Victor Barocas, Multi-Scale Mechanics of Bioengineered Tissues

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.

James Bassingthwaighte, Adaptive Multi-Scale Model Simulation, Reduction and Integration for Cardiac Muscle Physiology

Daniel Beard, Multi-Scale Modeling of the Heart in Metabolic Syndrome and Cardiovascular Disease

Our work to date on this project has focused on capturing the physiological state of the heart—specifically the integrated components of energy metabolism, electrophysiology, and coronary transport—in a computer model at the appropriate level of detail upon which metabolic dysfunction in cardiovascular disease can be naturally imposed. Several important outcomes have emerged from our analysis of the physiological system. The first concerns the mechanism of maintaining metabolic stability in the heart in response to changes in work rate. The mechanism of metabolic control has eluded explanation for three decades because it has been assumed that the substrates for oxidative phosphorylation (ADP and Pi) do not vary enough for feedback to significantly contribute to metabolic control in vivo. However, by analyzing data from 31phosphate-magnetic resonance spectroscopy (31P-MRS) we have determined that feedback-driven control is sufficient to explain the observed data. Our detailed mechanistic model of integrated oxygen transport and oxidative metabolism not only explains the observed data, but also predicts that the maximal work rate of the heart is an emergent property and is limited not simply by the maximal rate of ATP synthesis, but by the maximal rate at which ATP can be synthesized at a potential at which it can be utilized. Novel predictions associated with this finding are validated based on independent data obtain 31P-MRS data obtained during acute ischemia and recovery. In sum, our mass-, charge-, and energy-balanced model of oxygen transport and energy metabolism in the heart provides a unique and deeply validated platform for further investigations into roles of metabolism and mitochondrial function and dysfunction in cardiac health and disease.

James Brasseur, Micro-Scale Transport as a Critical Link between Molecular-Scale Absorption and Macro-Scale Mixing in Gut Physiology and Function

Abstract: Absorption and secretion of nutrients in the small intestine occur at the epithelial lining of the gut mucosa. The epithelial cells cover multitudes of villi, fingerlike protrusions ~ 200 m in scale that line the mucosal surface. The gut functions to transport nutrient molecules at the centimeter scale from the bulk flow to the epithelium, and secretions from the villus crypts to the bulk flow. Using combinations of multi-scale modeling with dynamic magnetic resonance imaging (MRI) of the motions of the gut lumen and villi, we have investigated the hypothesis that gut function requires the coupling of macro-scale mixing motions at the cm scale, with micro-scale mixing generated by villi motions at the 100 m scale. We developed a modeled within the lattice-Boltzmann framework with second order moving boundary conditions and passive scalar to predict the couplings between macro and micro scale velocity and passive scalar fields on coupled macro- and micro-scale grids. Macro-scale gut motions were quantified from time-resolved (dynamic) magnetic resonance imaging (MRI) of the in vivo rat jejunum using three-dimensional segmentation. The gut wall motions were analyzed using principle component analysis with “active shape models” combined with topographic representation of space-time deformation and frequency analysis.

Marco Cabrera, Time Course of Metabolic Adaptations during Loading and Unloading (Intracellular Mechanisms of Regulation of Muscle Metabolism During Exercise) Abstract: Skeletal muscle can maintain intracellular [ATP] constant during the transition from rest to exercise, while reaction rates may increase significantly. Among the key regulatory factors, the dynamics of cytosolic and mitochondrial NADH and NAD+ during exercise have not been characterized. To determine the extent of regulation exerted by these intracellular metabolic signals on skeletal muscle metabolism at the onset of exercise, a computational model was developed. In this model, transport and metabolic fluxes in distinct capillary, cytosolic, and mitochondrial domains are integrated. We hypothesized that during the transition from rest to exercise (60% VO2max), the dynamics of lactate concentration [Lac] in exercising muscle is independent of mitochondrial redox state. We tested this hypothesis by simulating the metabolic responses of skeletal muscle to exercise, while altering the transport rate of reducing equivalents from cytosol to mitochondria and muscle glycogen content. Simulation with optimal parameter estimates showed good agreement with experimental data from muscle biopsies in human subjects. Compared with the optimal values, a 20% increase (decrease) in NADH transport coefficient led to an 85% decrease (7-fold increase) in cytosolic redox state, and ~50% decrease (~85% increase) in muscle [Lac]. Doubling (halving) glycogen concentration resulted in a 30% increase (20% decrease) in cytosolic redox state, and ~10% increase (~25% decrease) in [Lac]. In both cases, mitochondrial redox states had minor changes. In conclusion, simulations suggest that the regulation of lactate production at the onset of exercise (~60% VO2max) is primarily dependent on the dynamics of cytosolic redox state and independent of mitochondrial redox state.

