Session X39: Biomechanics: From Subcellular to Multicellular Scales

Simple, Voltage Dependent Statistics Governing Cell-Substrate Contact Times

The distribution of contact times between a nanofilament-based contact sensor and individual pseudopods of \textit{D. discoideum} have been measured as a function of voltage applied to the filament. The distributions are well described by exponential distributions. The average duration of the pseudopod-filament contact was found to increase across the +20 mV to -50 mV range of filament-voltages. These results are consistent with the predictions of a simple model based on rather general considerations of energy usage by the cell. This analysis indicates that the exponential functionality (of the contact time distributions) results from competition between a large number of cellular processes for the available energy. The evolution of these distributions across the +20 mV to -50 mV voltage range suggests that the negatively biased filament enhances adhesion to the filament by activating additional adhesion molecules to bind to its surface. These results will be discussed in the context of recent findings on the coupling of voltage gated ion channels and cellular adhesion.   

Multiscale modeling of the dynamics of multicellular systems

Describing the biomechanical properties of cellular systems, regarded as complex highly viscoelastic materials, is a difficult problem of great conceptual and practical value. Here we present a novel approach, referred to as the Cellular Particle Dynamics (CPD) method, for: (i) quantitatively relating biomechanical properties at the cell level to those at the multicellular and tissue level, and (ii) describing and predicting the time evolution of multicellular systems that undergo biomechanical relaxations. In CPD cells are modeled as an ensemble of cellular particles (CPs) that interact via short range contact interactions, characterized by an attractive (adhesive interaction) and a repulsive (excluded volume interaction) component. The time evolution of the spatial conformation of the multicellular system is determined by following the trajectories of all CPs through integration of their equations of motion. Cell and multicellular level biomechanical properties (e.g., viscosity, surface tension and shear modulus) are determined through the combined use of experiments and theory of continuum viscoelastic media. The same biomechanical properties are also ``measured'' computationally by employing the CPD method, the results being expressed in terms of CPD parameters. Once these parameters have been calibrated experimentally, the formalism provides a systematic framework to predict the time evolution of complex multicellular systems during shape-changing biomechanical transformations. By design, the CPD method is rather flexible and most suitable for multiscale modeling of multicellular system. The spatial level of detail of the system can be easily tuned by changing the number of CPs in a cell. Thus, CPD can be used equally well to describe both cell level processes (e.g., the adhesion of two cells) and tissue level processes (e.g., the formation of 3D constructs of millions of cells through bioprinting).   

Theoretical estimation of the breakage intensity of microtubules at resonance using ultrasound waves

Microtubules (MTs) are protein filaments forming a major part of the cytoskeleton of all eukaryotic cells which directly contribute to the process of cell division by forming mitotic spindles and providing force for the segregation of chromosomes. In this work first we show the resonance condition for MTs subject to ultrasound wave by solving the beam equation for MT analytically. Then we estimate the required minimum intensity of the ultrasound at the location of the MT in order to break it. We have shown that this intensity is of the order of 100KW per unit of area which corresponds to 170 dB.   

Flexural Rigidity of MCF-7 Microtubules Measured from Thermal Fluctuations in Shape

Microtubules play a key role in the mechanical and elastic properties of eukaryotic cells. For this reason, measuring the flexural rigidity of bovine brain microtubules have been extensively investigated through different methods of measurement. Beta tubulin isotypes, a noticeable trait to consider as we transfer from mammalian neural microtubules to mammalian non-neural microtubules, are assembled differently in distributions among various types of microtubules. Different studies have shown that microtubules made from different beta-tubulin isotypes express unique polymerization and dynamic behavior. This study focuses on measuring mechanical properties of one of non-neural microtubules, MCF-7. We will discuss the structure differences between brain bovine microtubules and MCF-7, along with the rigidity of single microtubules polymerized from MCF-7 tubulin through monitoring the curvature of microtubule due to thermal fluctuations.   

