Morphogenesis of the Fission Yeast Cell through Cell Wall Expansion.

The shape of walled cells such as fungi, bacteria, and plants are determined by the cell wall. Models for cell morphogenesis postulate that the effects of turgor pressure and mechanical properties of the cell wall can explain the shapes of these diverse cell types. However, in general, these models await validation through quantitative experiments. Fission yeast Schizosaccharomyces pombe are rod-shaped cells that grow by tip extension and then divide medially through formation of a cell wall septum. Upon cell separation after cytokinesis, the new cell ends adopt a rounded morphology. Here, we show that this shape is generated by a very simple mechanical-based mechanism in which turgor pressure inflates the elastic cell wall in the absence of cell growth. This process is independent of actin and new cell wall synthesis. To model this morphological change, we first estimate the mechanical properties of the cell wall using several approaches. The lateral cell wall behaves as an isotropic elastic material with a Young's modulus of 50 ± 10 MPa inflated by a turgor pressure estimated to be 1.5 ± 0.2 MPa. Based upon these parameters, we develop a quantitative mechanical-based model for new end formation that reveals that the cell wall at the new end expands into its characteristic rounded shape in part because it is softer than the mature lateral wall. These studies provide a simple example of how turgor pressure expands the elastic cell wall to generate a particular cell shape.

The local forces acting on the mechanotransduction channel in hair cell stereocilia.

In hair cells, mechanotransduction channels are located in the membrane of stereocilia tips, where the base of the tip link is attached. The tip-link force determines the system of other forces in the immediate channel environment, which change the channel open probability. This system of forces includes components that are out of plane and in plane relative to the membrane; the magnitude and direction of these components depend on the channel environment and arrangement. Using a computational model, we obtained the major forces involved as functions of the force applied via the tip link at the center of the membrane. We simulated factors related to channels and the membrane, including finite-sized channels located centrally or acentrally, stiffness of the hypothesized channel-cytoskeleton tether, and bending modulus of the membrane. Membrane forces are perpendicular to the directions of the principal curvatures of the deformed membrane. Our approach allows for a fine vectorial picture of the local forces gating the channel; membrane forces change with the membrane curvature and are themselves sufficient to affect the open probability of the channel.

Manipulating cell shape by placing cells into micro-fabricated chambers.

Cell shape is an important cellular parameter that influences the spatial organization and function of cells. However, it has often been challenging to study the effects of cell shape because of difficulties in experimentally controlling cell shape in a defined way. We describe here a method of physically manipulating sea urchin cells into specified shapes by inserting them into micro-fabricated chambers of different shapes. This method allows for generation of large systematic and quantitative data sets and may be adaptable for different cell types and contexts.

Localization of cytokinesis factors to the future cell division site by microtubule-dependent transport.

The mechanism by which spindle microtubules (MTs) determine the site of cell division in animal cells is still highly controversial. Putative cytokinesis "signals" have been proposed to be positioned by spindle MTs at equatorial cortical regions to increase cortical contractility and/or at polar regions to decrease contractility [Rappaport, 1986; von Dassow, 2009]. Given the relative paucity of MTs at the future division site, it has not been clear how MTs localize cytokinesis factors there. Here, we test cytokinesis models using computational and experimental approaches. We present a simple lattice-based model in which signal-kinesin complexes move by transient plus-end directed movements on MTs interspersed with occasions of uniform diffusion in the cytoplasm. In simulations, complexes distribute themselves initially at the spindle midzone and then move on astral MTs to accumulate with time at the equatorial cortex. Simulations accurately predict cleavage patterns of cells with different geometries and MT arrangements and elucidate several experimental observations that have defied easy explanation by previous models. We verify this model with experiments on indented sea urchin zygotes showing that cells often divide perpendicular to the spindle at sites distinct from the indentations. These studies support an equatorial stimulation model and provide a simple mechanism explaining how cytokinesis factors localize to the future division site.

Stereocilia membrane deformation: implications for the gating spring and mechanotransduction channel.

