Electrodynamic eigenmodes in cellular morphology

Eigenmodes of the spherical and ellipsoidal dielectric electromagnetic resonator have been analysed. The sizes and shape of the resonators have been chosen to represent the shape of the interphase and dividing animal cell. Electromagnetic modes that have shape exactly suitable for positioning of the sufficiently large organelles in cell (centrosome, nucleus) have been identified. We analysed direction and magnitude of dielectrophoretic force exerted on large organelles by electric field of the modes. We found that the TM(1m1) mode in spherical resonator acts by centripetal force which drags the large organelles which have higher permittivity than the cytosol to the center of the cell. TM-kind of mode in the ellipsoidal resonator acts by force on large polarizable organelles in a direction that corresponds to the movement of the centrosomes (also nucleus) observed during the cell division, i.e. to the foci of the ellipsoidal cell. Minimal required force (10(-16)N), gradient of squared electric field and corresponding energy (10(-16)J) of the mode have been calculated to have biological significance within the periods on the order of time required for cell division. Minimal required energy of the mode, in order to have biological significance, can be lower in the case of resonance of organelle with the field of the cellular resonator mode. In case of sufficient energy in the biologically relevant mode, electromagnetic field of the mode will act as a positioning or steering mechanism for centrosome and nucleus in the cell, thus contribute to the spatial and dynamical self-organization in biological systems.     

Coupling cell shape and velocity leads to oscillation and circling in keratocyte galvanotaxis

During wound healing, fish keratocyte cells undergo galvanotaxis where they follow a wound-induced electric field. In addition to their stereotypical persistent motion, keratocytes can develop circular motion without a field or oscillate while crawling in the field direction. We developed a coarse-grained phenomenological model that captures these keratocyte behaviors. We fit this model to experimental data on keratocyte response to an electric field being turned on. A critical element of our model is a tendency for cells to turn toward their long axis, arising from a coupling between cell shape and velocity, which gives rise to oscillatory and circular motion. Galvanotaxis is influenced not only by the field-dependent responses, but also cell speed and cell shape relaxation rate. When the cell reacts to an electric field being turned on, our model predicts that stiff, slow cells react slowly but follow the signal reliably. Cells that polarize and align to the field at a faster rate react more quickly and follow the signal more reliably. When cells are exposed to a field that switches direction rapidly, cells follow the average of field directions, while if the field is switched more slowly, cells follow a “staircase” pattern. Our study indicated that a simple phenomenological model coupling cell speed and shape is sufficient to reproduce a broad variety of different keratocyte behaviors, ranging from circling to oscillation to galvanotactic response, by only varying a few parameters.     

The plastic cell: mechanical deformation of cells and tissues

Epithelial cells possess the ability to change their shape in response to mechanical stress by remodelling their junctions and their cytoskeleton. This property lies at the heart of tissue morphogenesis in embryos. A key feature of embryonic cell shape changes is that they result from repeated mechanical inputs that make them partially irreversible at each step. Past work on cell rheology has rarely addressed how changes can become irreversible in a complex tissue. Here, we review new and exciting findings dissecting some of the physical principles and molecular mechanisms accounting for irreversible cell shape changes. We discuss concepts of mechanical ratchets and tension thresholds required to induce permanent cell deformations akin to mechanical plasticity. Work in different systems has highlighted the importance of actin remodelling and of E-cadherin endocytosis. We also list some novel experimental approaches to fine-tune mechanical tension, using optogenetics, magnetic beads or stretching of suspended epithelial tissues. Finally, we discuss some mathematical models that have been used to describe the quantitative aspects of accounting for mechanical cell plasticity and offer perspectives on this rapidly evolving field.     

Bacterial Cell Wall Synthesis: New Insights from Localization Studies

In order to maintain shape and withstand intracellular pressure, most bacteria are surrounded by a cell wall that consists mainly of the cross-linked polymer peptidoglycan (PG). The importance of PG for the maintenance of bacterial cell shape is underscored by the fact that, for various bacteria, several mutations affecting PG synthesis are associated with cell shape defects. In recent years, the application of fluorescence microscopy to the field of PG synthesis has led to an enormous increase in data on the relationship between cell wall synthesis and bacterial cell shape. First, a novel staining method enabled the visualization of PG precursor incorporation in live cells. Second, penicillin-binding proteins (PBPs), which mediate the final stages of PG synthesis, have been localized in various model organisms by means of immunofluorescence microscopy or green fluorescent protein fusions. In this review, we integrate the knowledge on the last stages of PG synthesis obtained in previous studies with the new data available on localization of PG synthesis and PBPs, in both rod-shaped and coccoid cells. We discuss a model in which, at least for a subset of PBPs, the presence of substrate is a major factor in determining PBP localization.     

Bacterial cell wall synthesis: new insights from localization studies.

