The role of apical contractility in determining cell morphology in multilayered epithelial sheets and tubes.

A multilayered epithelium is made up of individual cells that are stratified in an orderly fashion, layer by layer. In such tissues, individual cells can adopt a wide range of shapes ranging from columnar to squamous. From histological images, we observe that, in flat epithelia such as the skin, the cells in the top layer are squamous while those in the middle and bottom layers are columnar, whereas in tubular epithelia, the cells in all layers are columnar. We develop a computational model to understand how individual cell shape is governed by the mechanical forces within multilayered flat and curved epithelia. We derive the energy function for an epithelial sheet of cells considering intercellular adhesive and intracellular contractile forces. We determine computationally the cell morphologies that minimize the energy function for a wide range of cellular parameters. Depending on the dominant adhesive and contractile forces, we find four dominant cell morphologies for the multilayered-layered flat sheet and three dominant cell morphologies for the two-layered curved sheet. We study the transitions between the dominant cell morphologies for the two-layered flat sheet and find both continuous and discontinuous transitions and also the presence of multistable states. Matching our computational results with histological images, we conclude that apical contractile forces from the actomyosin belt in the epithelial cells is the dominant force determining cell shape in multilayered epithelia. Our computational model can guide tissue engineers in designing artificial multilayered epithelia, in terms of figuring out the cellular parameters needed to achieve realistic epithelial morphologies.

Gigantic amoebic liver abscess in pregnancy: A case report.

Amoebic liver abscess in pregnancy is genuinely rare in its presentation. Yet, the main issue surrounding this agenda is the diagnostic challenge that it poses especially when symptomatology is vague and clues are subtle which altogether evades the diagnosis proper. We would like to dwell mainly on these issues in hopes of enlightening clinicians towards these diagnostic dilemmas. We report an extremely rare case of amoebic liver abscess occurring in the third trimester of pregnancy in a 29-year-old lady living in an interior village in Sabah. It was a combination of biochemical, radiographic and molecular investigations that ultimately led to the final diagnosis. In lieu of the high risk of mortality amongst pregnant mothers afflicted with amoebic liver abscess, the inherent need for early diagnosis requiring a high index of suspicion is vital. Elevated alkaline phosphatase alongside neutrophilia appears to be the most consistent liver parameters in guiding clinicians towards the presence of liver abscess.

Gigantic amoebic liver abscess in pregnancy: A case report

Amoebic liver abscess in pregnancy is genuinely rare in its presentation. Yet, the main issue surrounding this agenda is the diagnostic challenge that it poses especially when symptomatology is vague and clues are subtle which altogether evades the diagnosis proper. We would like to dwell mainly on these issues in hopes of enlightening clinicians towards these diagnostic dilemmas. We report an extremely rare case of amoebic liver abscess occurring in the third trimester of pregnancy in a 29-year-old lady living in an interior village in Sabah. It was a combination of biochemical, radiographic and molecular investigations that ultimately led to the final diagnosis. In lieu of the high risk of mortality amongst pregnant mothers afflicted with amoebic liver abscess, the inherent need for early diagnosis requiring a high index of suspicion is vital. Elevated alkaline phosphatase alongside neutrophilia appears to be the most consistent liver parameters in guiding clinicians towards the presence of liver abscess.

A forgotten clinical sign making a comeback.

We report a case of Staphylococcus aureus infective endocarditis in a patient presenting with fever and rare cutaneous manifestations of Osler Nodes and Janeway Lesions. There had not been any distinct risk factors. His echocardiography subsequently revealed vegetation at the anterior mitral valve leaflet. As Staphylococcus aureus infective endocarditis is of utmost significance in morbidity and mortality, a sharp clinical acumen and follow up investigations is required alongside a prolonged course of antibiotics. Our patient was then started on intravenous cloxacillin for 28 days and gentamicin for 5 days to which he made good progress and recovery.

A three-dimensional random network model of the cytoskeleton and its role in mechanotransduction and nucleus deformation.

