Ninety per cent of the world's data have been generated in the last 5 years ( Machine learning: the power and promise of computers that learn by example . Report no. DES4702. Issued April 2017. Royal Society). A small fraction of these data is collected with the aim of validating specific hypotheses. These studies are led by the development of mechanistic models focused on the causality of input–output relationships. However, the vast majority is aimed at supporting statistical or correlation studies that bypass the need for causality and focus exclusively on prediction. Along these lines, there has been a vast increase in the use of machine learning models, in particular in the biomedical and clinical sciences, to try and keep pace with the rate of data generation. Recent successes now beg the question of whether mechanistic models are still relevant in this area. Said otherwise, why should we try to understand the mechanisms of disease progression when we can use machine learning tools to directly predict disease outcome?

Biologically-informed neural networks (BINNs), an extension of physics-informed neural networks [1], are introduced and used to discover the underlying dynamics of biological systems from sparse experimental data. In the present work, BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE). By allowing the diffusion and reaction terms to be multilayer perceptrons (MLPs), the nonlinear forms of these terms can be learned while simultaneously converging to the solution of the governing PDE. Further, the trained MLPs are used to guide the selection of biologically interpretable mechanistic forms of the PDE terms which provides new insights into the biological and physical mechanisms that govern the dynamics of the observed system. The method is evaluated on sparse real-world data from wound healing assays with varying initial cell densities [2].

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.

Organoids made from dissociated progenitor cells undergo tissue-like organization. This in vitro self-organization process is not identical to embryonic organ formation, but it achieves a similar phenotype in vivo. This implies genetic codes do not specify morphology directly; instead, complex tissue architectures may be achieved through several intermediate layers of cross talk between genetic information and biophysical processes. Here we use newborn and adult skin organoids for analyses. Dissociated cells from newborn mouse skin form hair primordia-bearing organoids that grow hairs robustly in vivo after transplantation to nude mice. Detailed time-lapse imaging of 3D cultures revealed unexpected morphological transitions between six distinct phases: dissociated cells, cell aggregates, polarized cysts, cyst coalescence, planar skin, and hair-bearing skin. Transcriptome profiling reveals the sequential expression of adhesion molecules, growth factors, Wnts, and matrix metalloproteinases (MMPs). Functional perturbations at different times discern their roles in regulating the switch from one phase to another. In contrast, adult cells form small aggregates, but then development stalls in vitro. Comparative transcriptome analyses suggest suppressing epidermal differentiation in adult cells is critical. These results inspire a strategy that can restore morphological transitions and rescue the hair-forming ability of adult organoids: (i) continuous PKC inhibition and (ii) timely supply of growth factors (IGF, VEGF), Wnts, and MMPs. This comprehensive study demonstrates that alternating molecular events and physical processes are in action during organoid morphogenesis and that the self-organizing processes can be restored via environmental reprogramming. This tissue-level phase transition could drive self-organization behavior in organoid morphogenies beyond the skin.

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues ofparameter identifiabilityhave important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assessstructural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available onGithub.