1. Molecular Cell Biomechanics and Mechanotransduction. To contribute to the understanding of the fundamental principles underlying cell mechanics and mechanotransduction,
2. Multiscale Mechanics and Mechanotransduction in Cardiovascular Disease. To shed light on the multiscale mechanics and mechanotransduction processes (linking cell-, tissue- and organ-scale phenomena) involved in cardiovascular diseases like human aortic valve calcification.

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. To address this, models of the cell are required to map out the distribution of forces within the cell resulting from specific mechanical stimuli.

Multiscale Modeling of Active, Non-equilibrium Cytoskeletal Mechanics and Contractility. Mechanobiology of the cell is characterized by force exchanges between an actively remodeling and contractile cytoskeleton and the extracellular matrix. Modeling these force interactions is important because they underlie cell shape, migratory patterns and remodeling of tissues. The cytoskeletal force sensing is characterized by long-range force transmission without dissipation, network-like interactions between various components, and active feedback remodeling. These are not amenable to conventional modeling techniques; for instance continuum-based modeling techniques do not capture the discontinuous strain transmissions in cytoskeletal mechanics. Furthermore, with immense advances in the experimental techniques to probe cytoskeletal mechanics, interpretation of the experimental observations is limited by the complex nature of the cytoskeletal mechanics and by the lack of an appropriate model. We are developing models for the macro-molecular scale mechanics of the cytoskeleton in a discrete manner given the topology of force transmission within cell is determined by the organization of actin filaments in the cytoskeleton. The filamentous nature of actin is important and is best captured in a discrete model (for further details, please see Chandran & Mofrad, 2009).

Mechanics of Multicellular Populations in Epithelia Morphogenesis. The process of epithelial morphogenesis is ubiquitous in the development of multicellular organisms, but little is known about the cell level mechanics that shape these tissues. We use the Drosophila melanogaster egg chamber as a model system to study the cellular mechanics of morphogenesis. Drosophila oogenesis is an ideal system given the myriad experimental techniques available and the simplicity of the tissue architecture. The egg chamber consists of 16 interior germline cells (15 nurse cells and the oocyte) encased by a follicle cell epithelial (FCE) layer of approximately 900 cells. Of the many morphogenetic changes that the FCE undergoes, one of the most dramatic is the posterior migration. During posterior migration the initially cuboidal monolayer of follicle cells transitions into distinct populations of columnar and squamous cells. In collaboration with Prof. David Bilder (UC Berkeley, Molecular and Cellular Biology Department), we are performing a detailed quantitative analysis of cell morphologies at different time points during this process and developed a physically realistic computational mechanics model of the process.

Molecular Mechanics of Mechanosensing Proteins. Mechanical stimuli affect nearly every aspect of cellular function, yet the underlying mechanisms of transduction of force into biochemical signals are not 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 or the cytoskeleton, or through the cellular membrane. 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 the 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.
In collaboration with Prof. Roger Kamm (MIT), we have employed 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, Journal of Biomechanics). 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.
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. 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 (for further details, please see Lee et al., 2007, 2008). 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 (for further details, please see Kolahi & Mofrad 2008; Golji et al. 2009).

Role of the Nuclear Pore Complex in Cellular Mechanotransduction. We examine the structure and mechanics of the nuclear pore complex (NPC) to explore its role in the overall nuclear mechanics and mechanotransduction. Protein structures called Nuclear Pore Complexes support the perinuclear space between the inner and outer nuclear membranes while controlling all transport between the nucleus and cytoplasm. NPCs, protein macro-assemblies forming a gating mechanism, regulate cargo transport between the cytoplasm and the nucleoplasm. Given the NPC's unique structure and mysterious abilities in transporting cargo, many attempts have been made to analyze its properties. Yet, little concrete knowledge has been gathered about how the NPC functions, the mechanisms by which it transports cargo, and even the explicit structures of the nucleoporins comprising it. We are developing computational models inspired by experimental observations to better understand the role of NPC in mechanotransduction (for further details, please see Wolf and Mofrad, 2008).

A long-term goal of Mofrad Lab is to develop multiscale biomechanical models to understand the role of mechanics and mechanotransduction in cardiovascular diseases, in particular calcific aortic stenosis and arterial atherosclerois.

Multiscale Simulations of the Aortic Heart Valve Mechanics: Applications in Disease and Surgery. The aortic heart valve is a one-way valve located between the left ventricle and the aorta. 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 a 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 atherosclerotic vessels. 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. To understand the mechanisms of calcific aortic stenosis, and to evaluate methods of prevention and treatment for this disease, we are developing sophisticated models of aortic valve mechanics. (for further details, please see Weinberg & Mofrad, 2005-2008).