We have developed a three-dimensional random network model of the intracellular actin cytoskeleton and have used it to study the role of the cytoskeleton in mechanotransduction and nucleus deformation. We use the model to predict the deformation of the nucleus when mechanical stresses applied on the plasma membrane are propagated through the random cytoskeletal network to the nucleus membrane. We found that our results agree with previous experiments utilizing micropipette pulling. Therefore, we propose that stress propagation through the random cytoskeletal network can be a mechanism to effect nucleus deformation, without invoking any biochemical signaling activity. Using our model, we also predict how nucleus strain and its relative displacement within the cytosol vary with varying concentrations of actin filaments and actin-binding proteins. We find that nucleus strain varies in a sigmoidal manner with actin filament concentration, while there exists an optimal concentration of actin-binding proteins that maximize nucleus displacement. We provide a theoretical analysis for these nonlinearities in terms of the connectivity of the random cytoskeletal network. Finally, we discuss laser ablation experiments that can be performed to validate these results in order to advance our understanding of the role of the cytoskeleton in mechanotransduction.

Hydrodynamic interaction between two nonspherical capsules in shear flow.

The hydrodynamic interaction between two nonspherical capsules suspended in a simple shear flow is studied numerically using a front-tracking method. The capsules are enclosed by thin shells which develop in-plane tensions and bending moments due to a preferred three-dimensional unstressed configuration. Computations are performed for capsules with spherical, oblate spheroidal, and biconcave unstressed shapes for a wide range of dimensionless shear rates and initial separation distances between the two capsules. The bending modulus and viscosity ratio between the internal and surrounding fluids are chosen to be those of healthy red blood cells. Depending on the initial separation distance, we find that two spherical capsules in shear flow either cross over each other or undergo spiraling motion. In addition, the long-time interaction behavior of capsules also depends strongly on the unstressed shapes. More oblate or biconcave capsules exhibit two additional type of interactions, namely swapping and continuous rotation, which occur only when each capsule undergoes tumbling motion.

Investigating circular dorsal ruffles through varying substrate stiffness and mathematical modeling.

Circular dorsal ruffles (CDRs) are transient actin-rich ringlike structures that form on the dorsal surface of growth-factor stimulated cells. However, the dynamics and mechanism of formation of CDRs are still unknown. It has been observed that CDR formation leads to stress fibers disappearing near the CDRs. Because stress fiber formation can be modified by substrate stiffness, we examined the effect of substrate stiffness on CDR formation by seeding NIH 3T3 fibroblasts on glass and polydimethylsiloxane substrates of varying stiffnesses from 20 kPa to 1800 kPa. We found that increasing substrate stiffness increased the lifetime of the CDRs. We developed a mathematical model of the signaling pathways involved in CDR formation to provide insight into this lifetime and size dependence that is linked to substrate stiffness via Rac-Rho antagonism. From the model, increasing stiffness raised mDia1-nucleated stress fiber formation due to Rho activation. The increased stress fibers present increased replenishment of the G-actin pool, therefore prolonging Arp2/3-nucleated CDR formation due to Rac activation. Negative feedback by WAVE-related RacGAP on Rac explained how CDR actin propagates as an excitable wave, much like wave propagation in other excitable medium, e.g., nerve signal transmission.

Separation of deformable particles in deterministic lateral displacement devices.

Using numerical simulations, we study the separation of deformable bodies, such as capsules, vesicles, and cells, in deterministic lateral displacement devices, also known as bump arrays. These arrays comprise regular rows of obstacles such as micropillars whose arrangements are shifted between adjacent rows by a fixed amount. We show that, in addition to the zigzag and laterally displaced trajectories that have been observed experimentally, there exists a third type of trajectory which we call dispersive, characterized by seemingly random bumpings off the micropillars. These dispersive trajectories are observed only for large and rigid particles whose diameters are approximately more than half the gap size between micropillars and whose stiffness exceeds approximately 500 MPa. We then map out the regions in phase space, spanned by the row shift, row separation, particle diameter, and particle deformability, in which the different types of trajectories are expected. We also show that, in this phase space, it is possible to transition from zigzag to dispersive trajectories, bypassing lateral displacement. Experimentally, this is undesirable because it limits the ability of the device to sort particles according to size. Finally, we discuss how our numerical simulations may be of use in device prototyping and optimization.

Mechanochemical model of cell migration on substrates of varying stiffness.

