Session A42: Focus Session: Cytoskeleton and Biomechanics - Biochemical mechanisms

Stochastic simulations of the growth dynamics and organization of lamellipodia-like actin networks

Cell migration is essential to many biological processes such as embryonic development, wound healing and immune response. The crawling movement of cells is a complex process that involves the protrusion of the leading edge of a cell, adhesion to the substrate, generation of the traction force to move cell body and the subsequent release of adhesions. Lamellipodia are flat sheet-like membrane protrusions at the leading edge of the crawling cells. The dynamic remodeling of the dendritically branched actin network in lamellipodia generates force to drive the movement of cells. We have developed a simplified, three-dimensional computational model to study the growth of lamellipodia-like actin networks. Our model integrates the essential biochemical regulation processes as well as the mechanical aspect of actin polymerization, where the interactions between the semi-flexible filaments and the plasma membrane are taken into account. Using stochastic simulations, we study how membrane tension and external resistance on membrane affect the growth dynamics and organization of the actin network.   

How ion binding affects actin filament stability and flexural rigidity

Actin filaments are semi-flexible biopolymers essential for the mechanical support and cell motility. Ions strongly affect actin polymerization and the flexibility of actin filaments; however, the molecular basis for how ions are coupled to the mechanics of actin filaments remains elusive. Here, we demonstrate a linkage between cation binding and both actin filament polymerization and flexural rigidity. Our results show that the thermodynamic stability and flexural rigidity of actin filament increase with cation concentration in a manner that implicates specific cation binding as opposed to general electrostatic screening. Using structural bioinformatics, we identify two distinct cation-binding sites within the F-actin structure that help explain how specific cation binding is linked to actin polymerization and flexural rigidity. Site-specific substitution of a charged amino acid residue at one of the sites modulates the cation concentration-dependence of filament bending stiffness, consistent with a bound cation at this site increasing the flexural rigidity of actin filaments. Mutation of a charged amino acid at the other site causes ``polymerization incompetent'' G-actin.   

Mechanotransduction through the plasma membrane {\&} cytoskeleton

Mechanical forces initiate immediate and long-term changes in cells; however the exact mechanisms remain unclear, albeit crucial for understanding the pathology of disease. We used combined confocal and atomic force microscopy (AFM) to investigate changes in cell morphology and elasticity in response to a mechanical stimulus. The AFM was used as a nano-indentor to gauge the response of the membrane and cytoskeleton (CSK) of HeLa cells.~We observed their viscoelastic nature by probing cells transfected with a green fluorescent protein localized at the plasma membrane. Inhibition of acto-myosin contractility (AMc) resulted in a significant decrease of cellular elasticity, and a corresponding increase in mean deformation. We also investigated the rate at which the membrane and CSK deform and relax in response to a local force. The response to a local perturbation is nearly instantaneous for control cells and shows no statistical difference when compared to cells treated with CSK-inhibiting drugs. Inhibition of AMc affects the rate of recovery, in comparison to control cells which recover quite quickly (30-60s). Overall, we demonstrated short and long-term deformation and subsequent recovery of both the cell membrane and actin network in response to a local force.   

Leading at the Front: How EB Proteins Regulate Microtubule Dynamics

Microtubules are the most rigid of the cytoskeletal filaments, they provide the cell's scaffolding, form the byways on which motor proteins transport intracellular cargo and reorganize to form the mitotic spindle when the cell needs to divide. These biopolymers are composed of alpha and beta tubulin monomers that create hollow cylindrical nanotubes with an outer diameter of 25 nm and an inner diameter of 17 nm. At steady state concentrations, microtubules undergo a process known as dynamic instability. During dynamic instability the length of individual microtubules is changing as the filament alternates between periods of growth to shrinkage (catastrophe) and shrinkage to growth (rescue). This process can be enhanced or diminished with the addition of microtubule associated proteins (MAPs). MAPs are microtubule binding proteins that stabilize, destabilize, or nucleate microtubules. We will discuss the effects of the stabilizing end-binding proteins (EB1, EB2 and EB3), on microtubule dynamics observed in vitro. The EBs are a unique family of MAPs known to tip track and enhance microtubule growth by stabilizing the ends. This is a different mechanism than those employed by structural MAPs such as tau or MAP4.   

