Efficient exact inference for dynamical systems with noisy measurements using sequential approximate Bayesian computation

Missing data in amortized simulation-based neural posterior estimation

Amortized simulation-based neural posterior estimation provides a novel machine learning based approach for solving parameter estimation problems. It has been shown to be computationally efficient and able to handle complex models and data sets. Yet, the available approach cannot handle the in experimental studies ubiquitous case of missing data, and might provide incorrect posterior estimates. In this work, we discuss various ways of encoding missing data and integrate them into the training and inference process. We implement the approaches in the BayesFlow methodology, an amortized estimation framework based on invertible neural networks, and evaluate their performance on multiple test problems. We find that an approach in which the data vector is augmented with binary indicators of presence or absence of values performs the most robustly. Indeed, it improved the performance also for the simpler problem of data sets with variable length. Accordingly, we demonstrate that amortized simulation-based inference approaches are applicable even with missing data, and we provide a guideline for their handling, which is relevant for a broad spectrum of applications.

An in vitro agent-based modelling approach to optimization of culture medium for generating muscle cells

Methodologies for culturing muscle tissue are currently lacking in terms of quality and quantity of mature cells produced. We analyse images from in vitro experiments to quantify the effects of culture media composition on mouse-derived myoblast behaviour and myotube quality. Metrics of early indicators of cell quality were defined. Images of muscle cell differentiation reveal that altering culture media significantly affects quality indicators and myoblast migratory behaviours. To study the effects of early-stage cell behaviours on mature cell quality, metrics drawn from experimental images or inferred by approximate Bayesian computation (ABC) were applied as inputs to an agent-based model (ABM) of skeletal muscle cell differentiation with quality indicator metrics as outputs. Computational modelling was used to inform further in vitro experiments to predict the optimum media composition for culturing muscle cells. Our results suggest that myonuclei production in myotubes is inversely related to early-stage nuclei fusion index and that myonuclei density and spatial distribution are correlated with residence time of fusing myoblasts, the age at which myotube-myotube fusion ends and the repulsion force between myonuclei. Culture media with 5% serum was found to produce the optimum cell quality and to make muscle cells cultured in a neuron differentiation medium viable.

FitMultiCell: simulating and parameterizing computational models of multi-scale and multi-cellular processes

MOTIVATION

Biological tissues are dynamic and highly organized. Multi-scale models are helpful tools to analyse and understand the processes determining tissue dynamics. These models usually depend on parameters that need to be inferred from experimental data to achieve a quantitative understanding, to predict the response to perturbations, and to evaluate competing hypotheses. However, even advanced inference approaches such as approximate Bayesian computation (ABC) are difficult to apply due to the computational complexity of the simulation of multi-scale models. Thus, there is a need for a scalable pipeline for modeling, simulating, and parameterizing multi-scale models of multi-cellular processes.

RESULTS

Here, we present FitMultiCell, a computationally efficient and user-friendly open-source pipeline that can handle the full workflow of modeling, simulating, and parameterizing for multi-scale models of multi-cellular processes. The pipeline is modular and integrates the modeling and simulation tool Morpheus and the statistical inference tool pyABC. The easy integration of high-performance infrastructure allows to scale to computationally expensive problems. The introduction of a novel standard for the formulation of parameter inference problems for multi-scale models additionally ensures reproducibility and reusability. By applying the pipeline to multiple biological problems, we demonstrate its broad applicability, which will benefit in particular image-based systems biology.

AVAILABILITY AND IMPLEMENTATION

FitMultiCell is available open-source at https://gitlab.com/fitmulticell/fit.

Influence of cell type specific infectivity and tissue composition on SARS-CoV-2 infection dynamics within human airway epithelium

Human airway epithelium (HAE) represents the primary site of viral infection for SARS-CoV-2. Comprising different cell populations, a lot of research has been aimed at deciphering the major cell types and infection dynamics that determine disease progression and severity. However, the cell type-specific replication kinetics, as well as the contribution of cellular composition of the respiratory epithelium to infection and pathology are still not fully understood. Although experimental advances, including Air-liquid interface (ALI) cultures of reconstituted pseudostratified HAE, as well as lung organoid systems, allow the observation of infection dynamics under physiological conditions in unprecedented level of detail, disentangling and quantifying the contribution of individual processes and cells to these dynamics remains challenging. Here, we present how a combination of experimental data and mathematical modelling can be used to infer and address the influence of cell type specific infectivity and tissue composition on SARS-CoV-2 infection dynamics. Using a stepwise approach that integrates various experimental data on HAE culture systems with regard to tissue differentiation and infection dynamics, we develop an individual cell-based model that enables investigation of infection and regeneration dynamics within pseudostratified HAE. In addition, we present a novel method to quantify tissue integrity based on image data related to the standard measures of transepithelial electrical resistance measurements. Our analysis provides a first aim of quantitatively assessing cell type specific infection kinetics and shows how tissue composition and changes in regeneration capacity, as e.g. in smokers, can influence disease progression and pathology. Furthermore, we identified key measurements that still need to be assessed in order to improve inference of cell type specific infection kinetics and disease progression. Our approach provides a method that, in combination with additional experimental data, can be used to disentangle the complex dynamics of viral infection and immunity within human airway epithelial culture systems.

The chemical Langevin equation for biochemical systems in dynamic environments

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other - and mostly unknown - fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation-a physically motivated extension of the chemical Langevin equation- to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

Guidance by followers ensures long-range coordination of cell migration through α-catenin mechanoperception

Morphogenesis, wound healing, and some cancer metastases depend upon the migration of cell collectives that need to be guided to their destination as well as coordinated with other cell movements. During zebrafish gastrulation, the extension of the embryonic axis is led by the mesendodermal polster that migrates toward the animal pole, followed by the axial mesoderm that undergoes convergence and extension. Here, we investigate how polster cells are guided toward the animal pole. Using a combination of precise laser ablations, advanced transplants, and functional as well as in silico approaches, we establish that each polster cell is oriented by its immediate follower cells. Each cell perceives the migration of followers, through E-cadherin/α-catenin mechanotransduction, and aligns with them. Therefore, directional information propagates from cell to cell over the whole tissue. Such guidance of migrating cells by followers ensures long-range coordination of movements and developmental robustness.