Cells propel themselves along a substrate by organizing structures at the leading edge called lamellipodia that contain the actin network, myosin, integrin, and other proteins. In this article, we describe a quantitative model that couples the response of stretch-sensitive proteins in the lamellipodia to the dynamics of the actin cytoskeleton, therefore allowing the cell to respond to different substrate stiffnesses. Using this model, we predict the various phases of dynamics possible, including continuous protrusion, unstable retractions leading to ruffling, and periodic protrusion-retraction cycles. We explain the necessary conditions for each type of migratory behavior to occur. In particular, we show that, for periodic protrusion-retraction cycles to occur, the stiffness of the substrate must be high, the myosin-dependent maturation rate of nascent to focal adhesions must be high, and the myosin-independent integrin activation rate must be low. In addition, we also predict the dynamics expected at a given substrate stiffness, leading to a quantitative explanation of experimental data that showed that periodic protrusion-retraction cycles disappear when cells are placed on soft substrates. We also suggest experiments with downregulating α actinin and/or talin and upregulating p130Cas and make predictions on what types of migratory dynamics will be observed.

Cellular deformation and intracellular stress propagation during optical stretching.

Experiments have shown that mechanical stress can regulate many cellular processes. However, in most cases, the exact regulatory mechanisms are still not well understood. One approach in improving our understanding of such mechanically induced regulation is the quantitative study of cell deformation under an externally applied stress. In this paper, an axisymmetric finite-element model is developed and used to study the deformation of single, suspended fibroblasts in an optical stretcher in which a stretching force is applied onto the surface of the cell. A feature of our physical model is a viscoelastic material equation whose parameters vary spatially to mimic the experimentally observed spatial heterogeneity of cellular material properties. Our model suggests that cell size is a more important factor in determining the maximal strain of the optically stretched fibroblasts compared to the thickness of the actin cortical region. This result could explain the higher deformability observed experimentally for malignant fibroblasts in the optical stretcher. Our model also shows that maximal stress propagates into the nuclear region for malignant fibroblasts whereas for normal fibroblasts, it does not. We discuss how this may impact the transduction of cancer signaling pathways.

Adhesive dynamics of lubricated films.

Membrane waves have been observed near the leading edge of a motile cell. Such phenomenon is the result of the interplay between hydrodynamics and adhesive dynamics. Here we consider membrane dynamics on a thin fluid gap supported by adhesive bonds. Using coupled lubrication theory and adhesive dynamics, we derive an evolution equation to account for membrane tension, bending, adhesion, and viscous lubrication. Four adhesion scenarios are examined: no adhesion, uniform adhesion, clustered adhesion, and focal adhesion. Two contrasting traveling wave types are found, namely, tension and adhesion waves. Tension waves disperse with time and space, whereas adhesion waves show increased amplitudes and are highly persistent. We show that the transition from tension to adhesion waves depends on a necessary, but insufficient, criterion that the wave amplitude must exceed a critical gap height, which is dependent on adhesion binding probability. We also show that strong adhesion results in sharp tension-to-adhesion wave transitions. The present work could explain the strong persistence of the waves observed in adhered cells using differential inference contrast (DIC) microscopy and the observation that the wavelengths decrease shortly after leading edge retraction.

Computational model of cell positioning: directed and collective migration in the intestinal crypt epithelium.

The epithelium of the intestinal crypt is a dynamic tissue undergoing constant regeneration through cell growth, cell division, cell differentiation and apoptosis. How the epithelial cells maintain correct positioning and how they migrate in a directed and collective fashion are still not well understood. In this paper, we developed a computational model to elucidate these processes. We show that differential adhesion between epithelial cells, caused by the differential activation of EphB receptors and ephrinB ligands along the crypt axis, is necessary to regulate cell positioning. Differential cell adhesion has been proposed previously to guide cell movement and cause cell sorting in biological tissues. The proliferative cells and the differentiated post-mitotic cells do not intermingle as long as differential adhesion is maintained. We also show that, without differential adhesion, Paneth cells are randomly distributed throughout the intestinal crypt. In addition, our model suggests that, with differential adhesion, cells migrate more rapidly as they approach the top of the intestinal crypt. Finally, by calculating the spatial correlation function of the cell velocities, we observe that differential adhesion results in the differentiated epithelial cells moving in a coordinated manner, where correlated velocities are maintained at large distances, suggesting that differential adhesion regulates coordinated migration of cells in tissues.

Monte Carlo simulation and linear stability analysis of Turing pattern formation in reaction-subdiffusion systems.

