Supplementary data are available at Bioinformatics online.

Mechanistic understanding of multi-scale biological processes, such as cell proliferation in a changing biological tissue, is readily facilitated by computational models. While tools exist to construct and simulate multi-scale models, the statistical inference of the unknown model parameters remains an open problem. Here, we present and benchmark a parallel approximate Bayesian computation sequential Monte Carlo (pABC SMC) algorithm, tailored for high-performance computing clusters. pABC SMC is fully automated and returns reliable parameter estimates and confidence intervals. By running the pABC SMC algorithm for ∼10 hr, we parameterize multi-scale models that accurately describe quantitative growth curves and histological data obtained in vivo from individual tumor spheroid growth in media droplets. The models capture the hybrid deterministic-stochastic behaviors of 10-10 of cells growing in a 3D dynamically changing nutrient environment. The pABC SMC algorithm reliably converges to a consistent set of parameters. Our study demonstrates a proof of principle for robust, data-driven modeling of multi-scale biological systems and the feasibility of multi-scale model parameterization through statistical inference.

Summary: Likelihood-free methods are often required for inference in systems biology. While Approximate Bayesian Computation (ABC) provides a theoretical solution, its practical application has often been challenging due to its high computational demands. To scale likelihood-free inference to computationally demanding stochastic models we developed pyABC: a distributed and scalable ABC-Sequential Monte Carlo (ABC-SMC) framework. It implements computation-minimizing and scalable, runtime-minimizing parallelization strategies for multi-core and distributed environments scaling to thousands of cores. The framework is accessible to non-expert users and also enables advanced users to experiment with and to custom implement many options of ABC-SMC schemes, such as acceptance threshold schedules, transition kernels and distance functions without alteration of pyABC's source code. pyABC includes a web interface to visualize ongoing and finished ABC-SMC runs and exposes an API for data querying and post-processing. Availability and Implementation: pyABC is written in Python 3 and is released under the GPLv3 license. The source code is hosted on https://github.com/neuralyzer/pyabc and the documentation on http://pyabc.readthedocs.io. It can be installed from the Python Package Index (PyPI).

Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate segmentation. To this end, we reformulate the problem by imposing piecewise constancy of the parameter field, and derive a specific proximal splitting optimization scheme. A key component of our framework is an efficient one-dimensional piecewise-affine estimator for vector-valued signals. The first advantage of our approach over segmentation-based methods is its absence of initialization. The second advantage is its lower computational cost which is independent of the complexity of the motion field. In addition to these features, we demonstrate competitive accuracy with other piecewise-parametric methods on standard evaluation benchmarks. Our new regularization scheme also outperforms the more standard use of total variation and total generalized variation.