Loss of bimolecular reactions in reaction-diffusion master equations is consistent with diffusion limited reaction kinetics in the mean field limit.

We show that the resolution-dependent loss of bimolecular reactions in spatiotemporal Reaction-Diffusion Master Equations (RDMEs) is in agreement with the mean-field Collins-Kimball (C-K) theory of diffusion-limited reaction kinetics. The RDME is a spatial generalization of the chemical master equation, which enables studying stochastic reaction dynamics in spatially heterogeneous systems. It uses a regular Cartesian grid to partition space into locally well-mixed reaction compartments and treats diffusion as a jump reaction between neighboring grid cells.

Automated quantification of photoreceptor outer segments in developing and degenerating retinas on microscopy images across scales.

The functionality of photoreceptors, rods, and cones is highly dependent on their outer segments (POS), a cellular compartment containing highly organized membranous structures that generate biochemical signals from incident light. While POS formation and degeneration are qualitatively assessed on microscopy images, reliable methodology for quantitative analyses is still limited. Here, we developed methods to quantify POS (QuaPOS) maturation and quality on retinal sections using automated image analyses.

STENCIL-NET for equation-free forecasting from data.

We present an artificial neural network architecture, termed STENCIL-NET, for equation-free forecasting of spatiotemporal dynamics from data. STENCIL-NET works by learning a discrete propagator that is able to reproduce the spatiotemporal dynamics of the training data. This data-driven propagator can then be used to forecast or extrapolate dynamics without needing to know a governing equation.

Variational inference accelerates accurate DNA mixture deconvolution.

We investigate a class of DNA mixture deconvolution algorithms based on variational inference, and we show that this can significantly reduce computational runtimes with little or no effect on the accuracy and precision of the result. In particular, we consider Stein Variational Gradient Descent (SVGD) and Variational Inference (VI) with an evidence lower-bound objective. Both provide alternatives to the commonly used Markov-Chain Monte-Carlo methods for estimating the model posterior in Bayesian probabilistic genotyping.

Roadmap on Deep Learning for Microscopy.

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities.

Analysis of the Hamiltonian Monte Carlo genotyping algorithm on PROVEDIt mixtures including a novel precision benchmark.

We provide an internal validation study of a recently published precise DNA mixture algorithm based on Hamiltonian Monte Carlo sampling (Susik et al., 2022). We provide results for all 428 mixtures analysed by Riman et al.

A Gaussian jump process formulation of the reaction-diffusion master equation enables faster exact stochastic simulations.

We propose a Gaussian jump process model on a regular Cartesian lattice for the diffusion part of the Reaction-Diffusion Master Equation (RDME). We derive the resulting Gaussian RDME (GRDME) formulation from analogy with a kernel-based discretization scheme for continuous diffusion processes and quantify the limits of its validity relative to the classic RDME. We then present an exact stochastic simulation algorithm for the GRDME, showing that the accuracies of GRDME and RDME are comparable, but exact simulations of the GRDME require only a fraction of the computational cost of exact RDME simulations.

Collective cell migration during optic cup formation features changing cell-matrix interactions linked to matrix topology.

Cell migration is crucial for organismal development and shapes organisms in health and disease. Although a lot of research has revealed the role of intracellular components and extracellular signaling in driving single and collective cell migration, the influence of physical properties of the tissue and the environment on migration phenomena in vivo remains less explored. In particular, the role of the extracellular matrix (ECM), which many cells move upon, is currently unclear.

Design centering enables robustness screening of pattern formation models.

Motivation: Access to unprecedented amounts of quantitative biological data allows us to build and test biochemically accurate reaction-diffusion models of intracellular processes. However, any increase in model complexity increases the number of unknown parameters and, thus, the computational cost of model analysis. To efficiently characterize the behavior and robustness of models with many unknown parameters remains, therefore, a key challenge in systems biology.

Hamiltonian Monte Carlo with strict convergence criteria reduces run-to-run variability in forensic DNA mixture deconvolution.

Motivation: Analysing mixed DNA profiles is a common task in forensic genetics. Due to the complexity of the data, such analysis is often performed using Markov Chain Monte Carlo (MCMC)-based genotyping algorithms. These trade off precision against execution time.

Stability selection enables robust learning of differential equations from limited noisy data.

We present a statistical learning framework for robust identification of differential equations from noisy spatio-temporal data. We address two issues that have so far limited the application of such methods, namely their robustness against noise and the need for manual parameter tuning, by proposing stability-based model selection to determine the level of regularization required for reproducible inference. This avoids manual parameter tuning and improves robustness against noise in the data.

Parallel Discrete Convolutions on Adaptive Particle Representations of Images.

We present data structures and algorithms for native implementations of discrete convolution operators over Adaptive Particle Representations (APR) of images on parallel computer architectures. The APR is a content-adaptive image representation that locally adapts the sampling resolution to the image signal. It has been developed as an alternative to pixel representations for large, sparse images as they typically occur in fluorescence microscopy.

Quantifying Molecular Dynamics within Complex Cellular Morphologies using LLSM-FRAP.

