Dynamics and morphology of microvilli driven by actin polymerization

Destruction of the brush border by Salmonella enterica sv. Typhimurium subverts resorption by polarized epithelial cells

Salmonella enterica serovar Typhimurium is an invasive, facultative intracellular gastrointestinal pathogen that destroys the brush border of polarized epithelial cells (PEC). The brush border is critical for the functions of PEC because it resorbs nutrients from the intestinal lumen and builds a physical barrier to infecting pathogens. The manipuation of PEC during infection by Salmonella was investigated by live-cell imaging and ultrastructural analysed of the brush border. We demonstrate that the destruction of the brush border by Salmonella significantly reduces the resorption surface of PEC along with the abrogation of endocytosis at the apical side of PEC. Both these changes in the physiology of PEC were associated with the translocation of type III secretion system effector protein SopE. Additionally, the F-actin polymerization rate at the apical side of PEC was highly altered by SopE, indicating that reduced endocytosis observed in infected PEC is related to the manipulation of F-actin polymerization mediated by SopE and, to a lesser extent, by effectors SopE2 or SipA. We further observed that in the absence of SopE, Salmonella effaced microvilli and induced reticular F-actin by bacterial accumulation during prolonged infection periods. In contrast to strains translocating SopE, strains lacking SopE did not alter resorption by PEC. Finally, we observed that after engulfment of Salmonella, ezrin was lost from the apical side of PEC and found later in early endosomes containing Salmonella. Our observations suggest that the destruction of the brush border by Salmonella may contribute to the pathogenesis of diarrhea.

Cortical contraction drives the 3D patterning of epithelial cell surfaces

Cellular protrusions create complex cell surface topographies, but biomechanical mechanisms regulating their formation and arrangement are largely unknown. To study how protrusions form, we focused on the morphogenesis of microridges, elongated actin-based structures that are arranged in maze-like patterns on the apical surfaces of zebrafish skin cells. Microridges form by accreting simple finger-like precursors. Live imaging demonstrated that microridge morphogenesis is linked to apical constriction. A nonmuscle myosin II (NMII) reporter revealed pulsatile contractions of the actomyosin cortex, and inhibiting NMII blocked apical constriction and microridge formation. A biomechanical model suggested that contraction reduces surface tension to permit the fusion of precursors into microridges. Indeed, reducing surface tension with hyperosmolar media promoted microridge formation. In anisotropically stretched cells, microridges formed by precursor fusion along the stretch axis, which computational modeling explained as a consequence of stretch-induced cortical flow. Collectively, our results demonstrate how contraction within the 2D plane of the cortex can pattern 3D cell surfaces.

Hyperlipidemia Affects Tight Junctions and Pump Function in the Corneal Endothelium

Hyperlipidemia impacts on various diseases, such as atherosclerosis, hypertension, and diabetes mellitus. However, its influence, if any, on ocular tissues is largely unknown. Herein, we developed hyperlipidemic murine models by feeding 4-week-old male wild-type mice with a high-fat diet and apolipoprotein E knockout (ApoE^-/-) mice with a high-fat diet or standard diet to investigate the corneal endothelial change under hyperlipidemic conditions. Oil Red O staining showed an accumulation of lipid droplets in corneal endothelial cells (CECs) of hyperlipidemic mice. Other manifestations included a reduced cell density and distorted cell morphology, a disruption of the endothelial cell tight junctions and adhesion junctions, a reduced number of surface microvilli, down-regulation of Na⁺-K⁺-ATPase expression and function, activation of oxidative stress, changes in mitochondrial ultrastructure, and increased apoptosis. CEC recovery after injury, moreover, was diminished in hyperlipidemic mice; and high palmitate levels were found in the aqueous humor. In vitro hyperlipemia model, moreover, was found to be associated with dose-dependent CEC cytotoxicity, altered cell morphology, reduced pump function, and an induction of oxidative stress, leading to functional and pathologic changes in the corneal endothelium.

Physical model for the geometry of actin-based cellular protrusions

Actin-based cellular protrusions are a ubiquitous feature of cell morphology, e.g., filopodia and microvilli, serving a huge variety of functions. Despite this, there is still no comprehensive model for the mechanisms that determine the geometry of these protrusions. We present here a detailed computational model that addresses a combination of multiple biochemical and physical processes involved in the dynamic regulation of the shape of these protrusions. We specifically explore the role of actin polymerization in determining both the height and width of the protrusions. Furthermore, we show that our generalized model can explain multiple morphological features of these systems, and account for the effects of specific proteins and mutations.

