While biosystems have been analyzed using models appropriate for phenomena on given spatio-temperal scales, efforts to combine them into a unified, multiscale model have been hampered due to ambiguities arising from the need to interface the models. The theme of this minisymposium is that a rational development of the muliscale model should start with the finest scale model and then through various mathematical techniques the coarse-grained models should follow. Techniques of interest include homogenization and renormalization group analysis, information theory and statistical ensembles, asymptotic expansions, and multiscale computational approaches. The finest scale equations providing the starting points for the analysis include molecular physics (classical and quantum mechanical) and hydrodynamics. The benefits to the pure and applied life sciences that will follow this deductive approach will be models that require a minimum of calibration (e.g., the interatomic force field). Systems of interest will range from the nanoscale (e.g., viruses, nanocapsules for drug dilivery, and intracellular structures) to whole complex organisms.

Selection of challenges, presentations from MSM folks that would highlight science and key areas where novel mathematical models might help, international supercomputing projects and computing

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Abstracts

Accurate coarse-graining of red blood cell models -- I.V. Pivkin, P.D. Richardson, G.E. Karniadakis

We develop a systematic coarse-graining procedure for modeling red blood cells (RBCs) using arguments based on mean-field theory. The three-dimensional RBC membrane model takes into account the bending energy, in-plane shear energy, and constraints of fixed surface area and fixed enclosed volume. The sensitivity of the coarse-grained model is investigated and its behavior is validated against available experimental data and in Dissipative Particle Dynamics (DPD) simulations of RBCs in microcirculation.

Multi-scale modeling of blood vessels using a fluid-solid growth framework -- Alberto Figueroa

Blood vessels adapt and remodel in response to changes in their mechanical and biochemical environment during development and aging, and with diseases including atherosclerosis, aneurysms, and hypertension to name just a few examples. While computational methods have been utilized separately to quantify hemodynamic conditions and to simulate growth and remodeling processes, there is a pressing need for a unified approach to model vascular adaptation and disease in response to biomechanical and biochemical stimuli. This class of Fluid‐Solid Growth (FSG) problems are inherently multi‐scale in time since the biomechanical forces due to the heart beat change on the scale of seconds whereas vascular adaptation can occur over days to weeks and diseases progress over months to years. In addition, FSG problems are multi‐scale in space since biomechanical forces and biochemical stimuli, sensed at a molecular and cellular scale, elicit adaptive and maladaptive responses from molecular to organ scales. We describe herein a novel computational method to model fluid‐solid growth problems and illustrate this method by applying it to simulate the enlargement of a cerebral vascular aneurysm in response to shear and tensile stress.

Multiscale modeling of calcium responses in realistic cell geometry -- Bridget S. Wilson, Tomas Mazel, Shawn Means

Release of inflammatory mediators by mast cells in type 1 immediate hypersensitivity allergic reactions relies on the antigen-dependent increase in cytosolic calcium. Here we used a series of electron microscopy images to build a 3D reconstruction of a rat tumor mast cell, which then served as a basis for modeling of IP3-mediated calcium responses. Local proximity of the endoplasmic reticulum (ER) to both the plasma membrane and to mitochondria is considered. We found that local ER luminal calcium concentration during IP3R transport is markedly affected by nearby organelles. In addition to compartmental and PDE-based approaches, we describe the first application of stochastic reaction-diffusion modeling within a complete 3D cell geometry. These combined approaches help to bridge the gap between measured single molecule kinetic constants and overall calcium dynamics.

Multi-scale modeling of chemical-to-mechanical energy conversion in actin-based motility -- Tony Ladd

In actin-based motility, monomeric actin polymerizes into stiff filaments from surface-bound components, which crosslink and propel the surface forward. How the chemical energy involved in monomer addition is converted into mechanical work is critical in understanding cell motility. The scientific goal of this project is based on the hypothesis that the structural and force-producing properties of the network are critically dependent on whether working filaments remain tethered by end-tracking proteins or remain untethered as required by the conventional Brownian Ratchet model. The computational goal of the project is to develop and validate a biologically relevant, multi-scale model of force generation by actin polymerization.

We are designing a computational framework for modeling the mechanical properties of solutions of stiff biopolymers such as actin, accounting for its resistance to bending and torsion, position and orientation dependent chemical functionalization along the molecular backbone, and the coupling of the polymer dynamics to the surrounding solvent. In this talk I will outline the theory underlying the mechanical model of a stiff polymer and describe some tests of our numerical implmentation. Parallel work developing the means of modeling the fluid-mitigated hydrodynamic interactions will also be described. At longer times a quasi-static approach can replace the detailed dynamic model and we are also developing Monte-Carlo simulations of thermally fluctuating filaments. Finally under high load thermal fluctuations may be ignored and the classical equilbrium theory of flexible rods used instead. I will show some preliminary calculations for individual filaments and simple filament networks.

Multi-scale modeling of collagen gel mechanics -- Victor Barocas

Collagen gels consist of an interacting network of long, thin fibers, allowing even very dilute solutions (1-3 mg/ml) to solidify. The critical challenge in understanding the mechanics of these gels (and of collagenous tissues engineered from them or native tissues) is to incorporate the network behavior, which occurs on the micrometer length scale, into the tissue behavior, which occurs on the millimeter length scale. A two-scale scheme has been developed in which the average stress is calculated on a representative network at each integration point of a finite-element representation of the tissue. The strain from the finite-element model is used to generate boundary conditions for each micro-model, which in turn provides the stress for the macroscopic scale. Further developments include a biphasic formulation to account for interstitial and image-based construction of the networks.