In order to maintain shape and withstand intracellular pressure, most bacteria are surrounded by a cell wall that consists mainly of the cross-linked polymer peptidoglycan (PG). The importance of PG for the maintenance of bacterial cell shape is underscored by the fact that, for various bacteria, several mutations affecting PG synthesis are associated with cell shape defects. In recent years, the application of fluorescence microscopy to the field of PG synthesis has led to an enormous increase in data on the relationship between cell wall synthesis and bacterial cell shape. First, a novel staining method enabled the visualization of PG precursor incorporation in live cells. Second, penicillin-binding proteins (PBPs), which mediate the final stages of PG synthesis, have been localized in various model organisms by means of immunofluorescence microscopy or green fluorescent protein fusions. In this review, we integrate the knowledge on the last stages of PG synthesis obtained in previous studies with the new data available on localization of PG synthesis and PBPs, in both rod-shaped and coccoid cells. We discuss a model in which, at least for a subset of PBPs, the presence of substrate is a major factor in determining PBP localization.     

The theory of the frequency response of ellipsoidal biological cells in rotating electrical fields

In this paper we have presented in as compact a form as possible the theoretical formalism that is needed to predict the frequency response of a biological cell of arbitrary ellipsoidal shape to a frequency dependant rotating external field. The formalism is much more complicated than that for a spherical or cylindrical cell where the radial vector is always parallel to the surface normal at each point of the surface. In addition to providing the theory we have demonstrated that the spin rate and its frequency dependance is very intimately related to the electrical properties of the cell interior and to that of the suspending fluid. It is possible to probe these properties of the cell and its environment by utilizing this technique. This aspect has been demonstrated by examining rotational changes as a function of the conductivity of both the cell interior and its suspending liquid. We also have shown, by considering a very simple model for the cell and the two dielectric constants, that the frequency spectrum is shape dependant. All our calculations have been carried out for "lossy" systems with frictional dissipation where energy minimization methods are no longer applicable. The invariant form of the Poynting vector forms the basis of the method.     

Morphogenetic fields in embryogenesis, regeneration, and cancer: Non-local control of complex patterning

Establishment of shape during embryonic development, and the maintenance of shape against injury or tumorigenesis, requires constant coordination of cell behaviors toward the patterning needs of the host organism. Molecular cell biology and genetics have made great strides in understanding the mechanisms that regulate cell function. However, generalized rational control of shape is still largely beyond our current capabilities. Significant instructive signals function at long range to provide positional information and other cues to regulate organism-wide systems properties like anatomical polarity and size control. Is complex morphogenesis best understood as the emergent property of local cell interactions, or as the outcome of a computational process that is guided by a physically encoded map or template of the final goal state? Here I review recent data and molecular mechanisms relevant to morphogenetic fields: large-scale systems of physical properties that have been proposed to store patterning information during embryogenesis, regenerative repair, and cancer suppression that ultimately controls anatomy. Placing special emphasis on the role of endogenous bioelectric signals as an important component of the morphogenetic field, I speculate on novel approaches for the computational modeling and control of these fields with applications to synthetic biology, regenerative medicine, and evolutionary developmental biology.     

Lateral organization of membranes and cell shapes.

The relations among membrane structure, mechanical properties, and cell shape have been investigated. The fluid mosaic membrane models used contains several components that move freely in the membrane plane. These components interact with each other and determine properties of the membrane such as curvature and elasticity. A free energy equation is postulated for such a multicomponent membrane and the condition of free energy minimum is used to obtain differential equations relating the distribution of membrane components and the local membrane curvature. The force that moves membrane components along the membrane in a variable curvature field is calculated. A change in the intramembrane interactions can bring about phase separation or particle clustering. This, in turn, may strongly affect the local curvature. The numerical solution of the set of equations for the two dimensional case allows determination of the cell shape and the component distribution along the membrane. The model has been applied to describe certain erythrocytes shape transformations.     

Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells

The tensegrity hypothesis holds that the cytoskeleton is a structure whose shape is stabilized predominantly by the tensile stresses borne by filamentous structures. Accordingly, cell stiffness must increase in proportion with the level of the tensile stress, which is called the prestress. Here we have tested that prediction in adherent human airway smooth muscle (HASM) cells. Traction microscopy was used to measure the distribution of contractile stresses arising at the interface between each cell and its substrate; this distribution is called the traction field. Because the traction field must be balanced by tensile stresses within the cell body, the prestress could be computed. Cell stiffness (G) was measured by oscillatory magnetic twisting cytometry. As the contractile state of the cell was modulated with graded concentrations of relaxing or contracting agonists (isoproterenol or histamine, respectively), the mean prestress ((t)) ranged from 350 to 1,900 Pa. Over that range, cell stiffness increased linearly with the prestress: G (Pa) = 0.18(t) + 92. While this association does not necessarily preclude other interpretations, it is the hallmark of systems that secure shape stability mainly through the prestress. Regardless of mechanism, these data establish a strong association between stiffness of HASM cells and the level of tensile stress within the cytoskeleton.     