David Cai, Collaborative Research: Cortical Processing across Multiple Time and Space Scales

We have been modeling the dynamics of the primary visual cortex (V1), both computationally and theoretically, using a large, multi-scale neuronal network. We have been focusing on the role of the local (<0.5 mm), isotropic, and long-range (0.5-5mm), orientation specfic cortico-cortical connections, and their interplay with the LGN afferents, in the cortical dynamics. We have also investigated the roles of excitation and inhibition, in particular, the AMPA, NMDA, and GABA_A neuronal conductances. Within a single cortical architecture and operating state, we have been able to hypothesize mechanisms underlying several distinct experimentally-observed V1 phenomena within patches of about 8-by-8 orientation pinwheels containing about a million neurons. Two of these are large-scale phenomena, first observed experimentally in anesthetized cats. The first is spatio-temporal patterns of spontaneous cortical activity, which are highly correlated on the scales of about 4 mm, appear to become activated in multiple areas of iso-orientation preference, and tend to migrate to nearby such areas after about 80 ms, the NMDA conductance decay time-scale. The second is spatio-temporal activity in V1 associated with the pre-attentive Hikosaka line-motion illusion. This illusion is induced by showing a small square followed by a long bar to create the illusion of the square "growing" to become the bar. In V1, actual subthreshold cortical activity that corresponds to the "growth" of the square into the bar, similar to that caused by real motion, was detected on the mm spatial scale and 60-100 ms time scale. We have been able to reproduce these phenomena in a physiologically plausible operating state of the model cortical patch of V1. This state is characterized by high total conductance; strong inhibition; large synaptic fluctuations; important role of NMDA conductance in the orientation-specific, long-range interactions; and high degree of correlation among neuronal membrane potentials, NMDA-type conductances, and firing rates. The last phenomenon is neuronal orientation tuning in V1. We have found that an intricate bifurcation mechanism underlies the orientation tuning of complex cells in V1. We have been able to reproduce the correct distributions of neuronal membrane potentials and conductances (location-dependent), and firing rates (location-independent), with respect to the neuron's location in the orientation map. In addition to the large-scale neuronal model, we have also developed coarse-grained models based on kinetic theory.

Yoonsuck Choe, Multi-Scale Imaging, Analysis, and Integration of Brain Networks

Abstract: The mammalian nervous system exhibits intricate structural (anatomical) organization at multiple scales, subsuming specific functional roles. In this project, we investigated such structural organizations and their relationships in the mouse brain at three levels of detail: nanoscale (tens of nanometers), microscale (several micrometers), and macroscale (hundreds of micrometers up to several millimeters). The use of innovative volume microscopy techniques has played a key role in this respect. We employed data from the Serial Block-Face Scanning Electron Microscopy (nanoscale), Array Tomography (nanoscale and microscale), Knife-Edge Scanning Microscopy (KESM, microscale), and Magnetic Resonance Microscopy (MRM, macroscale) to obtain an accurate structural reconstruction of mouse brain circuits and analyze their functions. A major part of the project focused on developing the microscopy techniques (KESM and Array Tomography) and fully automating them, and another part focused on efficient 3D reconstruction algorithms, structural analysis algorithms, and data organization and dissemination methods for data and model sharing. We expect our extensive data and dissemination framework to enable major discoveries, both by us and other neuroscience researchers.

James Glazier, Multi-Scale Studies of Segmentation in Vertebrate Embryos

Trent Guess, Dynamic Simulation of Joints Using Multi-Scale Modeling

Abstract: Dynamic loading of the knee plays a significant role in the development and progression of tissue wear disease and injury. Dynamic rigid-body models provide insight into body-level biomechanics and their computational efficiency facilitates dynamic simulation of neuromusculoskeletal systems. A major limitation of rigid-body models is their simplistic (or non-existent) representation of tissue-level structures. This limitation prevents holistic computational approaches to investigating the complex interactions of knee structures and tissues, a limitation that hinders our understanding of the underlying mechanisms of knee injury and disease. This grant supports development of surrogate models, such as neural networks, that reproduce the dynamic behavior of menisci-tibio-femoral articulations within the rigid body framework. These surrogates learn from finite element method solutions and are validated using a dynamic knee loading machine.

