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. RESULTS: We propose a novel computational framework for efficient high-dimensional parameter space characterization of reaction-diffusion models in systems biology. The method leverages the Lp-Adaptation algorithm, an adaptive-proposal statistical method for approximate design centering and robustness estimation. Our approach is based on an oracle function, which predicts for any given point in parameter space whether the model fulfills given specifications. We propose specific oracles to efficiently predict four characteristics of Turing-type reaction-diffusion models: bistability, instability, capability of spontaneous pattern formation and capability of pattern maintenance. We benchmark the method and demonstrate that it enables global exploration of a model's ability to undergo pattern-forming instabilities and to quantify robustness for model selection in polynomial time with dimensionality. We present an application of the framework to pattern formation on the endosomal membrane by the small GTPase Rab5 and its effectors, and we propose molecular mechanisms underlying this system. AVAILABILITY AND IMPLEMENTATION: Our code is implemented in MATLAB and is available as open source under https://git.mpi-cbg.de/mosaic/software/black-box-optimization/rd-parameter-space-screening. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

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. We analyze the origin of this speedup and its scaling with problem dimension. The benchmarks suggest that the GRDME is a particularly beneficial model for diffusion-dominated systems in three dimensional spaces, often occurring in systems biology and cell biology.

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. It has been shown in fixed geometries that this mechanism enables patterning, but the interplay of these processes with shape changes of the material remains to be explored. In this work, we study the fully self-organized shape dynamics using the theory of active fluids on deforming surfaces and develop a numerical approach to solve the corresponding force and torque balance equations. We describe the spontaneous generation of nontrivial surface shapes, shape oscillations, and directed surface flows that resemble peristaltic waves from self-organized, mechanochemical processes on the deforming surface. Our approach provides opportunities to explore the dynamics of self-organized active surfaces and can help to understand the role of shape as an integral element of the mechanochemical organization of morphogenetic processes.

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. We refer to the method as the logarithmic measure of diffusion, or simply as the logarithmic measure. We provide a general protocol for deriving analytical expressions for the probability densities on the logarithmic domain. The protocol is applicable for any number of spatial dimensions with any number of diffusive states. The analytical form can be fitted to data to reveal multiple diffusive modes. We validate the theoretical distributions and benchmark the accuracy and sensitivity of the method by extracting multimodal diffusion coefficients from two-dimensional Brownian simulations of polydisperse filament bundles. Bundling the filaments allows us to control the system nonuniformity and hence quantify the sensitivity of the method. By exploiting the anisotropy of the simulated filaments, we generalize the logarithmic measure to rotational diffusion. By fitting the analytical forms to simulation data, we confirm the method's theoretical foundation. An error analysis in the single-mode regime shows that the proposed method is comparable in accuracy to the standard mean-squared displacement approach for evaluating diffusion coefficients. For the case of multimodal diffusion, we compare the logarithmic measure against other, more sophisticated methods, showing that both model selectivity and extraction accuracy are comparable for small data sets. Therefore, we suggest that the logarithmic measure, as a method for multimodal diffusion coefficient extraction, is ideally suited for small data sets, a condition often confronted in the experimental context. Finally, we critically discuss the proposed benefits of the method and its information content.

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. This allows changing either of them with minimal changes to the source code. The presented expression system is implemented in the high-performance computing platform OpenFPM, supporting simulations that transparently parallelize on multi-processor computer systems. We demonstrate that our expression system makes it easier to write scalable codes for simulating biological hydrodynamics in space and time. We showcase the present framework in numerical simulations of active polar fluids, as well as in classic simulations of fluid dynamics from the incompressible Navier-Stokes equations to Stokes flow in a ball. The presented expression system accelerates scalable simulations of spatio-temporal models that encode the physics and material properties of tissues in order to algorithmically study morphogenesis.

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. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechanochemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities.

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. It also provides tools for statistical analysis of simulation results and supports multiple output formats. It has previously been used for studies of biochemical reaction pathways and to benchmark other stochastic simulation methods. Here, we describe pSSAlib in detail and apply it to a new model of the endocytic pathway in eukaryotic cells, leading to the discovery of a stochastic counterpart of the cut-out switch motif underlying early-to-late endosome conversion. pSSAlib is provided as a stand-alone command-line tool and as a developer API. We also provide a plug-in for the SBMLToolbox. The open-source code and pre-packaged installers are freely available from http://mosaic.mpi-cbg.de.

Objective comparison of particle tracking methods.

Particle tracking is of key importance for quantitative analysis of intracellular dynamic processes from time-lapse microscopy image data. Because manually detecting and following large numbers of individual particles is not feasible, automated computational methods have been developed for these tasks by many groups. Aiming to perform an objective comparison of methods, we gathered the community and organized an open competition in which participating teams applied their own methods independently to a commonly defined data set including diverse scenarios. Performance was assessed using commonly defined measures. Although no single method performed best across all scenarios, the results revealed clear differences between the various approaches, leading to notable practical conclusions for users and developers.

