Mandar M. Inamdar

Forces during Bacteriophage DNA Packaging and Ejection

The conjunction of insights from structural biology, solution biochemistry, genetics, and single-molecule biophysics has provided a renewed impetus for the construction of quantitative models of biological processes. One area that has been a beneficiary of these experimental techniques is the study of viruses. In this article we describe how the insights obtained from such experiments can be utilized to construct physical models of processes in the viral life cycle. We focus on dsDNA bacteriophages and show that the bending elasticity of DNA and its electrostatics in solution can be combined to determine the forces experienced during packaging and ejection of the viral genome. Furthermore, we quantitatively analyze the effect of fluid viscosity and capsid expansion on the forces experienced during packaging. Finally, we present a model for DNA ejection from bacteriophages based on the hypothesis that the energy stored in the tightly packed genome within the capsid leads to its forceful ejection. The predictions of our model can be tested through experiments in vitro where DNA ejection is inhibited by the application of external osmotic pressure.

Dynamics of DNA Ejection from Bacteriophage

The ejection of DNA from a bacterial virus (i.e., phage) into its host cell is a biologically important example of the translocation of a macromolecular chain along its length through a membrane. The simplest mechanism for this motion is diffusion, but in the case of phage ejection a significant driving force derives from the high degree of stress to which the DNA is subjected in the viral capsid. The translocation is further sped up by the ratcheting and entropic forces associated with proteins that bind to the viral DNA in the host cell cytoplasm. We formulate a generalized diffusion equation that includes these various pushing and pulling effects and make estimates of the corresponding speedups in the overall translocation process. Stress in the capsid is the dominant factor throughout early ejection, with the pull due to binding particles taking over at later stages. Confinement effects are also investigated, in the case where the phage injects its DNA into a volume comparable to the capsid size. Our results suggest a series of in vitro experiments involving the ejection of DNA into vesicles filled with varying amounts of binding proteins from phage whose state of stress is controlled by ambient salt conditions or by tuning genome length.

Proteolytic and non-proteolytic regulation of collective cell invasion: tuning by ECM density and organization.

Cancer cells manoeuvre through extracellular matrices (ECMs) using different invasion modes, including single cell and collective cell invasion. These modes rely on MMP-driven ECM proteolysis to make space for cells to move. How cancer-associated alterations in ECM influence the mode of invasion remains unclear. Further, the sensitivity of the two invasion modes to MMP dynamics remains unexplored. In this paper, we address these open questions using a multiscale hybrid computational model combining ECM density-dependent MMP secretion, MMP diffusion, ECM degradation by MMP and active cell motility. Our results demonstrate that in randomly aligned matrices, collective cell invasion is more efficient than single cell invasion. Although increase in MMP secretion rate enhances invasiveness independent of cell–cell adhesion, sustenance of collective invasion in dense matrices requires high MMP secretion rates. However, matrix alignment can sustain both single cell and collective cell invasion even without ECM proteolysis. Similar to our in-silico observations, increase in ECM density and MMP inhibition reduced migration of MCF-7 cells embedded in sandwich gels. Together, our results indicate that apart from cell intrinsic factors (i.e., high cell–cell adhesion and MMP secretion rates), ECM density and organization represent two important extrinsic parameters that govern collective cell invasion and invasion plasticity.

Influence of cell spreading and contractility on stiffness measurements using AFM

Atomic Force Microscopy (AFM) is widely used for measuring mechanical properties of cells, and to understand how cells respond to their mechanical environments. A standard method for obtaining cell stiffness from experimental force–indentation curves is based on the simplified Hertz theory developed for studying the indentation of a semi-infinite elastic body by a spherical punch, assumptions that do not hold for biological cells. The modified Hertz theory developed by Dimitriadis et al., which takes the finite sample height into account, is widely used by experimentalists for greater accuracy. However, neither of these two models account for the finite lateral spread of the cells and cellular contractility. In this paper, we address the influence of cell geometry, cell pre-stress, and nuclear properties on cell stiffness measurements by modeling indentation of a cell of prescribed geometry with a spherical AFM probe using the finite element method. Using parametric studies, we develop scaling relationships between the effective stiffness probed by AFM and the bulk cell stiffness, taking cell and tip geometry into account. Taken together, our results demonstrate the need to take cell geometry into account while estimating the cell stiffness and provide simple expressions for doing so.

Statistical Mechanics Provides Novel Insights into Microtubule Stability and Mechanism of Shrinkage

Microtubules are nano-machines that grow and shrink stochastically, making use of the coupling between chemical kinetics and mechanics of its constituent protofilaments (PFs). We investigate the stability and shrinkage of microtubules taking into account inter-protofilament interactions and bending interactions of intrinsically curved PFs. Computing the free energy as a function of PF tip position, we show that the competition between curvature energy, inter-PF interaction energy and entropy leads to a rich landscape with a series of minima that repeat over a length-scale determined by the intrinsic curvature. Computing Langevin dynamics of the tip through the landscape and accounting for depolymerization, we calculate the average unzippering and shrinkage velocities of GDP protofilaments and compare them with the experimentally known results. Our analysis predicts that the strength of the inter-PF interaction (Ems) has to be comparable to the strength of the curvature energy (Emb) such that Ems−Emb≈1kBT, and questions the prevalent notion that unzippering results from the domination of bending energy of curved GDP PFs. Our work demonstrates how the shape of the free energy landscape is crucial in explaining the mechanism of MT shrinkage where the unzippered PFs will fluctuate in a set of partially peeled off states and subunit dissociation will reduce the length.