Persistence Length of Stable Microtubules

Microtubules are a vital component of the cytoskeleton. As the most rigid of the cytoskeleton filaments, they give shape and support to the cell. They are also essential for intracellular traffic by providing the roadways onto which organelles are transported, and they are required to reorganize during cellular division. To perform its function in the cell, the microtubule must be rigid yet dynamic. We are interested in how the mechanical properties of stable microtubules change over time. Some ``stable'' microtubules of the cell are recycled after days, such as in the axons of neurons or the cilia and flagella. We measured the persistence length of freely fluctuating taxol-stabilized microtubules over the span of a week and analyzed them via Fourier decomposition. As measured on a daily basis, the persistence length is independent of the contour length. Although measured over the span of the week, the accuracy of the measurement and the persistence length varies. We also studied how fluorescently-labeling the microtubule affects the persistence length and observed that a higher labeling ratio corresponded to greater flexibility.   

Modeling actin waves in dictyostelium cells

Actin networks in living cells demonstrate a high capacity for self-organization and are responsible for the formation of a variety of structures such as lamellopodia, phagocytic cups, and cleavage furrows. Recent experiments have studied actin waves formed on the surface of dictyostelium cells that have been treated with a depolymerizing agent. These waves are believed to be physiologically important, for example, for the formation of phagocytic cups. We propose and study a minimal model, based on the dendritic nucleation of actin polymers, to explain the formation of these waves. This model can be extended to study the dynamics of the coupled actin-membrane system.   

Force Generated by Actin Array

We study a theoretical model for a group of parallel filaments growing against a barrier held by a constant force. An array of N filaments nucleate on a fixed surface and grow towards a rigid barrier which is held in place by a constant force. Filaments are coupled only by mechanical contact against the barrier. We obtain the filament density distribution in terms of the distance from the barrier, and force-velocity curves. We apply our model to the case of an array of actin filaments. All results are validated by extensive Monte-Carlo simulations. For a small value of N we find the stall force to be N times the stall force of a single filament ($f_{stall}\approx Nf_{stall}^1$). For large N we find that the velocity \textit{appears} to be considerably smaller, an effect due to its exponential decrease as the theoretical stall force is approached.   

BSDB: the Biomolecule Stretching Database

Despite more than a decade of experiments on single biomolecule manipulation, mechanical properties of only several scores of proteins have been measured. A characteristic scale of the force of resistance to stretching, $F_{max}$, has been found to range between $\sim$10 and 480 pN. The Biomolecule Stretching Data Base (BSDB) described here provides information about expected values of $F_{max}$ for, currently, 17 134 proteins. The values and other characteristics of the unfolding proces, including the nature of identified mechanical clamps, are available at www://info.ifpan.edu.pl/BSDB/. They have been obtained through simulations within a structure-based model which correlates satisfactorily with the available experimental data on stretching. BSDB also lists experimental data and results of the existing all-atom simulations. The database offers a Protein-Data-Bank-wide guide to mechano-stability of proteins. Its description is provided by a forthcoming Nucleic Acids Research paper.   

The nonequilibrium thermodynamics and kinetics of focal adhesion dynamics

We consider a focal adhesion (FA) to be made up of molecular complexes consisting of ligands, integrins, and associated plaque proteins. Free energy changes drive the binding and unbinding of these complexes, thus controlling the FA's dynamic modes of growth, treadmilling and resorption via the following mechanisms: (\romannumeral 1) work done during the addition of molecular complexes, (\romannumeral 2) the chemical free energy of addition of a molecular complex, (\romannumeral 3) the elastic free energy of deformation of FAs and the cell membrane, and (\romannumeral 4) the work done on a molecular conformational change. We have developed a treatment of FA dynamics as a nonlinear rate process driven by out-of-equilibrium thermodynamic driving forces, and modulated by kinetics. The mechanisms governed by the above four effects allow FAs to exhibit a rich variety of behavior, predicting growth, treadmilling and resorption. Treadmilling requires symmetry breaking between the ends of the focal adhesion, and is achieved by driving force (\romannumeral 1) above. In contrast, the remaining mechanisms cause symmetric growth or resorption. These findings hold for a range of conditions: temporally-constant force or stress, and for spatially-uniform and non-uniform stress distribution over the FA. This treatment of FA dynamics can be coupled with models of cytoskeleton dynamics and contribute to the understanding of cell motility.