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public 01:29:50

Mark Alber : Modeling elastic properties of cells and fibrin networks

  -   Mathematical Biology ( 113 Views )

Viscoelastic interactions of Myxococcus xanthus cells in a low-density domain close to the edge of a swarm have been recently studied in [1] using a combination of a cell-based three-dimensional Subcellular Element (SCE) model [1,2] and cell-tracking experiments. The model takes into account the flexible nature of M. xanthus as well as the effects of adhesion between cells arising from the interaction of the capsular polysaccharide covering two cells in contact with each other. New image and dynamic cell curvature analysis algorithms were used to track and measure the change in cell shapes that occur as flexible cells undergo significant bending during collisions resulting in direct calibration of the model parameters. It will be shown in this talk that flexibility of cells and the adhesive cell–cell and cell–substrate interactions of M. xanthus together with cell to aspect-ratio and directional reversals [3], play an important role in smooth cell gliding and more efficient swarming. In the second part of the talk results of the analysis of the three dimensional structures of fibrin networks, with and without cells, reconstructed from two-dimensional z-stacks of confocal microscopy sections using novel image analysis algorithms, will be presented. These images were used to establish microstructure-based models for studying the relationship between the structural features and the mechanical properties of the fibrin networks in blood clots. The change in the fibrin network alignment under applied strain and the elastic modulus values will be shown to agree well with the experimental data [4]. 1. C.W. Harvey, F. Morcos, C.R. Sweet, D. Kaiser, S. Chatterjee, X. Lu, D. Chen and M. Alber [2011], Study of elastic collisions of M. xanthus in swarms, Physical Biology 8, 026016. 2. C.R. Sweet, S. Chatterjee, Z. Xu, K. Bisordi, E.D. Rosen and M. Alber [2011], Modeling Platelet-Blood Flow Interaction Using Subcellular Element Langevin Method, J R Soc Interface, 2011 May 18. [Epub ahead of print], doi: 10.1098/rsif.2011.0180. 3. Y. Wu, Y. Jiang, D. Kaiser and M. Alber [2009], Periodic reversal of direction allows Myxobacteria to swarm, Proc. Natl. Acad. Sci. USA 106 4 1222-1227. 4. E. Kim, O.V. Kim, K.R. Machlus, X. Liu, T. Kupaev, J. Lioi, A.S. Wolberg, D.Z. Chen, E.D. Rosen, Z. Xu and M. Alber [2011], Soft Matter 7, 4983-4992.

public 01:34:46

Gregory Herschlag : Optimal reservoir conditions for material extraction across pumping and porous channels

  -   Mathematical Biology ( 108 Views )

In this talk, I will discuss a new result in fluid flows through channels with permeable membranes with simple pumping dynamics. Fluid will be exchanged and metabolized in a simple reservoir and I will demonstrate the existence of optimal reservoir properties that may either maximize or minimized the amount of fluid being extracted across the channel walls. The biological relevance of this work may be seen by noting that all living organisms of a sufficient size rely on complex systems of tubular networks to efficiently collect, transport and distribute nutrients or waste. These networks exchange material with the interstitium via embedded channels leading to effective permeabilities across the wall separating the channel interior from the interstitium. In many invertebrates, for example, respiratory systems are made of complex tracheal systems that branch out through the entire body allowing for passive exchange of oxygen and carbon dioxide. In many of these systems, certain animals utilize various pumping mechanisms that alter the flow of the air or fluid being transported. Although the net effect of pumping of the averaged rates of fluid flow through the channel is typically well understood, it is still a largely open problem to understand how, and in what circumstances, pumping enables and enhances the exchange of material across channel walls. It has been demonstrated experimentally, for example, that when certain insects flap their wings, compression of the trachea allow for more efficient oxygen extraction, however it is unclear if this pumping is optimized for flight, oxygen uptake or neither, and understanding this problem quantitatively will shed insight on this biological process. Many of these interesting scenarios occur at low Reynolds number and this regime will be the focus of the presentation.

public 01:14:49

Leonid Berlyand : PDE/ODE models of motility in active biosystems

  -   Mathematical Biology ( 103 Views )

In the first part of the talk we present a review of our work on PDE models of swimming bacteria. First we introduce a stochastic PDE model for a dilute suspension of self-propelled bacteria and obtain an explicit asymptotic formula for the effective viscosity (E.V.) that explains the mechanisms of the drastic reduction of E.V.. Next, we introduce a model for semi-dilute suspensions with pairwise interactions and excluded volume constraints. We compute E.V. analytically (based on a kinetic theory approach) and numerically. Comparison with the dilute case leads to a phenomenon of stochasticity arising from a deterministic system. We develop a ODE/PDE model that captures the phase transition, an appearance of correlations and large scale structures due to interbacterial interactions. Collaborators: S. Ryan, B. Haines, (PSU students); I. Aronson, A. Sokolov, D. Karpeev (Argonne); In the second part of the talk we discuss a system of two parabolic PDEs arising in modeling of motility of eukaryotic cells on substrates. The two key properties of this system are (i) presence of gradients in the coupling terms (gradient coupling) and (ii) mass (volume) preservation constraints. We derive the equation of the motion of the cell boundary, which is the mean curvature motion perturbed by a novel nonlinear term and prove that the sharp interface property of initial conditions is preserved in time. This novel term leads to surprising features of the motion of the interface such as discontinuities of the interface velocity and hysteresis. This is joint work with V. Rybalko and M. Potomkin.

public 01:29:51

Karin Leiderman : Mathematical Modeling of Thrombosis

  -   Mathematical Biology ( 102 Views )