Mechanical phenomena affect nearly every aspect of cellular biology and function, yet the underlying mechanisms of how mechanical forces and biochemical signals interact is not clearly understood. We are interested in understanding the molecular basis of cell mechanics and mechanotransduction and shedding light on the role of these processes in human disease. Our specific attention is on the role of two macromolecular systems in cellular function, namely the integrin-mediated focal adhesions at the interface between the cell and extracellular matrix (ECM) and the nuclear pore complex (NPC). Focal adhesions are the immediate sites of cell interaction with the extracellular matrix, and as such they play a key role in mechanosensing and mechanotransduction at the the edge of the cell. Nuclear pores could also play a role in the overall process of cellular mechanotransduction by exquisitely controlling the material transport in and out of the nucleus, thereby regulating the gene expression and protein synthesis. Our current projects are as follows:

Cellular Mechanics, Adhesion and Mechanotransduction

Nuclear Mechanics and Transport

Biomechanics of Cardiovascular Disease


Mechanics of Integrin-Mediated Focal Adhesions: Looking “Under the Hood” of Cellular Mechanotransduction

The underlying mechanics and mechanisms of mechanotransduction are not yet clearly understood. One hypothesis is that forces transmitted via individual proteins, either at the site of cell adhesion to its surroundings or within the stress-bearing members of the cytoskeleton, cause conformational changes that change the binding affinity of these proteins to other intracellular molecules. This altered equilibrium state can subsequently initiate biochemical signaling cascades or produce immediate structural changes.


Force-induced conformational changes (‘deformations’) in proteins may play a critical role in initiating and controlling cell signaling pathways. To understand mechanotransduction at the molecular level requires detailed analysis of protein molecular conformational changes that occur in response to forces, which can be exerted by extracellular matrix through the cellular membrane or the cytoskeleton. One example is the recruitment of vinculin to reinforce initial contacts between a cell and the extracellular matrix due to tensile force. Talin, an essential structural protein in the adhesion, contains an N-terminal five-helix bundle in the rod domain with a known cryptic vinculin binding site 1, VBS1. The perturbation of this stable structure through elevated temperature or destabilizing mutation activates vinculin binding.


Molecular dynamics (MD) models to demonstrate a force-induced conformational change that exposes the cryptic vinculin-binding-residues of VBS1 to solvent under applied forces along a realistic pulling direction. VBS1 undergoes an intriguing rigid body rotation by an applied torque transmitted through hydrogen-bonds and salt bridges (Lee et al. 2007). The crystal structure of vinculin head subdomain (Vh1) bound to the talin VBS1 implies that vinculin undergoes a large conformational change upon binding to talin, but the molecular basis for this, or the precise nature of the binding pathway, remain elusive.

Talin Activation

In a separate work, we employed molecular dynamics models to investigate the binding mechanism of Vh1 and VBS1 with minimal constraints to facilitate the binding. One simulation demonstrates binding of the two molecules in the complete absence of external force. VBS1 makes early hydrophobic contact with Vh1 through an initial hydrophobic insertion. Then, other solvent-exposed hydrophobic residues of VBS1 gradually embed into the hydrophobic core of Vh1 further displacing helix 1 from helix 2. These highly conserved critical residues are experimentally shown to be essential in Vh1-VBS1 binding, and are also the same residues that are shown to become exposed by applied tension to talin (Lee et al. 2007). Similar mechanisms were demonstrated in separate MD simulations of Vh1 binding to other VBSs both in talin and alpha-actinin (Lee et al. 2008). Together, these results provide molecular insights, for the first time, into the early force-induced recruitment of vinculin to the mechanosensitive mechanisms of cell-matrix adhesion complex, and establish the basis for further numerical and experimental studies to fully understand the force response of focal adhesions.

Vinculin Activation

More recently, we used molecular dynamics models to investigate the mechanisms via which vinuclin reinforces contacts between ECM and F-actin through interaction with talin (Golji & Mofrad 2009). Vinculin is natively in an auto-inhibited conformation in which the VBS binding region of vinculin head domain (Vh) prevents interaction with vinculin tail domain (Vt) by steric hindrance. We explored two competing hypotheses suggested for how vinculin is activated via interaction with talin: (A) vinculin activation after simultaneous interaction with talin and actin, or (B) vinculin activation solely by interaction with talin VBS. To simulate activation by simultaneous interaction of vinculin with talin and actin, an external stretching force likely to result from the simultaneous interaction was applied to vinculin at its actin binding domain, Vt, while its VBS binding domain was constrained from movement. The result of the simulation was movement of the VBS binding region away form Vt, removing the auto-inhibition preventing Vt interaction with actin and activating vinculin. The same simulation was repeated only after talin VBS insertion, which required larger forces and a longer time to achieve a similar conformational change. Taken together, the molecular dynamics simulaitons of vinculin activation before and after talin VBS insersion suggest vinculin is more likely to become activated through simultaneous interaction than through talin VBS insersion alone.


