cell's property, called "contact following", to follow the other cells with which they are in contact. Analytical study and computer simulation using the model show that with contact following, cells form circular clusters within which cell rotation occurs. Unidirectional cell motion in a long belt of cells is another type of solution of the model. Besides, contact following has an effect to accelerate cell cluster merging. By considering the mechanism of cell movement, possible explanations of contact following are proposed.     

Comprehensive Analysis of Human Cells Motion under an Irrotational AC Electric Field in an Electro-Microfluidic Chip

AC electrokinetics is a versatile tool for contact-less manipulation or characterization of cells and has been widely used for separation based on genotype translation to electrical phenotypes. Cells responses to an AC electric field result in a complex combination of electrokinetic phenomena, mainly dielectrophoresis and electrohydrodynamic forces. Human cells behaviors to AC electrokinetics remain unclear over a large frequency spectrum as illustrated by the self-rotation effect observed recently. We here report and analyze human cells behaviors in different conditions of medium conductivity, electric field frequency and magnitude. We also observe the self-rotation of human cells, in the absence of a rotational electric field. Based on an analytical competitive model of electrokinetic forces, we propose an explanation of the cell self-rotation. These experimental results, coupled with our model, lead to the exploitation of the cell behaviors to measure the intrinsic dielectric properties of JURKAT, HEK and PC3 human cell lines.     

Area and Geometry Dependence of Cell Migration in Asymmetric Two-State Micropatterns

Microstructured surfaces provide a unique framework to probe cell migration and cytoskeletal dynamics in a standardized manner. Here, we report on the steady-state occupancy probability of cells in asymmetric two-state microstructures that consist of two fibronectin-coated adhesion sites connected by a thin guidance cue. In these dumbbell-like structures, cells transition between the two sites in a repeated and stochastic manner, and average dwell times in the respective microenvironments are determined from the cell trajectories. We study the dynamics of human breast carcinoma cells (MDA-MB-231) in these microstructures as a function of area, shape, and orientation of the adhesion sites. On square adhesive sites with different areas, we find that the occupancy probability ratio is directly proportional to the ratio of corresponding adhesion site areas. These asymmetries are well captured by a simple model for the stochastic nonlinear dynamics of the cells, which reveals generic features of the motion. Sites of equal area but different shape lead to equal occupancy if shapes are isotropic (e.g., squared or circular). In contrast, an asymmetry in the occupancy is induced by anisotropic shapes like rhombi, triangles, or rectangles that enable motion in the direction perpendicular to the transition axis. Analysis of the two-dimensional motion of cells between two rectangles with orthogonal orientation suggests that cellular transition rates depend on the cell polarization induced by anisotropic micropatterns. Taken together, our results illustrate how two-state micropatterns provide a dynamic migration assay with distinct dwell times and relative cell occupancy as readouts, which may be useful to probe cell-microenvironment interactions.     

Effects of electromagnetic fields on the motion of Euglena gracilis.

The orientation behavior of Euglena gracilis cultures in electromagnetic fields is shown to agree with the predictions of a model involving only a passive mechanism. The increase in Euglena motor activity with increasing field intensity is demonstrated by measuring various motion parameters by the laser scattering technique. The effect of electric field on the speed of Euglenas is compared with that of temperature. We conclude that the electric field warms up the culture, thus inducing an increase in cell motility.     

Gradient of rigidity in the lamellipodia of migrating cells revealed by atomic force microscopy

Changes in mechanical properties of the cytoplasm have been implicated in cell motility, but there is little information about these properties in specific regions of the cell at specific stages of the cell migration process. Fish epidermal keratocytes with their stable shape and steady motion represent an ideal system to elucidate temporal and spatial dynamics of the mechanical state of the cytoplasm. As the shape of the cell does not change during motion and actin network in the lamellipodia is nearly stationary with respect to the substrate, the spatial changes in the direction from the front to the rear of the cell reflect temporal changes in the actin network after its assembly at the leading edge. We have utilized atomic force microscopy to determine the rigidity of fish keratocyte lamellipodia as a function of time/distance from the leading edge. Although vertical thickness remained nearly constant throughout the lamellipodia, the rigidity exhibited a gradual but significant decrease from the front to the rear of the lamellipodia. The rigidity profile resembled closely the actin density profile, suggesting that the dynamics of rigidity are due to actin depolymerization. The decrease of rigidity may play a role in facilitating the contraction of the actin-myosin network at the lamellipodium/cell body transition zone.     

Emergence of large-scale cell morphology and movement from local actin filament growth dynamics

Variations in cell migration and morphology are consequences of changes in underlying cytoskeletal organization and dynamics. We investigated how these large-scale cellular events emerge as direct consequences of small-scale cytoskeletal molecular activities. Because the properties of the actin cytoskeleton can be modulated by actin-remodeling proteins, we quantitatively examined how one such family of proteins, enabled/vasodilator-stimulated phosphoprotein (Ena/VASP), affects the migration and morphology of epithelial fish keratocytes. Keratocytes generally migrate persistently while exhibiting a characteristic smooth-edged “canoe” shape, but may also exhibit less regular morphologies and less persistent movement. When we observed that the smooth-edged canoe keratocyte morphology correlated with enrichment of Ena/VASP at the leading edge, we mislocalized and overexpressed Ena/VASP proteins and found that this led to changes in the morphology and movement persistence of cells within a population. Thus, local changes in actin filament dynamics due to Ena/VASP activity directly caused changes in cell morphology, which is coupled to the motile behavior of keratocytes. We also characterized the range of natural cell-to-cell variation within a population by using measurable morphological and behavioral features—cell shape, leading-edge shape, filamentous actin (F-actin) distribution, cell speed, and directional persistence—that we have found to correlate with each other to describe a spectrum of coordinated phenotypes based on Ena/VASP enrichment at the leading edge. This spectrum stretched from smooth-edged, canoe-shaped keratocytes—which had VASP highly enriched at their leading edges and migrated fast with straight trajectories—to more irregular, rounder cells migrating slower with less directional persistence and low levels of VASP at their leading edges. We developed a mathematical model that accounts for these coordinated cell-shape and behavior phenotypes as large-scale consequences of kinetic contributions of VASP to actin filament growth and protection from capping at the leading edge. This work shows that the local effects of actin-remodeling proteins on cytoskeletal dynamics and organization can manifest as global modifications of the shape and behavior of migrating cells and that mathematical modeling can elucidate these large-scale cell behaviors from knowledge of detailed multiscale protein interactions.