Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, machine learning alone ignores the fundamental laws of physics and can result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large datasets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

The purpose of this letter is to investigate the geometry of new classes of solitonlike solutions for integrable nonlinear equations. One example is the class of peakons introduced by Camassa and Holm [1993] for a shallow water equation. We put this equation in the framework of complex integrable Hamiltonian systems on Riemann surfaces and using special limiting procedures, draw some consequences from this setting. Among these consequences, one obtains new solutions such as quasiperiodic solutions, n-solitons, solitons with quasiperiodic background, billiard, and n-peakon solutions and complex angle representations for them. Also, explicit formulas for phase shifts of interacting soliton solutions are obtained using the method of asymptotic reduction of the corresponding angle representations. The method we use for the shallow water equation also leads to a link between one of the members of the Dym hierarchy and geodesic flow on N -dimensional quadrics. Other topics, planned for a forthcoming paper, are outlined.

Many bacteria can rapidly traverse surfaces from which they are extracting nutrient for growth. They generate flat, spreading colonies, called swarms because they resemble swarms of insects. We seek to understand how members of any dense swarm spread efficiently while being able to perceive and interfere minimally with the motion of others. To this end, we investigate swarms of the myxobacterium, Myxococcus xanthus. Individual M. xanthus cells are elongated; they always move in the direction of their long axis; and they are in constant motion, repeatedly touching each other. Remarkably, they regularly reverse their gliding directions. We have constructed a detailed cell-and behavior-based computational model of M. xanthus swarming that allows the organization of cells to be computed. By using the model, we are able to show that reversals of gliding direction are essential for swarming and that reversals increase the outflow of cells across the edge of the swarm. Cells at the swarm edge gain maximum exposure to nutrient and oxygen. We also find that the reversal period predicted to maximize the outflow of cells is the same (within the errors of measurement) as the period observed in experiments with normal M. xanthus cells. This coincidence suggests that the circuit regulating reversals evolved to its current sensitivity under selection for growth achieved by swarming. Finally, we observe that, with time, reversals increase the cell alignment, and generate clusters of parallel cells.gliding motility ͉ stochastic model ͉ pattern formation ͉ cell alignment ͉ oscillate

ETOC: The behavior of a dimer-scale computational model predicts that short interprotofilament “cracks” (laterally unbonded regions between protofilaments) exist even at the tips of growing MTs and that rapid fluctuations in the depths of these cracks govern both catastrophe and rescue.

Binaries and source code for Microsoft Windows, Linux and Solaris are available for download from http://sourceforge.net/projects/compucell/

A two-dimensional multiscale model is introduced for studying formation of a thrombus (clot) in a blood vessel. It involves components for modelling viscous, incompressible blood plasma; non-activated and activated platelets; blood cells; activating chemicals; fibrinogen; and vessel walls and their interactions. The macroscale dynamics of the blood flow is described by the continuum Navier-Stokes equations. The microscale interactions between the activated platelets, the platelets and fibrinogen and the platelets and vessel wall are described through an extended stochastic discrete cellular Potts model. The model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus, which is confirmed by the preliminary experimental data. We also make predictions about different stages in thrombus development, which can be tested experimentally and suggest specific experiments. Lastly, we demonstrate that the dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.

Blood clot contraction plays an important role in prevention of bleeding and in thrombotic disorders. Here, we unveil and quantify the structural mechanisms of clot contraction at the level of single platelets. A key elementary step of contraction is sequential extension–retraction of platelet filopodia attached to fibrin fibers. In contrast to other cell–matrix systems in which cells migrate along fibers, the “hand-over-hand” longitudinal pulling causes shortening and bending of platelet-attached fibers, resulting in formation of fiber kinks. When attached to multiple fibers, platelets densify the fibrin network by pulling on fibers transversely to their longitudinal axes. Single platelets and aggregates use actomyosin contractile machinery and integrin-mediated adhesion to remodel the extracellular matrix, inducing compaction of fibrin into bundled agglomerates tightly associated with activated platelets. The revealed platelet-driven mechanisms of blood clot contraction demonstrate an important new biological application of cell motility principles.

Fibrin is a protein polymer that forms a 3D filamentous network, a major structural component of protective physiological blood clots as well as life threatening pathological thrombi. It plays an important role in wound healing, tissue regeneration and is widely employed in surgery as a sealant and in tissue engineering as a scaffold. The goal of this study was to establish correlations between structural changes and mechanical responses of fibrin networks exposed to compressive loads. Rheological measurements revealed nonlinear changes of fibrin network viscoelastic properties under dynamic compression, resulting in network softening followed by its dramatic hardening. Repeated compression/decompression enhanced fibrin clot stiffening. Combining fibrin network rheology with simultaneous confocal microscopy provided direct evidence of structural modulations underlying nonlinear viscoelasticity of compressed fibrin networks. Fibrin clot softening in response to compression strongly correlated with fiber buckling and bending, while hardening was associated with fibrin network densification. Our results suggest a complex interplay of entropic and enthalpic mechanisms accompanying structural changes and accounting for the nonlinear mechanical response in fibrin networks undergoing compressive deformations. These findings provide new insight into the fibrin clot structural mechanics and can be useful for designing fibrin-based biomaterials with modulated viscoelastic properties.