A Biophysical Model for the Staircase Geometry of Stereocilia

Cochlear hair cell bundles, made up of 10s to 100s of individual stereocilia, are essential for hearing, and even relatively minor structural changes, due to mutations or injuries, can result in total deafness. Consistent with its specialized role, the staircase geometry (SCG) of hair cell bundles presents one of the most striking, intricate, and precise organizations of actin-based cellular shapes. Composed of rows of actin-filled stereocilia with increasing lengths, the hair cell’s staircase-shaped bundle is formed from a progenitor field of smaller, thinner, and uniformly spaced microvilli with relatively invariant lengths. While recent genetic studies have provided a significant increase in information on the multitude of stereocilia protein components, there is currently no model that integrates the basic physical forces and biochemical processes necessary to explain the emergence of the SCG. We propose such a model derived from the biophysical and biochemical characteristics of actin-based protrusions. We demonstrate that polarization of the cell’s apical surface, due to the lateral polarization of the entire epithelial layer, plays a key role in promoting SCG formation. Furthermore, our model explains many distinct features of the manifestations of SCG in different species and in the presence of various deafness-associated mutations.

Stochastic models of cell protrusion arising from spatiotemporal signaling and adhesion dynamics

During cell migration, local protrusion events are regulated by biochemical and physical processes that are in turn coordinated with the dynamic properties of cell-substratum adhesion structures. In this chapter, we present a modeling approach for integrating the apparent stochasticity and spatial dependence of signal transduction pathways that promote protrusion in tandem with adhesion dynamics. We describe our modeling framework, as well as its abstraction, parameterization, and validation against experimental data. Analytical techniques for identifying and evaluating the effects of model bistability on simulation simulation results are shown, and implications of this analysis for understanding cell protrusion behavior are offered.

Theoretical model for cellular shapes driven by protrusive and adhesive forces

The forces that arise from the actin cytoskeleton play a crucial role in determining the cell shape. These include protrusive forces due to actin polymerization and adhesion to the external matrix. We present here a theoretical model for the cellular shapes resulting from the feedback between the membrane shape and the forces acting on the membrane, mediated by curvature-sensitive membrane complexes of a convex shape. In previous theoretical studies we have investigated the regimes of linear instability where spontaneous formation of cellular protrusions is initiated. Here we calculate the evolution of a two dimensional cell contour beyond the linear regime and determine the final steady-state shapes arising within the model. We find that shapes driven by adhesion or by actin polymerization (lamellipodia) have very different morphologies, as observed in cells. Furthermore, we find that as the strength of the protrusive forces diminish, the system approaches a stabilization of a periodic pattern of protrusions. This result can provide an explanation for a number of puzzling experimental observations regarding cellular shape dependence on the properties of the extra-cellular matrix.

Cells have highly varied and dynamic shapes, which are determined by internal forces generated by the cytoskeleton. These forces include protrusive forces due to the formation of new internal fibers and forces produced due to attachment of the cell to an external substrate. A long standing challenge is to explain how the myriad components of the cytoskeleton self-organize to form the observed shapes of cells. We present here a theoretical study of the shapes of cells that are driven only by protrusive forces of two types; one is the force due to polymerization of actin filaments which acts as an internal pressure on the membrane, and the second is the force due to adhesion between the membrane and external substrate. The key property is that both forces are localized on the cell membrane by protein complexes that have convex spontaneous curvature. This leads to a positive feedback that destabilizes the uniform cell shape and induces the spontaneous formation of patterns. We compare the resulting patterns to observed cellular shapes and find good agreement, which allows us to explain some of the puzzling dependencies of cell shapes on the properties of the surrounding matrix.

Robust patterns in the stochastic organization of filopodia

Background

Filopodia are actin-based cellular projections that have a critical role in initiating and sustaining directional migration in vertebrate cells. Filopodia are highly dynamic structures that show a rich diversity in appearance and behavior. While there are several mathematical models of filopodia initiation and growth, testing the capacity of these theoretical models in predicting empirical behavior has been hampered by a surprising shortage of quantitative data related to filopodia. Neither is it clear how quantitatively robust the cellular filopodial network is and how perturbations alter it.

Results

We have measured the length and interfilopodial separation distances of several thousand filopodia in the rodent cell line Rat2 and measured these parameters in response to genetic, chemical and physical perturbation. Our work shows that length and separation distance have a lognormal pattern distribution over their entire detection range (0.4 μm to 50 μm).