Quantifying molecular dynamics within the context of complex cellular morphologies is essential toward understanding the inner workings and function of cells. Fluorescence recovery after photobleaching (FRAP) is one of the most broadly applied techniques to measure the reaction diffusion dynamics of molecules in living cells. FRAP measurements typically restrict themselves to single-plane image acquisition within a subcellular-sized region of interest due to the limited temporal resolution and undesirable photobleaching induced by 3D fluorescence confocal or widefield microscopy.

A C++ expression system for partial differential equations enables generic simulations of biological hydrodynamics.

We present a user-friendly and intuitive C++ expression system to implement numerical simulations of continuum biological hydrodynamics. The expression system allows writing simulation programs in near-mathematical notation and makes codes more readable, more compact, and less error-prone. It also cleanly separates the implementation of the partial differential equation model from the implementation of the numerical methods used to discretize it.

Learning physically consistent differential equation models from data using group sparsity.

We propose a statistical learning framework based on group-sparse regression that can be used to (i) enforce conservation laws, (ii) ensure model equivalence, and (iii) guarantee symmetries when learning or inferring differential-equation models from data. Directly learning interpretable mathematical models from data has emerged as a valuable modeling approach. However, in areas such as biology, high noise levels, sensor-induced correlations, and strong intersystem variability can render data-driven models nonsensical or physically inconsistent without additional constraints on the model structure.

Robustness of topological defects in discrete domains.

Topological defects are singular points in vector fields, important in applications ranging from fingerprint detection to liquid crystals to biomedical imaging. In discretized vector fields, topological defects and their topological charge are identified by finite differences or finite-step paths around the tentative defect. As the topological charge is (half) integer, it cannot depend continuously on each input vector in a discrete domain.

Fundamentals of the logarithmic measure for revealing multimodal diffusion.

We develop a theoretical foundation for a time-series analysis method suitable for revealing the spectrum of diffusion coefficients in mixed Brownian systems, for which no prior knowledge of particle distinction is required. This method is directly relevant for particle tracking in biological systems, in which diffusion processes are often nonuniform. We transform Brownian data onto the logarithmic domain, in which the coefficients for individual modes of diffusion appear as distinct spectral peaks in the probability density.

A non-linear system patterns Rab5 GTPase on the membrane.

Proteins can self-organize into spatial patterns via non-linear dynamic interactions on cellular membranes. Modelling and simulations have shown that small GTPases can generate patterns by coupling guanine nucleotide exchange factors (GEF) to effectors, generating a positive feedback of GTPase activation and membrane recruitment. Here, we reconstituted the patterning of the small GTPase Rab5 and its GEF/effector complex Rabex5/Rabaptin5 on supported lipid bilayers.

Minimal Model of Cellular Symmetry Breaking.

The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry-breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species.

Self-organized shape dynamics of active surfaces.

Mechanochemical processes in thin biological structures, such as the cellular cortex or epithelial sheets, play a key role during the morphogenesis of cells and tissues. In particular, they are responsible for the dynamical organization of active stresses that lead to flows and deformations of the material. Consequently, advective transport redistributes force-generating molecules and thereby contributes to a complex mechanochemical feedback loop.

Adaptive particle representation of fluorescence microscopy images.

Modern microscopes create a data deluge with gigabytes of data generated each second, and terabytes per day. Storing and processing this data is a severe bottleneck, not fully alleviated by data compression. We argue that this is because images are processed as grids of pixels.

How Computational Models Enable Mechanistic Insights into Virus Infection.

An implicit aim in cellular infection biology is to understand the mechanisms how viruses, microbes, eukaryotic parasites, and fungi usurp the functions of host cells and cause disease. Mechanistic insight is a deep understanding of the biophysical and biochemical processes that give rise to an observable phenomenon. It is typically subject to falsification, that is, it is accessible to experimentation and empirical data acquisition.

pSSAlib: The partial-propensity stochastic chemical network simulator.

Chemical reaction networks are ubiquitous in biology, and their dynamics is fundamentally stochastic. Here, we present the software library pSSAlib, which provides a complete and concise implementation of the most efficient partial-propensity methods for simulating exact stochastic chemical kinetics. pSSAlib can import models encoded in Systems Biology Markup Language, supports time delays in chemical reactions, and stochastic spatiotemporal reaction-diffusion systems.

L -Adaptation: Simultaneous Design Centering and Robustness Estimation of Electronic and Biological Systems.

The design of systems or models that work robustly under uncertainty and environmental fluctuations is a key challenge in both engineering and science. This is formalized in the design-centering problem, which is defined as finding a design that fulfills given specifications and has a high probability of still doing so if the system parameters or the specifications fluctuate randomly. Design centering is often accompanied by the problem of quantifying the robustness of a system.

A Predictive 3D Multi-Scale Model of Biliary Fluid Dynamics in the Liver Lobule.

Bile, the central metabolic product of the liver, is transported by the bile canaliculi network. The impairment of bile flow in cholestatic liver diseases has urged a demand for insights into its regulation. Here, we developed a predictive 3D multi-scale model that simulates fluid dynamic properties successively from the subcellular to the tissue level.