The flagellar cytoskeleton of the spirochetes

The recent discoveries of prokaryotic homologs of all three major eukaryotic cytoskeletal proteins (actin, tubulin, intermediate filaments) have spurred a resurgence of activity in the field of bacterial morphology. In spirochetes, however, it has long been known that the flagellar filaments act as a cytoskeletal protein structure, contributing to their shape and conferring motility on this unique phylum of bacteria. Therefore, revisiting the spirochete cytoskeleton may lead to new paradigms for exploring general features of prokaryotic morphology. This review discusses the role that the periplasmic flagella in spirochetes play in maintaining shape and producing motility. We focus on four species of spirochetes: Borrelia burgdorferi, Treponema denticola, Treponema phagedenis and Leptonema (formerly Leptospira) illini. In spirochetes, the flagella reside in the periplasmic space. Rotation of the flagella in the above species by a flagellar motor induces changes in the cell morphology that drives motility. Mutants that do not produce flagella have a markedly different shape than wild-type cells.     

The origins of protein phosphorylation

The reversible phosphorylation of proteins is central to the regulation of most aspects of cell function but, even after the first protein kinase was identified, the general significance of this discovery was slow to be appreciated. Here I review the discovery of protein phosphorylation and give a personal view of the key findings that have helped to shape the field as we know it today.     

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.     

Equilibrium shapes in non-uniform fields of concentration

The special case of a metabolizing cell, with infinite permeability, suspended in the field of an equivalent cell is treated exactly to determine its equilibrium shape for small deformations. It is found that flattening takes place along the line of centers.     

Model of Red Blood Cell Rotation in the Flow toward a Cell Sizing Orifice: Application to Volume Distribution

The rotation of human red blood cells (RBC) as they flow in the shear field established by a Coulter type orifice is modeled. This model, based on hydrodynamics of ellipsoid rotation in laminar creeping flow, is used to calculate the probability of the cells entering the orifice with a specific orientation. The electrical resistance change produced by a cell passing through the orifice of an electronic cell volume detector is the product of an orientation-dependent shape factor and the cell volume. This paper presents a method to calculate the shape factor probability distribution which can be used to predict its effect on the cell volume distribution. Experimental results confirm the theoretical prediction that the right skewness of resistance change distributions is in part a result of the nonspherical shape of red cells.     

Strategies for cell shape control in tip-growing cells

? Premise of the study: Despite the large diversity in biological cell morphology, the processes that specify and control cell shape are not yet fully understood. Here we study the shape of tip-growing, walled cells, which have evolved a polar mode of cell morphogenesis leading to characteristic filamentous cell morphologies that extend only apically. ? Methods: We identified the relevant parameters for the control of cell shape and derived scaling laws based on mass conservation and force balance that connect these parameters to the resulting geometrical phenotypes. These laws provide quantitative testable relations linking morphological phenotypes to the biophysical processes involved in establishing and modulating cell shape in tip-growing, walled cells. ? Key results and conclusions: By comparing our theoretical results to the observed morphological variation within and across species, we found that tip-growing cells from plant and fungal species share a common strategy to shape the cell, whereas oomycete species have evolved a different mechanism.     

Tuning cell shape change with contractile ratchets

Throughout the lifespan of an organism, shape changes are necessary for cells to carry out their essential functions. Nowhere is this more dramatic than embryonic development and gastrulation, when cell shape changes drive large-scale rearrangements in tissue architecture to establish the body plan of the organism. A longstanding question for both cell and developmental biologists has been how are forces generated to change cell shape? Recent studies in both cell culture and developing embryos have combined live imaging, computational analysis, genetics, and biophysics to identify ratchet-like behaviors in actomyosin networks that operate to incrementally change cell shape, drive cell movement, and deform tissues. Our analysis of several cell shape changes leads us to propose four regulatory modules associated with ratchet-like deformations that are tuned to generate diverse cell behaviors, coordinating cell shape change across a tissue.     

Pulsation and stabilization: Contractile forces that underlie morphogenesis

Embryonic development involves global changes in tissue shape and architecture that are driven by cell shape changes and rearrangements within cohesive cell sheets. Morphogenetic changes at the cell and tissue level require that cells generate forces and that these forces are transmitted between the cells of a coherent tissue. Contractile forces generated by the actin-myosin cytoskeleton are critical for morphogenesis, but the cellular and molecular mechanisms of contraction have been elusive for many cell shape changes and movements. Recent studies that have combined live imaging with computational and biophysical approaches have provided new insights into how contractile forces are generated and coordinated between cells and tissues. In this review, we discuss our current understanding of the mechanical forces that shape cells, tissues, and embryos, emphasizing the different modes of actomyosin contraction that generate various temporal and spatial patterns of force generation.