Conclusions

We find that the lognormal distribution of length and separation is robust and highly resistant to perturbation. We also find that length and separation are independent variables. Most importantly, our empirical data is not entirely in agreement with predictions made based on existing theoretical models and that filopodial size and separation are an order of magnitude larger than what existing models suggest.

Effect of capping protein on a growing filopodium

Filopodia, or the growth of bundles of biological fibers outwards from a biological cell surface while enclosed in a membrane tube, are implicated in many processes vital to life. This study models the effect of capping protein on such filopodia, paying close attention to the polymerization dynamics of biological fiber bundles within long membrane tubes. Due to the effects of capping protein, the number of fibers in the filopodium bundle decreases down the length of the enclosing membrane tube. This decrease in the number of fibers down the length of a growing filopodium is found to have profound implications for the dynamics and stability of filopodia in general. This study theoretically finds that the presence of even a relatively modest amount of capping protein can have a large effect on the growth of typical filopodia, such as can be found in fibroblasts, keratocytes, and neuronal growth cones. As an illustration of this modeling work, this study investigates the striking example of the acrosomal reaction in the sea cucumber Thyone, whose filopodia can grow remarkably quickly to approximately 90 mum in approximately 10 s, and where the number of fibers is known to decrease down the length of the filopodium, presumably due to progressive fiber end-capping occurring as the filopodium grows. Realistic future dynamical theories for filopodium growth are likely to rely on an accurate treatment of the kinds of capping protein effects analyzed in this work.

Design of active transport must be highly intricate: a possible role of myosin and Ena/VASP for G-actin transport in filopodia

Recent modeling of filopodia--the actin-based cell organelles employed for sensing and motility--reveals that one of the key limiting factors of filopodial length is diffusional transport of G-actin monomers to the polymerizing barbed ends. We have explored the possibility of active transport of G-actin by myosin motors, which would be an expected biological response to overcome the limitation of a diffusion-based process. We found that in a straightforward implementation of active transport the increase in length was unimpressive, < or = 30%, due to sequestering of G-actin by freely diffusing motors. However, artificially removing motor sequestration reactions led to approximately threefold increases in filopodial length, with the transport being mainly limited by the motors failing to detach from the filaments near the tip, clogging the cooperative conveyer belt dynamics. Making motors sterically transparent led to a qualitative change of the dynamics to a different regime of steady growth without a stationary length. Having identified sequestration and clogging as ubiquitous constraints to motor-driven transport, we devised and tested a speculative means to sidestep these limitations in filopodia by employing cross-linking and putative scaffolding roles of Ena/VASP proteins. We conclude that a naïve design of molecular-motor-based active transport would almost always be inefficient--an intricately organized kinetic scheme, with finely tuned rate constants, is required to achieve high-flux transport.

Physical model for the width distribution of axons

The distribution of widths of axons was recently investigated, and was found to have a distinct peak at an optimized value. The optimized axon width at the peak may arise from the conflicting demands of minimizing energy consumption and assuring signal transmission reliability. The distribution around this optimized value is found to have a distinct non-Gaussian shape, with an exponential "tail". We propose here a mechanical model whereby this distribution arises from the interplay between the elastic energy of the membrane surrounding the axon core, the osmotic pressure induced by the neurofilaments inside the axon bulk, and active processes that remodel the microtubules and neurofilaments inside the axon. The axon's radius of curvature can be determined by the cell's control of the osmotic pressure difference across the membrane, the membrane tension or by changing the composition of the different components of the membrane. We find that the osmotic pressure, determined by the neurofilaments, seems to be the dominant control parameter.

Active gels as a description of the actin-myosin cytoskeleton

This short review presents a qualitative introduction to the hydrodynamic theory of active polar gels and its applications to the mechanics of the cytoskeleton. Active polar gels are viscoelastic materials formed by polar filaments maintained in a nonequilibrium state by constant consumption of energy. In the cytoskeleton of eukaryotic cells, actin filaments are treadmilling and form a viscoelastic gel interacting with myosin molecular motors driven by the hydrolysis of adenosine triphosphate; one can thus consider the actomyosin cytoskeleton as an active polar gel. The hydrodynamic description is generic as it only relies on symmetry arguments. We first use the hydrodynamic approach to discuss the spontaneous generation of flow in an active polar film. Then we give two examples of applications to lamellipodium motility and to instabilities of cortical actin.