Teresa Head-Gordon, Multi-Scale Models to Study How Spatial Organization of Cellular Components Influences Signaling

Roger Kamm, An Agent-Based Markovian Model for Angiogenesis

Abstract: Angiogenesis is the process by which blood vessels form from an endothelial monolayer. Development of angiogenesis models is essential to understand the contribution of various factors (biochemical and biomechanical) involved in the process. Many existing models fail to account for cell-cell communication or the response of each cell to various angiogenic factors. Also, a comprehensive analysis of signaling pathways is lacking. This study aims at understanding the response of cell populations, wherein each cell is modeled by using Markov process, responding to certain global and local conditions. Thus, feedback loops (local and global) which are crucial to the biological process are an integral part of the model. The overall model is stochastic and the probabilities of transition between cell states (quiescent/ migrating/ dividing/ dying) are based on output from the cue-signal-response model. The transition probabilities are functions of the current cell state and the cues added to the system. The direction of transition (migration/division) depends on matrix properties, which change every time step and affect the cell state in the following step. One mathematical challenge is dealing with the different timescales of intra-cellular and inter-cellular interactions. The overarching objective is to obtain a complete model of angiogenesis as it pertains to a controlled, in vitro experimental system with a reduced number of variables.

George Karniadakis, A Stochastic Molecular Dynamics Method for Multi-Scale Modeling of Blood Platelet Phenomena

Abstract: The goal of this project is to simulate platelet aggregation in capillaries and larger arteries and develop a seamless multiscale method that can also be applied to other microfluidic and nanofluidic problems. We developed and validated algorithms that make Dissipative Particle Dynamics (DPD) method a very effective simulation tool for biological flows. We formulated the DPD method for blood-platelet phenomena and validated it with in vivo experimental results. We have shown that DPD can be interfaced with molecular dynamics at the atomistic level as well as with Navier-Stokes at the continuum level. In addition, we developed a systematic coarse-graining procedure for modeling red blood cells (RBCs) using arguments based on mean-field theory. The sensitivity of the coarse-grained model was investigated and validated against available experimental data and in DPD simulations of RBCs in microcirculation.

Denise Kirschner,Stewart Chang, Jennifer Linderman, A Multi-Scale Approach for Understanding Antigen Presentation in Immunity

Robert Kunz, Multi-Scale Human Respiratory System Simulations to Study the Health Effects of Aging, Disease and Inhaled Substances Abstract: This project has focused on developing and integrating computational modeling tools for simulation of human respiration. The goal of the effort is to establish a software capability to perform end-to-end clinical imaging-through CFD simulation of patients with injury or disease, to aid in diagnosis. To date we have evolved all of the necessary components and integrated them in a semi-automated toolkit. Specifically, semi-automated or automated software has been adopted and/or modified and/or written to perform 1) segmentation of lung branch and lobe geometries from medical images, 2) "thinning" to obtain branch topology, 3) partitioning and truncation of upper airways, 4) Octree based grid generation with prism layers for the upper airways, 5) lobe volume filling with attendant quasi-1D arbitrary polyhedral meshing for the lower branches, including topology conserving unsteady volume filling (to accommodate lobe geometry change during respiration), 6) Incorporation of the near-head atmosphere and oro-pharyngeal cavity, 7) Adoption of time-dependent respiratory-unit volume based boundary conditions at the convective regime leaves, as well as unsteady 2nd order boundary conditions for wall and pressure boundaries, 8) Fluid-structure interaction modeling to accommodate bronchiole elasticity, 9) Master scripting to control the various component of the simulation system, and 10) Computational fluid dynamics software modifications to accommodate several components of these simulations including multiphase flow, "wall-less" Q1D elements with bulk turning and loss modeling, branch attribute propagation from the volume filling algorithm for branch loss modeling, "piston-like" volume boundary conditions. These posters present the status of this work.