Seeing Is Believing: Quantifying Is Convincing: Computational Image Analysis in Biology.

Imaging is center stage in biology. Advances in microscopy and labeling techniques have enabled unprecedented observations and continue to inspire new developments. Efficient and accurate quantification and computational analysis of the acquired images, however, are becoming the bottleneck. We review different paradigms of computational image analysis for intracellular, single-cell, and tissue-level imaging, providing pointers to the specialized literature and listing available software tools. We place particular emphasis on clear categorization of image-analysis frameworks and on identifying current trends and challenges in the field. We further outline some of the methodological advances that are required in order to use images as quantitative scientific measurements.

Modeling and simulation of biological systems from image data.

This essay provides an introduction to the terminology, concepts, methods, and challenges of image-based modeling in biology. Image-based modeling and simulation aims at using systematic, quantitative image data to build predictive models of biological systems that can be simulated with a computer. This allows one to disentangle molecular mechanisms from effects of shape and geometry. Questions like "what is the functional role of shape" or "how are biological shapes generated and regulated" can be addressed in the framework of image-based systems biology. The combination of image quantification, model building, and computer simulation is illustrated here using the example of diffusion in the endoplasmic reticulum.

Receptor concentration and diffusivity control multivalent binding of Sv40 to membrane bilayers.

Incoming Simian Virus 40 particles bind to their cellular receptor, the glycolipid GM1, in the plasma membrane and thereby induce membrane deformation beneath the virion leading to endocytosis and infection. Efficient membrane deformation depends on receptor lipid structure and the organization of binding sites on the internalizing particle. To determine the role of receptor diffusion, concentration and the number of receptors required for stable binding in this interaction, we analyze the binding of SV40 to GM1 in supported membrane bilayers by computational modeling based on experimental data. We measure the diffusion rates of SV40 virions in solution by fluorescence correlation spectroscopy and of the receptor in bilayers by single molecule tracking. Quartz-crystal microbalance with dissipation (QCM-D) is used to measure binding of SV40 virus-like particles to bilayers containing the viral receptor GM1. We develop a phenomenological stochastic dynamics model calibrated against this data, and use it to investigate the early events of virus attachment to lipid membranes. Our results indicate that SV40 requires at least 4 attached receptors to achieve stable binding. We moreover find that receptor diffusion is essential for the establishment of stable binding over the physiological range of receptor concentrations and that receptor concentration controls the mode of viral motion on the target membrane. Our results provide quantitative insight into the initial events of virus-host interaction at the nanoscopic level.

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. POS formation was examined during the development and in adulthood of wild-type mice via light microscopy (LM) and transmission electron microscopy (TEM). To quantify the number, size, shape, and fluorescence intensity of POS, retinal cryosections were immunostained for the cone POS marker S-opsin. Fluorescence images were used to train the robust classifier QuaPOS-LM based on supervised machine learning for automated image segmentation. Characteristic features of segmentation results were extracted to quantify the maturation of cone POS. Subsequently, this quantification method was applied to characterize POS degeneration in "cone photoreceptor function loss 1" mice. TEM images were used to establish the ultrastructural quantification method QuaPOS-TEM for the alignment of POS membranes. Images were analyzed using a custom-written MATLAB code to extract the orientation of membranes from the image gradient and their alignment (coherency). This analysis was used to quantify the POS morphology of wild-type and two inherited retinal degeneration ("retinal degeneration 19" and "rhodopsin knock-out") mouse lines. Both automated analysis technologies provided robust characterization and quantification of POS based on LM or TEM images. Automated image segmentation by the classifier QuaPOS-LM and analysis of the orientation of membrane stacks by QuaPOS-TEM using fluorescent or TEM images allowed quantitative evaluation of POS formation and quality. The assessments showed an increase in POS number, volume, and membrane coherency during wild-type postnatal development, while a decrease in all three observables was detected in different retinal degeneration mouse models. All the code used for the presented analysis is open source, including example datasets to reproduce the findings. Hence, the QuaPOS quantification methods are useful for in-depth characterization of POS on retinal sections in developmental studies, for disease modeling, or after therapeutic interventions affecting photoreceptors.

MosaicIA: an ImageJ/Fiji plugin for spatial pattern and interaction analysis.

