To prevent the loss of blood following a break in blood vessels, components in blood and the vessel wall interact rapidly to form a thrombus (clot) to limit hemorrhage. In this talk we will describe a multiscale model of thrombus formation consisting of components for modeling viscous, incompressible blood plasma; coagulation pathway; quiescent and activated platelets; blood cells; activating chemicals; fibrinogen; the vessel walls and their interactions. At macro scale blood flow field is described by the incompressible Navier-Stokes equations and is numerically solved using the projection method. At micro scale, cell movement, cell-cell adhesion, cell-flow and cell-vessel wall interactions are described through an extended stochastic discrete Cellular Potts Model (CPM). 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 conformed 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 dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.
This talk will describe an interacting particle model for the spawning migration of the capelin around Iceland, and scaling laws associated with models of this type. The capelin is important to the region both economically and ecologically. Researchers must be able to locate the stock in order to make accurate stock assessments and develop reasonable fishing quotas to prevent a stock collapse. Recently, however, the migration route has shifted and the stock has been difficult to locate. This past February, our model accurately predicted an unusual path for 2008's yearly migration. The same parameters were used to successfully reproduce the migration routes from two previous years. We will describe our model, including how environmental data is incorporated, and show simulation results alongside data collected by the Marine Research Institute of Iceland. The derivation of scaling laws between the radii of the interaction zones, the number of particles in the simulation, and the timestep will also be given, and the implications of these scaling laws will be discussed.
We simulate myxobacteria in a petri dish as an interacting particle system. This simulation of the motion of the bacteria on a plane is not tied to a lattice and the different states of the life-cycle of the bacteria can be simulated including swarming, fruiting-body formation and sporulation. We incorporate Dynamic Energy Budget (DEB) into our model, successfully linking the internal dynamics of the individual cell with the dynamics of the population. Our simulation shows that the DEB simulation, with an additional equation modeling the level of C-signalling molecule on the surface of each cell, automates the transition from the swarming to the fruiting body stages and also the transition between the states of the fruiting body formation, concluding with sporulation.
In this talk we discuss recent as well as well-established approaches in obtaining coarse-grained approximations of many-body microscopic systems. We focus on mathematical, numerical and statistical methods allowing us to assess the parameter regimes where such approximations are valid; we also discuss several counter-examples where coarse-graining gives rise to marked discrepancies with the original microscopic models.
We will first discuss temporal coarse-graining approaches such SDE approximations of master equations in chemical kinetics and stochastic averaging methods in systems with temporal scale separation. Second, we will present spatial coarse-graining methods and related challenges arising in distributed many-particle systems both in equilibrium and out-of-equilibrium settings. Coarse-grained models can be - at different resolutions - macroscopic PDE, Stochastic PDE or Coarse-Grained Kinetic Monte Carlo algorithms. We also demonstrate, with direct comparisons between microscopic (DNS) and coarse-grained simulations, that the derived mesoscopic models can provide a substantial CPU reduction in the computational effort.
Furthermore we discuss the feasibility of spatiotemporal adaptivity methods for the coarse-graining of microscopic simulations, having the capacity of automatically adjusting during the simulation if substantial deviations are detected in a suitable error indicator. Here we will show that in some cases the adaptivity criterion is based on a posteriori estimates on the loss of information in the transition from a microscopic to a coarse-grained system.
Finally, motivated by related problems in the simulation of macromolecular systems, we discuss mathematical strategies for reversing the coarse-graining procedure. The principal purpose of such a task is recovering local microscopic information in a large system by first employing inexpensive coarse-grained solvers.
The advent of precise and high-throughput methods for analysis of biological function heralded the new age of quantitative biology. It has now become possible to engage in truly predictive modeling and hypothesis generation based on continuously improving quantitative understanding of the underlying biochemical cellular and molecular interactions. In this talk, I will illustrate how computational models can be successfully constrained with experimental data to yield a detailed quantitative view of function, with applications to two distinct signaling pathways, and how these constrained models can reveal important biological insights into cellular function. I will also briefly discuss other examples of less conventional modeling efforts and their interplay with experimental results obtained in one inter-disciplinary lab.
Most of the work in the physics community on the dynamics of neural systems has assumed that the synapse is a simple, deterministic passer of information between neurons and that these neurons often act via simple linear summation followed by thresholding. This perspective, dating all the way back to the work of McCullough and Pitts in the 1940's, may be completely inadequate; real neurons, other interacting cell types, and synapses have multiple degrees of freedom (and concomitant time-scales) which might be playing a critical role in neural information processing. In this talk, we will focus on the biophysics of these degrees of freedom, mostly on presynaptic calcium dynamics and its role in facilitation but also on astrocytes which envelop most synapses and active dendritic trees for the post-synaptic neuron. We then discuss the efforts we are making towards understanding how including these can change the dynamical properties of both single neurons and small neuronal networks.