In hair cells, although mechanotransduction channels have been localized to tips of shorter stereocilia of the mechanically sensitive hair bundle, little is known about how force is transmitted to the channel. Here, we use a biophysical model of the membrane-channel complex to analyze the nature of the gating spring compliance and channel arrangement. We use a triangulated surface model and Monte Carlo simulation to compute the deformation of the membrane under the action of tip link force. We show that depending on the gating spring stiffness, the compliant component of the gating spring arises from either the membrane alone or a combination of the membrane and a tether that connects the channel to the actin cytoskeleton. If a bundle is characterized by relatively soft gating springs, such as those of the bullfrog sacculus, the need for membrane reinforcement by channel tethering then depends on membrane parameters. With stiffer gating springs, such as those from rat outer hair cells, the channel must be tethered for all biophysically realistic parameters of the membrane. We compute the membrane forces (resultants), which depend on membrane tension, bending modulus, and curvature, and show that they can determine the fate of the channel.

Reflectivity and topography of cells grown on glass-coverslips measured with phase-shifted laser feedback interference microscopy.

In spite of the advantages associated with the molecular specificity of fluorescence imaging, there is still a significant need to augment these approaches with label-free imaging. Therefore, we have implemented a form of interference microscopy based upon phase-shifted, laser-feedback interferometry and developed an algorithm that can be used to separate the contribution of the elastically scattered light by sub-cellular structures from the reflection at the coverslip-buffer interface. The method offers an opportunity to probe protein aggregation, index of refraction variations and structure. We measure the topography and reflection from calibration spheres and from stress fibers and adhesions in both fixed and motile cells. Unlike the data acquired with reflection interference contrast microscopy, where the reflection from adhesions can appear dark, our approach demonstrates that these regions have high reflectivity. The data acquired from fixed and live cells show the presence of a dense actin layer located ≈ 100 nm above the coverslip interface. Finally, the measured dynamics of filopodia and the lamella in a live cell supports retrograde flow as the dominate mechanism responsible for filopodia retraction.

Membrane deformation at integrin adhesions.

In order to measure the nucleation of nouveau adhesions on the ventral surface of a cell, we have combined phase shifting laser feedback interferometry with a high numerical aperture inverted fluorescence microscope. We use fluorescence to image molecules at the adhesion site and stage scanning interference microscopy in order to measure the distance between the ventral surface of a cell and the substratum with several nanometer precision. Our analytic and Monte Carlo simulations of integrin mediated adhesions predict several features of these nouveau adhesions. An analysis of the energetics of membrane bending and the effects of a composite system of freely diffusing repellers and receptors and a fixed network of ligands on the extracellular matrix predicts that a small bundle of actin filaments should be able to push the membrane down to the extracellular matrix and nucleate a nouveau adhesion with critical radius below the diffraction limit. We have obtained a map of the reflectivity of the ventral surface of fixed metastatic mammary adenocarcinoma cells and we have shown that the data are correlated with markers for a focal adhesion adaptor protein. We are modeling the interference of the incident electric field with the field reflected from the ventral surface so as to obtain the surface topography at focal adhesions from the optical phase data.

Nucleation and growth of integrin adhesions.

We present a model that provides a mechanistic understanding of the processes that govern the formation of the earliest integrin adhesions ex novo from an approximately planar plasma membrane. Using an analytic analysis of the free energy of a dynamically deformable membrane containing freely diffusing receptors molecules and long repeller molecules that inhibit integrins from binding with ligands on the extracellular matrix, we predict that a coalescence of polymerizing actin filaments can deform the membrane toward the extracellular matrix and facilitate integrin binding. Monte Carlo simulations of this system show that thermally induced membrane fluctuations can either zip-up and increase the radius of a nucleated adhesion or unzip and shrink an adhesion, but the fluctuations cannot bend the ventral membrane to nucleate an adhesion. To distinguish this integrin adhesion from more mature adhesions, we refer to this early adhesion as a nouveau adhesion.

Chapter 23: Stochastic modeling methods in cell biology.

Stochastic methods have been a staple for understanding complex systems in chemistry and physics. In the biological context, they are useful for understanding phenomena ranging from molecular-level fluctuations to cellular movement. We review the basic formalism behind stochastic methods and outline how they can be implemented for quantifying gene expression, movement of molecular motors, and the dynamics of cytoplasmic components. We show that stochastic methods are quantitative checks for proposed molecular mechanisms and can pose new questions for experiments. Structural information of cellular components can be incorporated into stochastic models to reveal new biological insights.

Shape transitions in lipid membranes and protein mediated vesicle fusion and fission.