The stochastic dynamics of filopodial growth

A filopodium is a cytoplasmic projection, exquisitely built and regulated, which extends from the leading edge of the migrating cell, exploring the cell's neighborhood. Commonly, filopodia grow and retract after their initiation, exhibiting rich dynamical behaviors. We model the growth of a filopodium based on a stochastic description which incorporates mechanical, physical, and biochemical components. Our model provides a full stochastic treatment of the actin monomer diffusion and polymerization of each individual actin filament under stress of the fluctuating membrane. We investigated the length distribution of individual filaments in a growing filopodium and studied how it depends on various physical parameters. The distribution of filament lengths turned out to be narrow, which we explained by the negative feedback created by the membrane load and monomeric G-actin gradient. We also discovered that filopodial growth is strongly diminished upon increasing retrograde flow, suggesting that regulating the retrograde flow rate would be a highly efficient way to control filopodial extension dynamics. The filopodial length increases as the membrane fluctuations decrease, which we attributed to the unequal loading of the membrane force among individual filaments, which, in turn, results in larger average polymerization rates. We also observed significant diffusional noise of G-actin monomers, which leads to smaller G-actin flux along the filopodial tube compared with the prediction using the diffusion equation. Overall, partial cancellation of these two fluctuation effects allows a simple mean field model to rationalize most of our simulation results. However, fast fluctuations significantly renormalize the mean field model parameters. The biological significance of our filopodial model and avenues for future development are also discussed.

Phase transitions of the coupled membrane-cytoskeleton modify cellular shape

Formation of protrusions and protein segregation on the membrane is of a great importance for the functioning of the living cell. This is most evident in recent experiments that show the effects of the mechanical properties of the surrounding substrate on cell morphology. We propose a mechanism for the formation of membrane protrusions and protein phase separation, which may lay behind this effect. In our model, the fluid cell membrane has a mobile but constant population of proteins with a convex spontaneous curvature. Our basic assumption is that these membrane proteins represent small adhesion complexes, and also include proteins that activate actin polymerization. Such a continuum model couples the membrane and protein dynamics, including cell-substrate adhesion and protrusive actin force. Linear stability analysis shows that sufficiently strong adhesion energy and actin polymerization force can bring about phase separation of the membrane protein and the appearance of protrusions. Specifically, this occurs when the spontaneous curvature and aggregation potential alone (passive system) do not cause phase separation. Finite-size patterns may appear in the regime where the spontaneous curvature energy is a strong factor. Different instability characteristics are calculated for the various regimes, and are compared to various types of observed protrusions and phase separations, both in living cells and in artificial model systems. A number of testable predictions are proposed.

Flexibility of single microvilli on live neutrophils and lymphocytes

We measured the flexural stiffness of single microvilli on live human neutrophils and lymphocytes using 40-nm fluorescent beads. The beads were bound to the tips of the microvilli by anti-L-selectin antibodies. Digital bead images were acquired with an exposure time of 3 s at high magnification. Using a Gaussian point spread function, we obtained an analytical expression that relates the image profile to the flexural stiffness. We found that the flexural stiffnesses were 7 and 4 pN/microm for single microvilli on human neutrophils and lymphocytes, respectively. We also verified with live cells that 75% of neutrophil L-selectin and 72% of lymphocyte L-selectin were on the microvillus tips. Our results indicate that the leukocyte microvilli in contact with the endothelium or other surfaces will bend easily under physiological shear stresses.

Dynamical control of the shape and size of stereocilia and microvilli

We discuss theoretically the shape of actin-based protrusions such as stereocilia or microvilli that have important functions in many biological systems. These linear protrusions are dynamical structures continuously renewed by treadmilling: actin polymerizes at the tip of the cilium and depolymerizes in its bulk. They also often have a well-controlled length such as in the hair bundles of the inner ear cells where they appear in a graded staircase structure. Recent experimental results by another group of researchers show that the treadmilling velocity of the hair cell stereocilia is proportional to their length. We use generic arguments to describe the physics of stereocilia taking into account the effect of many individual proteins at a coarse-grained level by a few phenomenological parameters. At the tip of the cilium, we find that actin polymerization induces an effective pressure. Below the tip, the shape of the cilium is determined by depolymerization: Agreement with the observed shape requires that depolymerization occurs at least in two steps. Under these conditions, we calculate the cilium shape and provide physical grounds for the proportionality between treadmilling velocity and cilium length. We also calculate the penetration of the stereocilium in the actin cortical layer.