In this talk we will present three hybrid individual cell-based models for aspects of tumour growth. The talk will focus on applications. An open question which will not be addressed will be how to derive, if possible, fully continuum descriptions of these models.
Embryogenesis, or embryonic development, is a prime example of a biological phenomenon which spans multiple scales - from gene expression due to intercellular signaling, up to cell-cell interactions, and finally morphogenesis at the embryonic scale. Development has always inspired scientists to draw heavily on metaphors from mathematics (e.g. catastrophe theory) and the physical sciences (e.g. viewing embryonic tissue as a liquid). Such metaphors have had modest impact on biologists, for whom developmental genetics and live-cell imaging, the result of experimental research, have become the major research tools. I will discuss this topic, very much in the spirit of open questions to the participants, and mention some of the work form my own group in which we have applied many-body theory methods to model and compute aspects of development observed in the experiments of Cornelis Weijer on the chick embryo.
We study fronts of cells such as those invading a wound or in a growing tumor. First we look at a discrete stochastic model in which cells can move, proliferate, and experience cell-cell adhesion. We compare this with a coarse-grained, continuum description of this phenomenon by means of a generalized Cahn-Hilliard equation (GCH) with a proliferation term.
There are two interesting regimes. For subcritical adhesion, there are propagating "pulled" fronts, similarly to those of Fisher-Kolmogorov equation. The problem of front velocity selection is examined, and our theoretical predictions are in a good agreement with a numerical solution of the GCH equation. For supercritical adhesion, there is a nontrivial transient behavior. The results of continuum and discrete models are in a good agreement with each other for the different regimes we analyzed.
An accurate model for cell motility is important for understanding tumor invasion, wound healing, vasculogenesis, and artificial tissue design. Cell motility is frequently studied in 3d collagen gels. A variety of mathematical models for cell-gel interactions have been developed treating the collagen as a linear, viscoelastic, material, but on the microscale, collagen is a network of fibrils, and it is not clear if such models are valid, especially at the large deformations cells impose on the gel. Our goal is to accurately describe cell-gel interactions on the microscale level by treating the collagen as a discrete network of fibers. This first requires the development of micromechanical models of the collagen gel itself. Here, we will first present a new image processing algorithm for extracting the collagen network architecture from a stack of 3d images obtained by confocal microscopy. We then explore the behavior of different micromechanical models and compare the model to experimental data.
In this talk, we present two modeling problems from bioengineering and computational biology. The first problem concerns with foreign body reactions to bio-material implants. The collagen capsulations to implants within human can reduce the effectiveness of the devices, and a predictive model can help to determine quantitatively how to influence adherent protein, phagocytes, and foreign body giant cells to minimize the recruitment of fibroblasts and/or produce matrix metalloproteinase to degrade the fibrotic capsules on the implants. However signaling machinery for the process is very complex. Using the well known continuum model of Dale, Sherratt and Maini (1996, Proc. R. Soc. Lond.), our preliminary modeling data indicated a good agreement of model and experiments. To account for the rest of the discrepancy, the discrete aspect of the cell movement is necessary. In second problem, we discuss the modeling of NMDA receptor kinetics in a synapse. Under the Calcium action inside pre-synaptic terminals, small vesicles (containing about 4000 glutamate molecules) migrate towards cleft and release its contents there. Classical diffusion model has been able to account for the peaks actions of post-synaptic current (Atasoy et al, 2008, J. Neuroscience). The modeling of vesicle motions and release mechanism is still under way by a hybrid discrete/continuous approach.
Cell adhesion plays a critical role in tumor formation, invasion and metastasis. The complex processes underlying adhesion to other cells and the extra-cellular matrices are dynamic and inherently multi-scale. Unfortunately, computational and mathematical models aimed at understanding adhesion have traditionally focused on a single length-scale and have been unable to link events at the atomic and molecular scale to bulk behaviors seen in experiments. In addition, most adhesion models have been blind to the effects of matrix structure and mechanics, molecular sequence and conformations and hence can only make qualitative predictions.
Using a combination of molecular dynamics to generate conformations, coarse-graining of these results for single-chain mean field theory and then further coarse graining too study processes at the bulk level, we have developed a fully multi-scale model of cell-matrix and cell-cell interactions. Our models are rooted in principles of thermodynamics, statistical and continuum mechanics and are able to capture cell-matrix and cell-cell adhesion events at a single molecular, cellular, multi-cellular and tissue level. We are also able to study the effects of soluble and insoluble ligands, functionalized nano-particles and tethered surfaces. Thus our model is able to make quantitative predictions in both in vivo and in vitro environments. My talk will discuss the development of the model, the comparison with in vivo and in vitro data and efforts to further scale up the model at the tumor level using mixture theory and its applications in prostate cancer.