In the cell, the plasma membrane is often densely decorated by transmembrane proteins. The morphology and dynamics of the membrane are strongly influenced by the presence of proteins. In this paper, we use a coarse-grained model to explore the composite membrane-protein system and develop a simulation methodology based on thermodynamic integration to examine free energy changes during membrane shape transitions. The authors show that a critical concentration of conical membrane proteins or proteins with nonzero spontaneous curvature can drive the formation of small vesicles. The driving force of vesicle budding stems from the preference of proteins to gather in regions of high curvature. A sufficiently high concentration of proteins therefore can influence the topology of the membrane. The biological significance of our results is discussed.

Mechanics and dynamics of actin-driven thin membrane protrusions.

Motile cells explore their surrounding milieu by extending thin dynamic protrusions, or filopodia. The growth of filopodia is driven by actin filament bundles that polymerize underneath the cell membrane. We compute the mechanical and dynamical features of the protrusion growth process by explicitly incorporating the flexible plasma membrane. We find that a critical number of filaments are needed to generate net filopodial growth. Without external influences, the filopodium can extend indefinitely up to the buckling length of the F-actin bundle. Dynamical calculations show that the protrusion speed is enhanced by the thermal fluctuations of the membrane; a filament bundle encased in a flexible membrane grows much faster. The protrusion speed depends directly on the number and spatial arrangement of the filaments in the bundle and whether the filaments are tethered to the membrane. Filopodia also attract each other through distortions of the membrane. Spatially close filopodia will merge to form a larger one. Force-velocity relationships mimicking micromanipulation experiments testing our predictions are computed.

Morphology of the lamellipodium and organization of actin filaments at the leading edge of crawling cells.

Lamellipodium extension, incorporating actin filament dynamics and the cell membrane, is simulated in three dimensions. The actin filament network topology and the role of actin-associated proteins such as Arp2/3 are examined. We find that the orientational pattern of the filaments is in accord with the experimental data only if the spatial orientation of the Arp2/3 complex is restricted during each branching event. We hypothesize that branching occurs when Arp2/3 is bound to Wiskott-Aldrich syndrome protein (WASP), which is in turn bound to Cdc42 signaling complex; Arp2/3 binding geometry is restricted by the membrane-bound complex. Using mechanical and energetic arguments, we show that any membrane protein that is conical or trapezoidal in shape preferentially resides at the curved regions of the plasma membrane. We hypothesize that the transmembrane receptors involved in the recruitment of Cdc42/WASP complex has this property and concentrate at the leading edge. These features, combined with the mechanical properties of the cell membrane, explain why lamellipodium is a flat organelle.

Equilibrium free energy estimates based on nonequilibrium work relations and extended dynamics.

Jarzynski's relation and the fluctuation theorem have established important connections between nonequilibrium statistical mechanics and equilibrium thermodynamics. In particular, an exact relationship between the equilibrium free energy and the nonequilibrium work is useful for computer simulations. In this paper, we exploit the fact that the free energy is a state function, independent of the pathway taken to change the equilibrium ensemble. We show that a generalized expression is advantageous for computer simulations of free energy differences. Several methods based on this idea are proposed. The accuracy and efficiency of the proposed methods are evaluated with a model problem.

An application of error reduction and harmonic inversion schemes to the semiclassical calculation of molecular vibrational energy levels.

A singular value decomposition based harmonic inversion signal processing scheme is applied to the semiclassical initial value representation (IVR) calculation of molecular vibrational states. Relative to usual IVR procedure of Fourier analysis of a signal made from the Monte Carlo evaluation of the phase space integral in which many trajectories are needed, the new procedure obtains acceptable results with many fewer trajectories. Calculations are carried out for vibrational energy levels of H2O to illustrate the overall procedure.

Classical, semiclassical, and quantum investigations of the four-sphere scattering system.

A genuinely three-dimensional system, viz. the hyperbolic four-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional three-disk system. While in systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods, this situation can be reversed with increasing dimension of the problem. For the four-sphere system with large separations between the spheres, we demonstrate the superiority of semiclassical versus quantum calculations, i.e., semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques. The four-sphere system with touching spheres is a challenging problem for both quantum and semiclassical techniques. Here, semiclassical resonances are obtained via harmonic inversion of a cross-correlated periodic orbit signal.