Other examples of mechanosensing proteins involved in cellular mechanics and mechanotransduction include actin-binding proteins like filamin and alpha-actinin. The mechanical properties of the cell result mainly from the actin filament networks. These cytoskeletal networks are held together by a series of actin crosslinkers and membrane-associated actin binding proteins. We are interested to explore how filamin, an actin binding protein that orients filaments orthogonally, can contribute to the mechanics and function of the cytoskeleton. The mechanical properties of the active functional domain of filamin, its rod domain, were examined to determine the molecular mechanisms governing cellular activity. Constant force pulling simulations were performed with forces ranging from 25pN to 125pN for 2.5ns. Force transmitted through filamin can lead to breakage of specific intramolecular interactions and thereby increasing flexibility of the molecule as a whole. Such gains in flexibility can physiologically function to preserve cytoskeletal crosslinking and geometry in response to stress. Conformational changes induced by force may promote interaction with filamin-interacting protein (Kolahi & Mofrad, 2008). We then (Chen et al. 2009) used a recently solved high-resolution crystal structure of immunoglobulin-like repeats 19 to 21 of filamin (IgFLNa-R19 to -R21), which contain the binding site for integrins and facilitate filamin’s dynamic ability to communicate with the ECM, and employed molecular dynamics models to demonstrate that an axial tensile force of 40pN is sufficient to ‘initiate’ the partial removal of the auto-inhibition on IgFLNa-R21’s integrin binding site. However, we found 40pN does not completely remove the auto-inhibition and activate filamin’s integrin-binding capacity. It has been recently suggested that a phosphorylation site on IgFLNa-R20 may promote, or be sufficient for, integrin binding. To explore the effects of phosphorylation (specifically, of ser amino acid residue) on IgFLNa-R20 on the mechanism of filamin’s integrin binding, we used molecular dynamics models to simulate the application of forces of ~40pN on the filamin rod domain repeats R19 to R21 (IgFLNa-R19-21) using both phosphorylated and non-phosphorylated models. After phosphorylation, a minimum of 40pN tensile force on IgFLNa-R19 resulted in the dissociation of IgFLNa-R20’s beta-strand inhibitor within a short time. Our models illustrated that phosphoryl modification at ser amino acid residue on IgFLNa-R20 sufficiently allows the complete removal of autoinhibition through phosphoserine’s increased affinity for the previously IgFLNa-R20 bound beta-strand inhibitor, thus stabilizing the removal of inhibition (Chen et al. 2009).

Alpha Actinin

Alpha-actinin is another major actin crosslinker responsible for maintaining the parallel arrangement of actin filaments in the cytoskeleton. It can serve as a scaffold and maintain dynamic actin filament networks. As a crosslinker in the stressed cytoskeleton, alpha-actinin can retain conformation, function, and strength. Alpha-Actinin has an actin binding domain and a calmodulin homology domain separated by a long rod domain. Using molecular dynamics and normal mode analysis techniques, we suggested that the alpha-actinin rod domain has flexible terminal regions which can twist and extend under mechanical stress, yet has a highly rigid interior region stabilized by aromatic packing within each spectrin repeat, by electrostatic interactions between the spectrin repeats, and by strong salt bridges between its two anti-parallel monomers (Golji et al. 2009). By exploring the natural vibrations of the alpha-actinin rod domain and by conducting bending molecular dynamics simulations we also predicted that bending of the rod domain is possible with minimal force. We have introduced computational methods for analyzing the torsional strain of molecules using rotating constraints. Molecular dynamics extension of the alpha-actinin rod was also performed, exploring the regional rigidity of the rod domain (Zaman & Mofrad 2004) and demonstrating transduction of the unfolding forces across salt bridges to the associated monomer of the alpha-actinin rod domain (Golji et al. 2009).

