Arne T. Bittig

Adapting rule-based model descriptions for simulating in continuous and hybrid space

Space plays an ever increasing role in cell biological modeling and simulation. This ranges from compartmental dynamics, via mesh-based approaches, to individuals moving in continuous space. An attributed, multi-level, rule-based language, ML-Space, is presented that allows to integrate these different types of spatial dynamics within one model. The associated simulator combines Gillespies method, the Next Subvolume method, and Brownian dynamics. This allows the simulation of reaction diffusion systems as well as taking excluded volume effects into account. A small example illuminates the potential of the approach in dealing with complex spatial dynamics like those involved in studying the dynamics of lipid rafts and their role in receptor co-localization.

Spatial modeling in cell biology at multiple levels

Most modeling and simulation approaches applied in cell biology assume a homogeneous distribution of particles in space, although experimental studies reveal the importance of space to understand the dynamics of cells. There are already numerous spatial approaches focusing on the simulation of cells. Recently, they have been complemented by a set of spatial modeling languages whose operational semantics are tied partly to existing simulation algorithms. These modeling languages allow an explicit description of spatial phenomena, and facilitate analysis of the temporal spatial dynamics of cells by a clear separation between model, semantics, and simulator. With the supported level of abstraction, each of those offers a different perception of the spatial phenomena under study. In this paper, we give an overview of existing modeling formalisms and discuss some ways of combining approaches to tackle the problem the computational costs induced by spatial dynamics.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

Membrane related dynamics and the formation of actin in cells growing on micro-topographies: a spatial computational model

BackgroundIntra-cellular processes of cells at the interface to an implant surface are influenced significantly by their extra-cellular surrounding. Specifically, when growing osteoblasts on titanium surfaces with regular micro-ranged geometry, filaments are shorter, less aligned and they concentrate at the top of the geometric structures. Changes to the cytoskeleton network, i. e., its localization, alignment, orientation, and lengths of the filaments, as well as the overall concentration and distribution of key-actors are induced. For example, integrin is distributed homogeneously, whereas integrin in activated state and vinculin, both components of focal adhesions, have been found clustered on the micro-ranged geometries. Also, the concentration of Rho, an intracellular signaling protein related to focal adhesion regulation, was significantly lower.ResultsTo explore whether regulations associated with the focal adhesion complex can be responsible for the changed actin filament patterns, a spatial computational model has been developed using ML-Space, a rule-based model description language, and its associated Brownian-motion-based simulator. The focus has been on the deactivation of cofilin in the vicinity of the focal adhesion complex. The results underline the importance of sensing mechanisms to support a clustering of actin filament nucleations on the micro-ranged geometries, and of intracellular diffusion processes, which lead to spatially heterogeneous distributions of active (dephosphorylated) cofilin, which in turn influences the organization of the actin network. We find, for example, that the spatial heterogeneity of key molecular actors can explain the difference in filament lengths in cells on different micro-geometries partly, but to explain the full extent, further model assumptions need to be added and experimentally validated. In particular, our findings and hypothesis referring to the role, distribution, and amount of active cofilin have still to be verified in wet-lab experiments.ConclusionLetting cells grow on surface structures is a possibility to shed new light on the intricate mechanisms that relate membrane and actin related dynamics in the cell. Our results demonstrate the need for declarative expressive spatial modeling approaches that allow probing different hypotheses, and the central role of the focal adhesion complex not only for nucleating actin filaments, but also for regulating possible severing agents locally.

Towards Modelling and Simulation of Crowded Environments in Cell Biology

In modelling and simulation of cell biological processes, spatial homogeneity in the distribution of components is a common but not always valid assumption. Spatial simulation methods differ in computational effort and accuracy, and usually rely on tool‐specific input formats for model specification. A clear separation between modelling and simulation allows a declarative model specification thereby facilitating reuse of models and exploiting different simulators. We outline a modelling formalism covering both stochastic spatial simulation at the population level and simulation of individual entities moving in continuous space as well as the combination thereof. A multi‐level spatial simulator is presented that combines populations of small particles simulated according to the Next Subvolume Method with individually represented large particles following Brownian motion. This approach entails several challenges that need to be overcome, but nicely balances between calculation effort and required levels of ...

Feature-Driven Visual Analytics of Chaotic Parameter-Dependent Movement

Analyzing movements in their spatial and temporal context is a complex task. We are additionally interested in understanding the movements’ dependency on parameters that govern the processes behind the movement. We propose a visual analytics approach combining analytic, visual, and interactive means to deal with the added complexity. The key idea is to perform an analytical extraction of features that capture distinct movement characteristics. Different parameter configurations and extracted features are then visualized in a compact fashion to facilitate an overview of the data. Interaction enables the user to access details about features, to compare features, and to relate features back to the original movement. We instantiate our approach with a repository of more than twenty accepted and novel features to help analysts in gaining insight into simulations of chaotic behavior of thousands of entities over thousands of data points. Domain experts applied our solution successfully to study dynamic groups in such movements in relation to thousands of parameter configurations.

Lattice Monte Carlo simulation of Galilei variant anomalous diffusion

The observation of an increasing number of anomalous diffusion phenomena motivates the study to reveal the actual reason for such stochastic processes. When it is difficult to get analytical solutions or necessary to track the trajectory of particles, lattice Monte Carlo (LMC) simulation has been shown to be particularly useful. To develop such an LMC simulation algorithm for the Galilei variant anomalous diffusion, we derive explicit solutions for the conditional and unconditional first passage time (FPT) distributions with double absorbing barriers. According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit. However, the error introduced in the second moment of the displacement diverges according to a power law as the simulation time progresses. We give an explicit criterion for choosing a small enough lattice step to limit the error within the specified tolerance. We further validate the LMC simulation algorithm and confirm the theoretical error analysis through numerical simulations. The numerical results agree with our theoretical predictions very well.

Predictive Modelling of Mitochondrial Spatial Structure and Health

Mitochondria are mobile cellular organelles that form networks by fusion and fission. These events lead to an exchange of components responsible for maintaining membrane potential, i.e. mitochondrial health. Membrane potential can be disturbed by an imbalance of fission-triggering proteins. We expand an existing computational model of fusing and splitting mitochondria by representations of fission protein 1 (Fis1) and dynamin related protein 1 (Drp1) and perform parameter scans on simulations of it. Our relatively basic model already shows an effect of lower Fis1 and Drp1 recruitment rates, i.e. lower availability, on network structure and overall health. Various aspects of the real system can be incorporated into model, e.g. further regulatory proteins, a varying spatial distribution of Fis1 and Drp1, or consequences of changed mitochondrial network structure and health on their behaviour, e.g. under oxidative stress.