Redundancy and cooperativity in the mechanics of compositely crosslinked cytoskeletal networks

The cytoskeleton contains many types of crosslinkers. Some crosslinkers allow free rotations between filaments and others do not. The mechanical interplay between different crosslinkers is an open issue in cytoskeletal mechanics. Therefore, we develop a theoretical framework based on rigidity percolation to study a generic filamentous system containing both stretching and bond-bending forces to address this issue. The framework involves both analytical calculations via effective medium theory and numerical simulations on a percolating triangular lattice with very good agreement between both. We find that the introduction of angle-constraining crosslinkers to a semiflexible filamentous network with freely-rotating crosslinks can cooperatively lower the onset of rigidity to the connectivity percolation threshold---a result speculated for years but never before obtained via effective medium theory. In other words, the system can attain rigidity at the lowest concentration of material possible. We further demonstrate that introducing angle-constraining crosslinks results in mechanical behaviour similar to just freely-rotating crosslinked semflexible filaments, indicating redundancy. Our results also impact upon collagen and fibrin networks in biological and bio-engineered tissues.   

The origins of strain stiffening in fibrin networks

Fibrin networks form the structural scaffold of blood clots; their non-linear mechanical properties are crucial to stem the flow of blood at a site of vascular injury. A hallmark of these networks is strain stiffening: a stiffness that increases non-linearly as a network is strained. Deformations of the fibers and the network combine to control the mechanical properties of the bulk and must lead to the strain stiffening behavior of the networks; however, the details of this process are unknown. Here, we study fibrin networks undergoing shear on a confocal microscope and compare this to bulk rheological measurements. We track individual fiber branchpoints as function of system strain. We characterize the non-affinity of the motion and show that the low strain, linear regime corresponds to highly non-affine motion while the high strain, nonlinear regime corresponds to affine motion. Moreover, we show that the non-linear bulk response can be well approximated by considering the fibers to be linear elastic elements with soft compressive behavior and, therefore, is a result of the topology of the network itself rather than nonlinearity of its constituents.   

Semiflexible filament networks viewed as fluctuating beam frames

We present a new method combining structural and statistical mechanics to study the entropic elasticity of semiflexible filament networks. We view a filament network as a frame structure and use structural mechanics to determine its static equilibrium configuration under applied loads in the first step. To account for thermal motion around this static equilibrium state, we then approximate the potential energy of the deformed frame structure up to the second order in kinematic variables and obtaina deformation-dependent stiffness matrix characterizing the flexibility of the network. Using statistical mechanics, we then evaluate the partition function, free energy and thermo-mechanical properties of the network in terms of the stiffness matrix. We show that penalty methods commonly used in finite elements to account for constraints, are applicable even when statistical and structural mechanics are combined in our method. We apply our framework to understand the expansion, shear, uniaxial tension and compression behavior of some simple filament networks. We are able to capture the stress-stiffening behavior due to filament reorientation and stretching out of thermal fluctuations, as well as the reversible stress-softening behavior due to filament buckling.   

Spindle Assembly and Architecture: From Laser Ablation to Microtubule Nucleation

Spindles are arrays of microtubules that segregate chromosomes during cell division. It has been difficult to validate models of spindle assembly due to a lack of information on the organization of microtubules in these structures. Here we present a novel method, based on femtosecond laser ablation, capable of measuring the detailed architecture of spindles. We used this method to study the metaphase spindle and find that microtubules are shortest near poles and become progressively longer towards the center of the spindle. These data, in combination with mathematical modeling, high resolution imaging, and biochemical perturbations, are sufficient to reject previously proposed mechanisms of spindle assembly. Our results support a new model of spindle assembly in which microtubule polymerization dynamics are not spatially regulated, microtubule transport locally sorts microtubules -- determining their proper organization in the spindle without moving them appreciable distances --, and the profile of microtubule nucleation controls the length of the spindle.   