Mechanics of the Nuclear Pore and Nucleocytoplasmic Transport

The nuclear pore complex (NPC) is the exclusive pathway of material transport in and out of the cell nucleus in eukaryotes. It is a supramolecular assembly with a species-dependent mass of about 40-60 MDa in yeast and vertebrates having an octagonal structure that is highly symmetric. NPCs span and perforate the nuclear envelope with a density of about 5-12 NPCs per squared micrometers, although this might also depend on the species and the cell-cycle. The number of NPCs varies, depending on the cell size and activity, between ~200 in yeast, ~2000-5000 in a proliferating human cell.


Since many vital activities of the cell happen and are managed inside the nucleus, it is extremely important to control the material transport into and out of the nucleus. If a potentially harmful agent can penetrate into the nucleus and possibly affect the genome or interfere with the transcription process lethal consequences may arise, as in the case of viral infection (Jamali et al. 2011). Thus, despite the high throughput of about 1000 translocations per NPC per second, as the gatekeeper of the cell nucleus, the NPC strictly controls the passage of individual cargos by vigorously discriminating between the active and inert cargos. However, the dynamic mechanism of nucleocytoplasmic transport is poorly understood. It is believed that central to transport across the NPC is the role of phenylalanine-glycine (FG) repeat domains, which are found all over the NPC structure. These repeat domains are natively unfolded and highly dynamic in nature. Of the main challenges in understanding the nucleocytoplasmic transport mechanism is the inaccessibility of the NPC central channel along with the highly dynamic FG-repeat domains during transport to experimental approaches. Currently, only computational techniques can elucidate the detailed events happening at this tiny pore with an angstrom spatial and nanosecond temporal resolutions to account for transient bonds.

In the Mofrad lab, the NPC group is dedicated to understand the function of this pore from a computational perspective, validated by experimental data. In our initial work, we investigated structural features of the NPC by employing the finite element method and establishing a coarse-grained model of the octagonal structure of the NPC central channel. We found the underlying mechanical reason for the symmetric octagonal structure and showed that this octagonality leads to maximizing the bending stiffness of the pore (Wolf & Mofrad 2008), a fact that might be crucial for structural stability during the transport of large cargos, potentially preventing mechanical rupture of this supramolecular assembly. Next, we turned to the biophysics, kinetics, and atomic principles behind nucleocytoplasmic transport by establishing de novo computational models.

Biophysical approach: While much is known about the biochemical pathways of nucleocytoplasmic transport, it seems that the role of biophysical factors has been largely underestimated in proposed models. Therefore, in our biophysical approach, we have recently established a polymer-based model of the NPC structure, taking into account the fine unstructured FG-repeat domains. The model allows us to investigate the nucleocytoplasmic transport process with fine spatiotemporal resolution of about one nanometer and a hundredth of nanosecond (Moussavi-Baygi et al. 2011b). Using this model, we showed that a layer of FG-repeat domains forms on the inner wall of the central channel, leaving an open pore of about 18 nm and proposed a new mechanism for transport (Moussavi-Baygi et al. 2011a).

Our model also suggests that the biophysical role of the cytoplasmic filaments plays a significant role in the selectivity barrier given that NPCs lacking these filaments are far more permeable to inert particles than intact NPCs. Moreover, we analyzed the path of the cargo-complex (active cargo) and showed that it is mainly attached to the NPC inner wall during transport.

Biochemical approach: Here we established an agent-based model (Azimi et al. 2011) of nucleocytoplasmic transport, taking into account available experimentally reported kinetic values of different reactions happening in a complete nucleocytoplasmic transport cycle. In this approach, we discretize the space inside the NPC channel into cells and allow individual biochemical factors (agents) to move throughout the system and interact with other agents with distinct probabilities of movement based on their diffusion coefficients and probabilities of interaction based on their reaction rate constants. Using this model, we are studying effects such as sensitivity to concentrations of different agents, pairwise affinities, and the localization of agents within the NPC on transport rate and efficiency (Azimi et al., in preparation). Moreover, since this model is coarser than the biophysical model, it allows us to investigate an aggregation of NPCs and study their potential mutual effects on transport kinetics at longer time scales.

All-atomic approach: In this approach, we are employing molecular dynamics (MD) simulations to study specific domains of transport receptors and those nups which are believed to play a role in nucleocytoplasmic transport. Currently we have focused on the interaction of the C-terminal of Tpr, an NPC-related protein found in the nuclear basket, with Crm1, a transport receptor that exports proteins carrying a leucine-rich nuclear export signal (NES), a subset of mRNA, snRNPís, and some rRNA. In this study, using extensive all-atomic MD simulations in explicit water molecules, we have located the binding sites of Crm1 with C-Tpr in the presence of RanGTP (Zhao et al., submitted to Structure). We are specifically interested in Crm1-related functions since it is believed to have critical role in the export of the RNA genomes of lentiviruses such as HIV.