Subdiffusion is an important physical phenomenon observed in many systems. However, numerical techniques to study it, especially when coupled to reactions, are lacking. In this paper, we develop an efficient Monte Carlo algorithm based on the Gillespie algorithm and the continuous-time random walk to simulate reaction-subdiffusion systems. Using this algorithm, we investigate Turing pattern formation in the Schnakenberg model with subdiffusion. First, we show that, as the system becomes more subdiffusive, the homogeneous state becomes more difficult to destablize and Turing patterns form less easily. Second, we show that, as the number of particles in the system decreases, the magnitude of fluctuations increases and again the Turing patterns form less easily. Third, we show that, as the system becomes more subdiffusive, the ratio between the two diffusive constants must be higher in order to observe Turing patterns. Finally, we also carry out linear stability analysis to validate the results obtained from our algorithm.

Oscillations in intracellular signaling cascades.

In this paper, we study the oscillatory dynamics of intracellular signaling cascades. We derive a reaction-diffusion model of the mitogen-activated protein kinase cascade, and use it to show how oscillations of the protein kinase concentrations can occur as a function of the depth of the cascade. We find that only cascades with depths of three or more layers undergo oscillatory instabilities. In addition, the oscillatory instability is spatially uniform. Thus, the oscillations synchronize the protein kinase concentrations and result in them being uniformly distributed in the cytosol, despite the presence of protein kinase diffusion. Finally, we show how the oscillations are perturbed when parallel cascades "crosstalk." We find that the protein kinases in the downstream layers of the cascade are less perturbed than those in the upstream layers. In particular, cascades of three layers are able to maintain the total power of the protein kinase activities at approximately the unperturbed level. Taken together, our results suggest that only cascades of at least three layers can synchronize the oscillations of protein kinases in the cytosol and operate in parallel in the presence of crosstalk without loss of signaling fidelity.

Hybrid simulations of stochastic reaction-diffusion processes for modeling intracellular signaling pathways.

In the intracellular environment, signaling takes place in a nonideal environment that is spatially heterogeneous and that is noisy, with the noise arising from the low copy numbers of the signaling molecules involved. In this paper, we model intracellular signaling pathways as stochastic reaction-diffusion processes and adapt techniques commonly used by physicists to solve for the spatiotemporal evolution of the signaling pathways. We then apply it to study two problems of relevance to the modeling of intracellular signaling pathways. First, we show that, in the limit of small protein diffusion which is typically the case for proteins in the cytosol crowded by other macromolecules, the extent of diffusion control, in the transient regime, on reactions is greater than previous predictions. Second, we show that the presence of scaffold proteins can modify the phosphorylation activity of a mitogen-activated protein kinase cascade, and explain how this activity is modulated by the scaffold protein concentration.

Enhanced tracer transport by the spiral defect chaos state of a convecting fluid.

To understand how spatiotemporal chaos may modify material transport, we use direct numerical simulations of the three-dimensional Boussinesq equations and of an advection-diffusion equation to study the transport of a passive tracer by the spiral defect chaos state of a convecting fluid. The simulations show that the transport is diffusive and is enhanced by the spatiotemporal chaos. The enhancement in tracer diffusivity follows two regimes. For large Péclet numbers (that is, small molecular diffusivities of the tracer), we find that the enhancement is proportional to the Péclet number. For small Péclet numbers, the enhancement is proportional to the square root of the Péclet number. We explain the presence of these two regimes in terms of how the local transport depends on the local wave numbers of the convection rolls. For large Péclet numbers, we further find that defects cause the tracer diffusivity to be enhanced locally in the direction orthogonal to the local wave vector but suppressed in the direction of the local wave vector.

Rayleigh-Bénard convection in large-aspect-ratio domains.

The coarsening and wave number selection of striped states growing from random initial conditions are studied in a nonrelaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as t0.12, the orientational correlation length scales as t0.54, and the density of defects scale as t(-0.45). The final pattern evolves toward the wave number where isolated dislocations become motionless, suggesting a possible wave number selection mechanism for large-aspect-ratio convection.

Efficient algorithm on a nonstaggered mesh for simulating Rayleigh-Bénard convection in a box.

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Bénard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single nonstaggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.

Mean flow and spiral defect chaos in Rayleigh-Bénard convection.

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. First, we show that, in the absence of the mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wave numbers that approach those uniquely selected by focus-type singularities, which, in the absence of the mean flow, lie at the zigzag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how the mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of the mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with the Rayleigh number.