Anthony Ladd, Multi-Scale Modeling of Chemical-to-Mechanical Energy Conversion in Actin-Based Motility

Ching-Long Lin, Multi-Scale Simulation of Gas Flow Distribution in the Human Lung

Abstract: This poster describes the methodologies and technologies developed for multi-scale simulations of subject-specific pulmonary air flow. Variation in individual airway geometry makes subject-specific models essential for the study of pulmonary air flow and drug delivery. Recent evidence also suggests that early exposure to environmental pollutants has chronic, adverse effects on lung development in children from the age of 10 to 18 years. Thus, the capability of predicting air flow and particle deposition in the subject-specific human lungs is essential in understanding the correlation between structure and function, and for assessing individual differences in vulnerability to airborne pollutants. This project aims to develop a comprehensive computational fluid dynamics (CFD) model for pulmonary flow that utilizes subject-specific airway geometries, spans spatial scales from the largest bronchial airways to alveolar sac, and employs a Computed Tomography (CT) data-driven, multistage approach to provide accurate predictions of regional ventilation and gas transport through the entire moving airway tree. This effort brings together expertise in medical imaging, geometric modeling, high-performance computing, and physiology and medicine. The potential applications of the model include optimizing pharmaceutical aerosol drug delivery, advancing xenon or helium enhanced CT/MRI imaging, and predicting subject-specific regional ventilation for diagnosis of patterns related to pathologic changes in airway geometry and parenchyma.

Ernst Georg Luebeck, Scales of Carcinogenesis: Cells, Crypts and Cancer

Abstract: Carcinogenesis is an inherently multiscale phenomenon. Most cancer research is currently focused on the intracellular effects of mutations or epidemiological observations on populations. Relatively little is known about the dynamics of cells structured into the proliferative units of tissues and the neoplastic clones possibly comprised of hundreds of thousands of those proliferative units, and their roles in cancer. Our project addresses the question how tissue architecture, in particular the crypt structure of intestinal epithelia, modulates the accumulation of (epi)genetic lesions, how clonal expansions arise in neoplasms, and importantly, what are the temporal and spatial scales of clonal expansions on the pathway to cancer. Our project is an attempt to synthesize the various aspects of this problem (ultimately integrating cell biology, microenvironment, cell-cell interactions, evolutionary biology, mutation accumulation and clonal evolution) into a more informed theory of multistage and multiscale carcinogenesis.

The main achievement of this project is the development of a computational (Java-based) model of neoplastic progression in a 2-D tissue of proliferative units (crypts) that spans spatial scales from the level of the cell to the level of the neoplasm in the tissue, and temporal scales that span days (say, the time between cell divisions) to years of somatic clonal evolution. This model can be used to interrogate the system with 'what-if' questions to better understand the roles of tissue stem cells, crypt architecture, and to generate testable hypotheses for the dynamics of neoplastic progression. We summarize the main results and conclusions of 4 papers related to this project .

Andrew McCulloch, Stuart Campbell, Roy Kerckhoffs, ANushka Michailova. Multi-Scale Modeling of the Mouse Heart: From Genotype to Phenotype

Abstract: The goal of this project is to develop mechanistic multi-scale models that can predict the electromechanical function of the failing heart in genetically engineered mouse models with defects in genes responsible for the regulation of cardiac contraction. We have studied several different mouse models and are currently focusing on mice harboring mutations in MLC2v which render the regulatory light chain of myosin non-phosphorylatable. The multi-scale models span the following scales protein states in the regulatory unit, regulatory network, whole cell, multi-cellular, tissue, whole organ, and circulatory system. This poster will show new results especially in relation to: Markov model of the regulation of thin filament activation and the role of cooperative interactions between adjacent regulatory units; Whole cell systems models of the myocyte excitation contraction coupling; Microstructural modeling of murine ventricular myocardium fiber and sheet architecture; Whole organ continuum modeling of ventricular electromechanics and the influence of regional heterogeneities in protein expression. Much of this work uses the multi-scale modeling package Continuity, developed with support of a MSM grant from NSF and the National Biomedical Computation Resource, an NIH P41 grant.