Indeed, by expanding the knowledge of NPC transport via in-vivo, in-vitro and in-silico experiments it will be possible to better understand and investigate the role of the NPC in various human diseases.

Mechanics of Human Disease

A long-term goal of the research program in Mofrad Lab has been to understand the role of mechanics and mechanotransduction in human diseases, in particular cardiovascular diseases like atherosclerosis and aortic valve calcification.

Multiscale Mechanics of the Aortic Heart Valve: A Mechanotransduction Perspective on Calcific Aortic Stenosis.

The human heart is a pump system consisting of four chambers and four valves. When functioning correctly, the valves open widely to allow blood through and seal securely shut. Valvular disease inhibits a valve’s ability to open and close, decreasing the efficiency of the heart and

leading to a variety of further cardiovascular disorders. Aortic valves (AV) control the flow of oxygen-rich blood from the left ventricle to the aorta and thereby the rest of the body. Normally, the aortic valve functions very efficiently, providing negligible resistance to forward flow and allowing minimal backflow. The mechanical function of aortic valve can, however, be affected by pathological conditions. The most common valvular disease is calcific aortic stenosis (CAS). In CAS, the aortic valve undergoes changes very similar to those seen in atherosclerosis. First, inflammatory cells migrate to the site. Monocytes adhere to the endothelial layer, infiltrate it, and differentiate into macrophages. The macrophages send intracellular signals to nearby fibroblasts, causing the fibroblasts to promote cellular proliferation and matrix remodeling. Macrophages add calcium deposits to the matrix. Eventually, the remodeled matrix and calcium deposits build up to yield a thickened, stiffened leaflet. These changes can affect mechanical function, a result known as stenosis.

Take up some space. And even more Space

To understand the mechanisms of calcific aortic stenosis, and to evaluate methods of prevention and treatment for this disease, my lab has developed novel models of aortic valve mechanics. We have created a set of multiscale models to examine the dynamic behavior of the human aortic valve at the cell, tissue, and organ length scales. Each model is fully three-dimensional and includes appropriate nonlinear, anisotropic material models. The organ-scale model incorporates a dynamic fluid-structure interaction that predicts the motion of the blood, cusps, and aortic root throughout the full cycle of opening and closing. The tissue-scale model simulates the behavior of the aortic valve cusp tissue including the sub-millimeter features of multiple layers and undulated geometry. The cell-scale model predicts cellular deformations of individual cells within the cusps. Each simulation has been verified against experimental data. The three simulations are linked: deformations from the organ-scale model are applied as boundary conditions to the tissue-scale model, and the same is done between the tissue and cell scales. This set of simulations is a major advance in the study of the aortic valve as it allows analysis of transient, three-dimensional behavior of the aortic valve over the range of length scales from cell to organ. The complete set of simulations has enabled unprecedented analysis of the AV mechanical behavior across the range of length scales needed to examine biological processes in the valve (Weinberg & Mofrad, 2007). Multiscale computational comparison of the bicuspid and tricuspid aortic valves in relation to calcific aortic stenosis. While the aortic valve is normally comprised of three cusps and their surrounding tissue, some patients are however born with aortic valves that have two cusps or leaflets. It is well known that patients with bicuspid aortic valve (BAV) are more likely to develop a calcific aortic stenosis (CAS) than their cohorts with normal tricuspid aortic valves (TAV). In healthy valves, each cusp is

thin and pliable. In the disease CAS, calcified nodes develop and spread across the cusps. It is not currently known whether the increase in risk of CAS is caused by the geometric differences between the tricuspid and bicuspid valves or whether the increase in risk is caused by the same underlying factors that produce the geometric difference. We employed our multiscale models of the aortic valve and isolated the effect of one geometric factor, namely the number of cusps, to explore its effect on multiscale valve mechanics, particularly in relation to CAS (Weinberg & Mofrad 2008). The BAV and TAV were modeled by a set of simulations describing the cell, tissue, and organ length scales. These models were linked across the length scales to create a coherent multiscale model. At each scale, the models were three-dimensional, dynamic, and incorporate accurate nonlinear constitutive models of the valve leaflet tissue. We compared results between the TAV and BAV at each length scale. At the cell scale, our region of interest was the location where calcification develops, near the aortic-facing surface of the leaflet. Our preliminary simulations have shown the expected differences between the tricuspid and bicuspid valves at the organ scale: the bicuspid valve shows greater flexure in the solid phase and stronger jet formation in the fluid phase relative to the tricuspid. At the cell-scale, however, our results suggested that the region of interest may be shielded against strain by the wrinkling of the fibrosa. Thus, the cellular deformations are not significantly different between the TAV and BAV in the calcification-prone region. Our results suggested that the difference in calcification observed in the BAV versus TAV is due primarily to factors other than the simple geometric difference between the two valves (Weinberg & Mofrad, 2008).