BACKGROUND: Analyzing spatial distributions of objects in images is a fundamental task in many biological studies. The relative arrangement of a set of objects with respect to another set of objects contains information about potential interactions between the two sets of objects. If they do not "feel" each other's presence, their spatial distributions are expected to be independent of one another. Spatial correlations in their distributions are indicative of interactions and can be modeled by an effective interaction potential acting between the points of the two sets. This can be used to generalize co-localization analysis to spatial interaction analysis. However, no user-friendly software for this type of analysis was available so far. RESULTS: We present an ImageJ/Fiji plugin that implements the complete workflow of spatial pattern and interaction analysis for spot-like objects. The plugin detects objects in images, infers the interaction potential that is most likely to explain the observed pattern, and provides statistical tests for whether an inferred interaction is significant given the number of objects detected in the images and the size of the space within which they can distribute. We benchmark and demonstrate the present software using examples from confocal and PALM single-molecule microscopy. CONCLUSIONS: The present software greatly simplifies spatial interaction analysis for point patterns, and makes it available to the large user community of ImageJ and Fiji. The presented showcases illustrate the usage of the software.

Cell-free transmission of human adenovirus by passive mass transfer in cell culture simulated in a computer model.

Viruses spread between cells, tissues, and organisms by cell-free and cell-cell transmissions. Both mechanisms enhance disease development, but it is difficult to distinguish between them. Here, we analyzed the transmission mode of human adenovirus (HAdV) in monolayers of epithelial cells by wet laboratory experimentation and a computer simulation. Using live-cell fluorescence microscopy and replication-competent HAdV2 expressing green fluorescent protein, we found that the spread of infection invariably occurred after cell lysis. It was affected by convection and blocked by neutralizing antibodies but was independent of second-round infections. If cells were overlaid with agarose, convection was blocked and round plaques developed around lytic infected cells. Infected cells that did not lyse did not give rise to plaques, highlighting the importance of cell-free transmission. Key parameters for cell-free virus transmission were the time from infection to lysis, the dose of free viruses determining infection probability, and the diffusion of single HAdV particles in aqueous medium. With these parameters, we developed an in silico model using multiscale hybrid dynamics, cellular automata, and particle strength exchange. This so-called white box model is based on experimentally determined parameters and reproduces viral infection spreading as a function of the local concentration of free viruses. These analyses imply that the extent of lytic infections can be determined by either direct plaque assays or can be predicted by calculations of virus diffusion constants and modeling.

Histone deacetylase 8 is required for centrosome cohesion and influenza A virus entry.

Influenza A virus (IAV) enters host cells by endocytosis followed by acid-activated penetration from late endosomes (LEs). Using siRNA silencing, we found that histone deacetylase 8 (HDAC8), a cytoplasmic enzyme, efficiently promoted productive entry of IAV into tissue culture cells, whereas HDAC1 suppressed it. HDAC8 enhanced endocytosis, acidification, and penetration of the incoming virus. In contrast, HDAC1 inhibited acidification and penetration. The effects were connected with dramatic alterations in the organization of the microtubule system, and, as a consequence, a change in the behavior of LEs and lysosomes (LYs). Depletion of HDAC8 caused loss of centrosome-associated microtubules and loss of directed centripetal movement of LEs, dispersing LE/LYs to the cell periphery. For HDAC1, the picture was the opposite. To explain these changes, centrosome cohesion emerged as the critical factor. Depletion of HDAC8 caused centrosome splitting, which could also be induced by depleting a centriole-linker protein, rootletin. In both cases, IAV infection was inhibited. HDAC1 depletion reduced the splitting of centrosomes, and enhanced infection. The longer the distance between centrosomes, the lower the level of infection. HDAC8 depletion was also found to inhibit infection of Uukuniemi virus (a bunyavirus) suggesting common requirements among late penetrating enveloped viruses. The results established class I HDACs as powerful regulators of microtubule organization, centrosome function, endosome maturation, and infection by IAV and other late penetrating viruses.

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. We demonstrate that both SVGD and VI significantly reduce computational costs over the current state of the art. Importantly, VI does so without sacrificing precision or accuracy, presenting an overall improvement over previously published methods.

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. (2021) and compare the results with two state-of-the-art software products: STRmix™  v2.6 and Euroformix v3.4.0. The comparison shows that the Hamiltonian Monte Carlo method provides reliable values of likelihood ratios (LRs) close to the other methods. We further propose a novel large-scale precision benchmark and quantify the precision of the Hamiltonian Monte Carlo method, indicating its improvements over existing solutions. Finally, we analyse the influence of the factors discussed by Buckleton et al. (2022).

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. STENCIL-NET does not learn a governing equation, nor an approximation to the data themselves. It instead learns a discrete propagator that reproduces the data. It therefore generalizes well to different dynamics and different grid resolutions. By analogy with classic numerical methods, we show that the discrete forecasting operators learned by STENCIL-NET are numerically stable and accurate for data represented on regular Cartesian grids. A once-trained STENCIL-NET model can be used for equation-free forecasting on larger spatial domains and for longer times than it was trained for, as an autonomous predictor of chaotic dynamics, as a coarse-graining method, and as a data-adaptive de-noising method, as we illustrate in numerical experiments. In all tests, STENCIL-NET generalizes better and is computationally more efficient, both in training and inference, than neural network architectures based on local (CNN) or global (FNO) nonlinear convolutions.

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. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.