MFBM Subgroup Contributed Talks

Miroslav Phan

ETH Zurich, Department of Biosystems Science and Engineering, Basel, Switzerland

"A Rejection Based Gillespie Algorithm for non-Markovian Stochastic Processes with Individual Reactant Properties"

The Gillespie algorithm is commonly applied for simulating memoryless processes that follow an exponential waiting-time. However, stochastic processes governing biological interactions, such as cell apoptosis and epidemic spreading, are empirically known to exhibit properties of memory, an inherently non-Markovian feature. The presence of such non-Markovian processes can significantly influence the outcome of a simulation. While several extensions to the Gillespie algorithm have been proposed, most of them suffer from either a high computational cost, or are only applicable to a narrow selection of probability distributions that do not match the experimentally observed biological data distributions. To tackle the aforementioned issues, we developed a Rejection Gillespie for non-Markovian Reactions (REGINR) that is capable of generating simulations with non-exponential waiting-times, while remaining an order of magnitude faster than alternative approaches. REGINR uses the Weibull distribution, which interpolates between the exponential, normal, and heavy-tailed distributions. We applied our algorithm to a mouse stem cell dataset with known non-Markovian dynamics and found it to faithfully recapitulate the underlying biological processes. We conclude that our algorithm is suitable for gaining insight into the role of molecular memory in stochastic models, as well as for accurately simulating real-world biological processes.

Elba Raimundez

University of Bonn

"Efficient sampling by marginalization of scaling parameters for mechanistic models with relative data"

Mathematical models are standard tools for understanding the underlying mechanisms of biological systems. Generally, the parameters of these models are unknown and they need to be inferred from experimental data using statistical methods. Most common measurement techniques only provide relative information about the absolute molecular state and often data is noise-corrupted. Therefore, introducing scaling and noise parameters in the model observables is necessary. Since frequently these parameters are also unknown, the dimensionality of the estimation problem is augmented. Sampling methods are widely used in systems biology to assess parameter and prediction uncertainties. However, the evaluation of sampling methods is usually demanding and often on the border of computational feasibility. Hence, efficient sampling algorithms are required.We propose a marginal sampling scheme for estimating the parameter uncertainties of mechanistic models with relative data. We integrate out the scaling and noise parameters from the original problem, leading to a dimension reduction of the parameter space. Herewith, only reaction rate constants have to be sampled. We find that the marginal sampling scheme retrieves the same parameter probability distributions and outperforms sampling on the full parameter space by substantially increasing the effective sample size and smoothing the transition probability between posterior modes.

Aden Forrow

Mathematical Institute, University of Oxford

"Learning stochastic dynamics with measurement noise"

A core challenge of modern mathematical biology is fitting models to the ever increasing quantities of biological data. Frequently, the data is affected by both measurement noise and stochasticity intrinsic to the underlying system in ways that are difficult to disentangle. Building on prior work addressing the two kinds of stochasticity independently, we present a method for inferring dynamics without assuming either noise-free measurements or an underlying deterministic system. Our approach is motivated by measurement techniques available in single-cell sequencing and generically applicable for learning stochastic differential equations from noisy data.

Marco Berghoff

Karlsruhe Institute of Technology

"Cells In Sillico – Parallel Tissue Development Simulation"

Insights in cell dynamics and tissue development are constantly changing our understanding of fundamental biological processes including embryogenesis, wound healing, and tumorigenesis. The availability of high-quality microscopy data and an increasing understanding of single-cell effects are speeding up discoveries. However, many computational models still describe either a few cells in high detail or larger cell ensembles and tissues in rather coarse detail. We combine these two scales, therefore we developed a highly parallel version of the cellular Potts model and provides an agent-based model for controlling cellular events. The model can be modularly extended to a multimodel simulation at both scales. Based on the NAStJA framework, we implemented a scalable version that runs efficiently on high-performance computing systems.Our model scales beyond 10,000 cores in an approximately linear manner, enabling the simulation of large three-dimensional tissues. The strictly modular design allows flexible configuration of arbitrary models and enables applications in a wide range of research questions. Cells in Silico can be easily adapted to different modeling assumptions and helps computational scientists to extend their simulations to a new area of tissue simulations. As an example, we show a 1000^3 voxel cancer tissue simulation with sub-cellular resolution.