A computational model of aging and calcification in the aortic heart valve.
The aortic heart valve undergoes geometric and mechanical changes over time as we age and drastically so during diseases like CAS. The cusps of a normal, healthy valve thicken and become less extensible over time. In the disease calcific aortic stenosis (CAS), calcified nodules progressively stiffen the cusps. The local mechanical changes in the cusps, due to either normal aging or pathological processes, affect overall function of the valve. We recently developed a computational model for the aging aortic valve that connects local changes to overall valve function (Weinberg et al. 2009), extending our previous model for the healthy valve to describe aging. To model normal/uncomplicated aging, leaflet thickness and extensibility were varied versus age according to experimental data. To model calcification, initial sites were defined and a simple growth law is assumed. The nodules were then let to grow over time, so that the area of calcification increases from one model to the next model representing greater age. The overall valve function was recorded for each individual model to yield a single simulation of valve function over time. This model is the first theoretical tool to describe the temporal behavior of aortic valve calcification. The ability to better understand and predict disease progression will aid in design and timing of patient treatments for CAS.

Hemodynamic environments from opposing sides of human aortic valve leaflets evoke distinct endothelial phenotypes in vitro. While the cellular and molecular mechanisms leading to valvular pathogenesis remain unknown, the effect the hemodynamic environment has on valvular endothelial cells, as well as the valve structure and function, has gained recent attention. In

a recent and ongoing collaboration with Prof. Fred Schoen and Prof. Guillermo Garcia-Cardena, both at Harvard Medical School, we described the specific shear waveforms to which the two sides of the aortic valve cusp are subjected, and thus recreated the specific hemodynamic environment of the valve surfaces in vitro. The shear waveforms applied by the blood to the aortic and ventricular valve endothelium were extracted from our computational model of the aortic valve (Weinberg & Mofrad 2007) and applied to cultured human endothelial cells in order to investigate whether these waveforms influence endothelial gene expression. Using this in vitro model, the cells exposed to the ventricular waveform were found to display an anti-inflammatory endothelial molecular phenotype, compared to cells exposed to the waveform from the aortic side of the leaflet (Weinberg et al. 2010).

Role of Mechanics and Mechanotransduction in Arterial Disease.
An important disease believed to be related to cellular mechanotransduction is atherosclerosis. We have had a long-term interest in understanding and characterization of atherosclerotic plaques. Due to focal nature of this disease, mechanical factors (namely, arterial wall mechanics, hemodynamics, and mass transport patterns) are widely believed to play a key role in initiation and progression of atherosclerosis. Rigorous assessment of potential links between such mechanical factors and atherosclerosis, however, requires detailed studies using realistic, subject-specific models. Over the past several years, we have developed models for computational simulation of hemodynamics and wall mechanics in patient-specific carotid bifurcations.

In recent years, we have focused this effort mostly on developing diagnostic methods (namely, vascular elastography) for non-invasive characterization of the vulnerability of atherosclerotic plaques to rupture. Elastography is a non-invasive technique for mechanical characterization of tissues in terms of strain, stress or elastic modulus patterns. To make elastography techniques robustly applicable to vascular tissues (regardless of imaging modality), we exploited the kinematics of incompressible tissue as a side-constraint term in registration (Khalil et al. 2005; Karimi et al. 2006). We have also developed lumped-model parameter estimation techniques for arterial elastography that have led to more efficient reconstruction of modulus maps in linear elastic (Khalil et al 2006) and nonlinear (Karimi et al. 2008) models of arterial plaques.

One interesting derivative of this research involves our application of these novel elastography techniques in cell scale mechanics using confocal images. Our cell scale elastography promises to be a significant contribution to cell mechanics and mechanotransduction research as it provides a unique approach for local and in-depth measurement of strain maps in the cell without any physical interference with their natural state.