Coupling stochastic kinetics and mechanics uncovers new dynamics induced by focal adhesions in filopodia

Cell motility recently became a target for physical chemists and biophysicists. It is generally understood that in real biological systems, chemical and mechanical processes are coupled, sometimes in a very complex manner. Focal adhesions (FAs) represent a biologically relevant example of multi molecular assemblies that serve a mechanical function and have intriguing biochemical properties. FAs and their role in filopodial dynamics have been extensively studied experimentally from a biological standpoint. Although there are many biochemical studies of FAs kinetics in the literature, only a few works study FA dynamics from a physical perspective. In our work we developed a robust stochastic model of the filopodia coupled to mechanical properties of FAs, retrograde flow and the substrate. We carried out extensive simulations of the filopodial stochastic growth on the timescales of minutes, as well as a detailed theoretical description of a steady state, mapping multi dimensional phase space of mechanical and kinetic parameters onto various dynamics regimes. The combination of mean field analyses with detailed microscopic simulations provides a united platform for treating mechanochemical processes underlying complex behavior of the filopodial system.   

Growth Cone Biomechanics in Peripheral and Central Nervous System Neurons

The growth cone, a highly motile structure at the tip of an axon, integrates information about the local environment and modulates outgrowth and guidance, but little is known about effects of external mechanical cues and internal mechanical forces on growth-cone mediated guidance. We have investigated neurite outgrowth, traction forces and cytoskeletal substrate coupling on soft elastic substrates for dorsal root ganglion (DRG) neurons (from the peripheral nervous system) and hippocampal neurons (from the central) to see how the mechanics of the microenvironment affect different populations. We find that the biomechanics of DRG neurons are dramatically different from hippocampal, with DRG neurons displaying relatively large, steady traction forces and maximal outgrowth and forces on substrates of intermediate stiffness, while hippocampal neurons display weak, intermittent forces and limited dependence of outgrowth and forces on substrate stiffness. DRG growth cones have slower rates of retrograde actin flow and higher density of localized paxillin (a protein associated with substrate adhesion complexes) compared to hippocampal neurons, suggesting that the difference in force generation is due to stronger adhesions and therefore stronger substrate coupling in DRG growth cones.   

An Atomic Force Microscopy based investigation of specific biomechanical properties for various types of neuronal cells

Here we describe the use of Atomic Force Microscope (AFM) based techniques to characterize and explore the influence of biochemical and biomechanical cues on the growth and interaction of neuronal cells with surrounding guidance factors. Specifically, we use AFM topography and AFM force spectroscopy measurements to systematically investigate the morphology, elasticity, and real time growth of neuronal processes in the presence of different types of extracellular matrix proteins and growth factors. We therefore create a series of systems containing specified neuron densities where the type of the underlying growth promoting protein is different from sample to sample. For each system we measure key biomechanical parameters related to neuronal growth such as height and elastic modulus at multiple growth points on several types of neurons. We show that systematic measurements of these parameters yield fundamental information about the role played by substrate-plated guidance factors in determining elastic and morphological properties of neurons during growth.   

Nuclear Physics in a biological context

A solid tissue can be soft like fat or brain, stiff like striated muscle and heart, or rigid like bone -- and of course every cell has a nucleus that contributes in some way small or large to tissue mechanics. Indeed, nuclei generally exhibit rheology and plasticity that reflects both the chromatin and the nuclear envelope proteins called lamins, all of which change in differentiation. Profiling of tissue nuclei shows that the nuclear intermediate filament protein Lamin-A/C varies over 30-fold between adult tissues and scales strongly with micro-elasticity of tissue, while other nuclear envelope components such as Lamin-B exhibit small variations. Lamin-A/C has been implicated in aging syndromes that affect muscle and fat but not brain, and we find nuclei in brain-derived cells are indeed dominated by Lamin-B and are much softer than nuclei derived from muscle cells with predominantly Lamin-A/C. In vitro, matrix elasticity can affect expression of nuclear envelope components in adult stem cells, and major changes in Lamin-A/C are indeed shown to direct lineage with lower levels favoring soft tissue and higher levels promoting rigid tissue lineage. Further molecular studies provide evidence that the nucleus transduces physical stress. References: (1) J.D. Pajerowski, K.N. Dahl, F.L. Zhong, P.J. Sammak, and D.E. Discher. Physical plasticity of the nucleus in stem cell differentiation. PNAS 104: 15619-15624 (2007). (2) A. Buxboim, I. Ivanova, and D.E. Discher. Matrix Elasticity, Cytoskeletal Forces, and Physics of the Nucleus: how deeply do cells `feel' outside and in? Journal of Cell Science 123: 297-308 (2010).