Binding of DNA-bending non-histone proteins destabilizes regular 30-nm chromatin structure.

Why most of the in vivo experiments do not find the 30-nm chromatin fiber, well studied in vitro, is a puzzle. Two basic physical inputs that are crucial for understanding the structure of the 30-nm fiber are the stiffness of the linker DNA and the relative orientations of the DNA entering/exiting nucleosomes. Based on these inputs we simulate chromatin structure and show that the presence of non-histone proteins, which bind and locally bend linker DNA, destroys any regular higher order structures (e.g., zig-zag). Accounting for the bending geometry of proteins like nhp6 and HMG-B, our theory predicts phase-diagram for the chromatin structure as a function of DNA-bending non-histone protein density and mean linker DNA length. For a wide range of linker lengths, we show that as we vary one parameter, that is, the fraction of bent linker region due to non-histone proteins, the steady-state structure will show a transition from zig-zag to an irregular structure—a structure that is reminiscent of what is observed in experiments recently. Our theory can explain the recent in vivo observation of irregular chromatin having co-existence of finite fraction of the next-neighbor (i + 2) and neighbor (i + 1) nucleosome interactions.

Reliability-Based Design Optimization of Frame-Supported Tensile Membrane Structures

AbstractDue to the inherent flexibility of tensile membrane structures (TMS), they need to remain in a stable equilibrium condition in the presence of gusty winds as well as in their absence. This paper is aimed at the reliability-based optimization of frame-supported tensile membrane structures subjected to uncertain wind loads. The transient membrane displacement is minimized under this random loading constrained to a stable TMS form and a maximum failure probability against membrane tearing. A particle swarm optimization algorithm is used, combined with Latin hypercube sampling and response surface approach, for obtaining the optimum initial prestress required. These algorithms balance the computationally demanding dynamic relaxation method required for the membrane structural analysis. The proposed methodology is demonstrated through the example of a frame-supported conic membrane structure. The results show that the proposed method can effectively optimize the TMS performance under random wind forces...

Coherent Motion of Monolayer Sheets under Confinement and Its Pathological Implications.

Coherent angular rotation of epithelial cells is thought to contribute to many vital physiological processes including tissue morphogenesis and glandular formation. However, factors regulating this motion, and the implications of this motion if perturbed, remain incompletely understood. In the current study, we address these questions using a cell-center based model in which cells are polarized, motile, and interact with the neighboring cells via harmonic forces. We demonstrate that, a simple evolution rule in which the polarization of any cell tends to orient with its velocity vector can induce coherent motion in geometrically confined environments. In addition to recapitulating coherent rotational motion observed in experiments, our results also show the presence of radial movements and tissue behavior that can vary between solid-like and fluid-like. We show that the pattern of coherent motion is dictated by the combination of different physical parameters including number density, cell motility, system size, bulk cell stiffness and stiffness of cell-cell adhesions. We further observe that perturbations in the form of cell division can induce a reversal in the direction of motion when cell division occurs synchronously. Moreover, when the confinement is removed, we see that the existing coherent motion leads to cell scattering, with bulk cell stiffness and stiffness of cell-cell contacts dictating the invasion pattern. In summary, our study provides an in-depth understanding of the origin of coherent rotation in confined tissues, and extracts useful insights into the influence of various physical parameters on the pattern of such movements.

Probing Cellular Mechanoadaptation Using Cell-Substrate De-Adhesion Dynamics: Experiments and Model

Physical properties of the extracellular matrix (ECM) are known to regulate cellular processes ranging from spreading to differentiation, with alterations in cell phenotype closely associated with changes in physical properties of cells themselves. When plated on substrates of varying stiffness, fibroblasts have been shown to exhibit stiffness matching property, wherein cell cortical stiffness increases in proportion to substrate stiffness up to 5 kPa, and subsequently saturates. Similar mechanoadaptation responses have also been observed in other cell types. Trypsin de-adhesion represents a simple experimental framework for probing the contractile mechanics of adherent cells, with de-adhesion timescales shown to scale inversely with cortical stiffness values. In this study, we combine experiments and computation in deciphering the influence of substrate properties in regulating de-adhesion dynamics of adherent cells. We first show that NIH 3T3 fibroblasts cultured on collagen-coated polyacrylamide hydrogels de-adhere faster on stiffer substrates. Using a simple computational model, we qualitatively show how substrate stiffness and cell-substrate bond breakage rate collectively influence de-adhesion timescales, and also obtain analytical expressions of de-adhesion timescales in certain regimes of the parameter space. Finally, by comparing stiffness-dependent experimental and computational de-adhesion responses, we show that faster de-adhesion on stiffer substrates arises due to force-dependent breakage of cell-matrix adhesions. In addition to illustrating the utility of employing trypsin de-adhesion as a biophysical tool for probing mechanoadaptation, our computational results highlight the collective interplay of substrate properties and bond breakage rate in setting de-adhesion timescales.

Spatial anisotropy and heterogeneity in contractility and adhesion distribution may contribute to cell steering during migration

Transition from random to persistent cell motility requires spatiotemporal organization of the cytoskeleton and focal adhesions. The influence of these two structures on cell steering can also be gleaned from trypsin de-adhesion experiments, wherein cells exposed to trypsin round up, exhibiting a combination of rotation and translation. Here, we present a model to evaluate the contributions of contractility and bond distribution to experimentally observed de-adhesion. We show that while asymmetry in bond distribution causes only cell translation, a combination of asymmetric bond distribution and non-uniform contractility is required for translation and rotation and may guide cell migration.