Peter Ortoleva, Bifurcation and Self-Organized Cellular Structure and Dynamics: Intercellular Genomics of Subsurface Microbial Colonies

Stephen Pankavich, Yinglong Miao, Zeina Shreif, Peter Ortoleva. All-atom Multiscale Analysis (AMA) Theory and Application to Virology

Abstract: Viruses and other bionanosystems undergo structural processes across multiple time and length scales. We introduce order parameters generated with orthogonal polynomials to capture their slowly-varying nanoscale dynamics and derive a stochastic (Fokker-Planck or Smoluchowski) equation for the order parameters through a multiscale analysis of the N-atom Liouville equation. The AMA theory justifies a Molecular Dynamics/Order Parameter eXtrapolation (MD/OPX) approach for simulating large bionanosystems. It greatly accelerates MD code and is demonstrated on viral structural transitions.

Niles Pierce, Analysis of Coarse-Grained Nucleic Acid Free Energy Landscapes

Jay Schieber, CISE: Multi-Scale Modeling to Develop a Cyberinfrastructure for the Dynamics of Flexible and Stiff Entangled Macromolecules

Stanislav Shvartsman, Collaborative Research: Multi-Scale Analysis of Epithelial Patterning: Modeling and Experiments

Michela Taufer, DAPLDS: A Dynamically Adaptive Protein-Ligand Docking System Based on Multi-Scale Modeling

Abstract: The DAPLDS project, aims to build a computational environment to assist scientists in understanding the atomic details of protein-ligand interactions. High-throughput, protein-ligand docking simulations are performed on a computational environment that deploys a large number of volunteer computers (donated compute cycles) connected to the Internet. The scales proposed in DAPLDS are not the traditional scales currently used in the life sciences. We deal with computational rather than experimental multi-scales. Our multi-scale approach comprises three spanning scales (dimensions) of docking assumptions: protein-ligand representation, solvent representation, and sampling strategy. Within a scale, different scale values require different models and different algorithms to represent the models.In such a scenario, the two most critical challenges in dealing with multiple scales computationally are: (1) the ability to model biological systems with algorithms that dynamically adapt to the most appropriate value of each scale and (2) the ability to assure that the algorithms can, indeed, be executed in the “required” amount of time using large numbers of distributed volunteer computing systems. The latter point refers to having the necessary computational resources (CPU cycles, memory, network, etc.). The nature of these challenges requires collaboration among computational biophysicists, computational scientists, computer scientists, and system architects. These challenges and our main achievements are presented in this poster.

Bridget Wilson, Mapping and Modeling ErbB Receptor Membrane Topography

Abstract:Our goal is to understand the topographical regulation of ErbB signaling in breast and endometrial cancers, where amplification of ErbB1 (the EGFR) or ErbB2 genes is associated with poor outcome. Specifically, we propose: 1) to map the topography of ErbB receptors and their associated signaling molecules using innovative electron microscopy techniques; 2) to apply rigorous biochemical and statistical analyses to establish quantities of signaling molecules, their distributions and their relationships; and 3) to use these spatial and quantitative data as a framework for multiscale simulations of the signaling process. In work that is now in press, we report on first electron microscopy images mapping distributions of ErbB receptors on SKBR3 breast cancer cell membranes. We found the most abundant receptor, ErbB2, is phosphorylated, clustered and active. Kinase inhibitors ablate ErbB2 phosphorylation without dispersing clusters. Modest coclustering of ErbB2 and EGFR, even after EGF treatment, suggests that both are predominantly involved in homointeractions. This observation, in particular, suggests that previous mathematical models overestimate heterodimerzation. We also show some usual topographic distributions for receptors and associated signaling molecules. For example, Heregulin leads to dramatic clusters surrounded by PI 3-kinase. Other docking proteins, Shc and STAT5, respond differently to receptor activation. Levels of Shc at the membrane increase 2-5 fold with EGF while preassociated STAT5 becomes strongly phosphorylated. These data suggest that the distinct topography of receptors and their docking partners modulates signaling activities. We are using several mathematical modeling approaches to evaluate these data and to build predictive models of signal transduction during carcinogenesis and response to therapy. We report on novel use of Markov Random Field modeling to simulate relative locations of receptors and signaling molecules, revealing “hidden states” or associations. We also report on results using an agent-based, stochastic model designed to simulate receptor diffusion, clustering, dimerization & signal propagation in a spatially realistic manner.