Physics and mechanics of the cytoskeleton

With the unprecedented advancements in microscopy and data acquisition in small time and length scales we are closer than ever to take on the long standing quest of deciphering the physics of life. This journey begins with the basic, structural unit of life: The Cell. Cytoskeleton is a complex assembly of filaments, motor proteins, and organelles and perhaps one of the most intriguing examples of complex fluids. Through reorganizing its underlying microstructure, cytoskeleton regulates several vital cellular processes including motility, organelle transport, and cell division. We are interested in understanding the underlying physical principles that determine the collective behavior of cytoskeletal assemblies.

Dynamic simulation of cytoskeletal assemblies

The many-body interactions between the filaments and motor-proteins, the geometrical complexity of the shape of filaments, and nonlocal interactions of filaments and other structures with the cytoplasm makes simulating cytoskeletal assemblies very challenging from a computational physics standpoint. We combine highly efficient computational platforms for simulating fluid-structure interactions in complex fluids with biophysical modeling to develop fast and accurate platforms for simulating cytoskeletal assemblies. We use these tools to understand the collective behavior of these structures in terms of their microscopic interactions. For more details, see our paper in Journal of Computational Physics. You can find some of these examples and videos in Gallery.

Fluid-structure interactions in the cytoskeleton

There has been a large number of studies on the mechanics of the cytoskeletal assemblies. Most studies only focus on local interactions between the filaments and motor proteins, and ignore the nonlocal hydrodynamic interactions between the filaments and other structures with the cytoplasmic fluid. Our goal, here, is to use theory, computation, and experiment to study the important consequences of hydrodynamic interactions in the mechanics of these cellular structures. As an example, we have been studying the effect of hydrodynamic interactions in the mitotic spindle positioning during cell division. See our recent work on the topic for more details.

The positioning of the mitotic spindle during cell division

The mitotic spindle apparatus is the cellular structure that divides chromosomes in cell division. The position of the spindle determines the position of the cleavage plane, and is thus crucial for cell division. Despite of the large number of studies on spindle positioning, the underlying forces that move the spindle remain poorly understood. In a collaborative study with Dan Needleman's Lab, we combine experimentally measured flows using particle-tracking and laser ablation experiments with biophysical modeling and detailed simulations to understand the the origin of forces that position the mitotic spindle in different stages of the first cell division of C. elegans.

Utilizing electron tomography to study mitotic spindle structure

Electron tomography is a technique used to obtain 3D static image of subcellular structures with significantly higher spatial accuracy than optical and confocal microscopy. Mueller-Reichert Lab use electron tomography to obtain a detailed description of the length, spatial distribution, and shape of microtubules within the mitotic spindle in C. elegans. In a collaboration with their Lab we use this data to understand how microtubules mechanically interact with themselves, motor proteins, and with the chromosomes. These findings can help us understand the underlying forces that drive chromosome segregation and spindle formation. For more details checkout our recent paper accepted for publication in Nature Communications

Microstructure and rheology of complex fluids

Hard-sphere Colloidal dispersions are arguably the simplest complex fluids, as the structure and rheology is entirely determined by volume fraction and the ratio of viscous to thermal forces defined by Peclet number. This makes them ideal model-systems for fundamental studies. In my doctoral studies, I developed a theory for predicting structure and rheology of dense colloidal suspensions far from equilibrium. This theory extends the classical liquid-state theory for simple liquids to non-equilibrium conditions while explicitly taking into account the many-body hydrodynamic interactions between the particles. The coupling of flow and microstructure is described through Smoluchowski equation for probability distribution function. The many-body hydrodynamic and inter-particle interactions are described by integrals over probabilistic third particles. The result is a differential integral equation for pair distribution function.

I have used the theory to predict the structure and rheology of hard-sphere dispersions and particles interacting through soft repulsive forces in simple shear flows. The predictions are corroborated with direct numerical simulations using Accelerated Stokesian Dynamics (ASD). The theory gives very good predictions of the structure and nonlinear rheology including shear viscosity and normal stress differences over a wide range of shear rates and volume fractions. Another novel part of the theory is accounting for the shear-induced dispersion through a diffusive flux that scales with shear rate in Smoluchowski equation.

I have also studied active microrheology of colloidal dispersions where a probe particle is pulled through the suspension bath. Two forcing models are studied (a) dragging the probe with a constant velocity which models the laser tweezer experimental setup and (b) moving the probe with a constant force similar to magnetic bead experiments. We develop a microscopic theory that computes the structure as a function of the external force/velocity of the probe and the resulting apparent viscosity of the suspension.