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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].

Scientific analysis often relies on the ability to make accurate predictions of a system's dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model state and parameters prior to prediction is necessary, but may be complicated by issues such as noisy data and uncertainty in parameters and initial conditions. At the other end of the spectrum exist nonparametric methods, which rely solely on data to build their predictions. While these nonparametric methods do not require a model of the system, their performance is strongly influenced by the amount and noisiness of the data. In this article, we consider a hybrid approach to modeling and prediction which merges recent advancements in nonparametric analysis with standard parametric methods. The general idea is to replace a subset of a mechanistic model's equations with their corresponding nonparametric representations, resulting in a hybrid modeling and prediction scheme. Overall, we find that this hybrid approach allows for more robust parameter estimation and improved short-term prediction in situations where there is a large uncertainty in model parameters. We demonstrate these advantages in the classical Lorenz-63 chaotic system and in networks of Hindmarsh-Rose neurons before application to experimentally collected structured population data.

Angiogenesis is the process by which blood vessels form from pre-existing vessels. It plays a key role in many biological processes, including embryonic development and wound healing, and contributes to many diseases including cancer and rheumatoid arthritis. The structure of the resulting vessel networks determines their ability to deliver nutrients and remove waste products from biological tissues. Here we simulate the Anderson-Chaplain model of angiogenesis at different parameter values and quantify the vessel architectures of the resulting synthetic data. Specifically, we propose a topological data analysis (TDA) pipeline for systematic analysis of the model. TDA is a vibrant and relatively new field of computational mathematics for studying the shape of data. We compute topological and standard descriptors of model simulations generated by different parameter values. We show that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology. The methodologies proposed here are widely applicable to other synthetic and experimental data including wound healing, development, and plant biology.

Background Access to quantitative information is crucial to obtain a deeper understanding of biological systems. In addition to being low-throughput, traditional image-based analysis is mostly limited to error-prone qualitative or semi-quantitative assessment of phenotypes, particularly for complex subcellular morphologies. The PVD neuron in Caenorhabditis elegans , which is responsible for harsh touch and thermosensation, undergoes structural degeneration as nematodes age characterized by the appearance of dendritic protrusions. Analysis of these neurodegenerative patterns is labor-intensive and limited to qualitative assessment. Results In this work, we apply deep learning to perform quantitative image-based analysis of complex neurodegeneration patterns exhibited by the PVD neuron in C. elegans . We apply a convolutional neural network algorithm (Mask R-CNN) to identify neurodegenerative subcellular protrusions that appear after cold-shock or as a result of aging. A multiparametric phenotypic profile captures the unique morphological changes induced by each perturbation. We identify that acute cold-shock-induced neurodegeneration is reversible and depends on rearing temperature and, importantly, that aging and cold-shock induce distinct neuronal beading patterns. Conclusion The results of this work indicate that implementing deep learning for challenging image segmentation of PVD neurodegeneration enables quantitatively tracking subtle morphological changes in an unbiased manner. This analysis revealed that distinct patterns of morphological alteration are induced by aging and cold-shock, suggesting different mechanisms at play. This approach can be used to identify the molecular components involved in orchestrating neurodegeneration and to characterize the effect of other stressors on PVD degeneration.

Kidney transplant recipients require a lifelong protocol of immunosuppressive therapy to prevent graft rejection. However, these same medications leave them susceptible to opportunistic infections. One pathogen of particular concern is human polyomavirus 1, also known as BK virus (BKPyV). This virus attacks kidney tubule epithelial cells and is a direct threat to the health of the graft. Current standard of care in BK virus-infected transplant recipients is reduction in immunosuppressant therapy, to allow the patient’s immune system to control the virus. This requires a delicate balance; immune suppression must be strong enough to prevent rejection, yet weak enough to allow viral clearance. We seek to model viral and immune dynamics with the ultimate goal of applying optimal control methods to this problem. In this paper, we begin with a previously published model and make simplifying assumptions that reduce the number of parameters from 20 to 14. We calibrate our model using newly available patient data and a detailed sensitivity analysis. Numerical results for multiple patients are given to show that the newer model reflects observed dynamics well.

In the study of brain tumors, patient-derived three-dimensional sphere cultures provide an important tool for studying emerging treatments. The growth of such spheroids depends on the combined effects of proliferation and migration of cells, but it is challenging to make accurate distinctions between increase in cell number versus the radial movement of cells. To address this, we formulate a novel model in the form of a system of two partial differential equations (PDEs) incorporating both migration and growth terms, and show that it more accurately fits our data compared to simpler PDE models. We show that traveling-wave speeds are strongly associated with population heterogeneity. Having fitted the model to our dataset we show that a subset of the cell lines are best described by a “Go-or-Grow”-type model, which constitutes a special case of our model. Finally, we investigate whether our fitted model parameters are correlated with patient age and survival.

We investigate methods for learning partial differential equation (PDE) models from spatio-temporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select candidate terms from a denoised set of data, including approximated partial derivatives. We analyse the performance in using previous methods to denoise data for the task of discovering the governing system of PDEs. We also develop a novel methodology that uses artificial neural networks (ANNs) to denoise data and approximate partial derivatives. We test the methodology on three PDE models for biological transport, i.e. the advection–diffusion, classical Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) and nonlinear Fisher–KPP equations. We show that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.

Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models’ performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k -means clustering to predict the number of subpopulations based on the recovered distributions.

Methylation of DNA is an epigenetic mechanism that influences patterns of gene expression. DNA methylation marks contribute to adaptive phenotypic variation but are erased during development. The role of DNA methylation in adaptive evolution is therefore unclear. We propose that environmentally-induced DNA methylation causes phenotypic heterogeneity that provides a substrate for selection via forces that act on the epigenetic machinery. For example, selection can alter environmentally-induced methylation of DNA by acting on the molecular mechanisms used for the genomic targeting of DNA methylation. Another possibility is that specific methylation marks that are environmentally-induced, yet non-heritable, could influence preferential survival and lead to consistent methylation of the same genomic regions over time. As methylation of DNA is known to increase the likelihood of cytosine-to-thymine transitions, non-heritable adaptive methylation marks can drive an increased likelihood of mutations targeted to regions that are consistently marked across several generations. Some of these mutations could capture, genetically, the phenotypic advantage of the epigenetic mark. Thereby, selectively favored transitory alterations in the genome invoked by DNA methylation could ultimately become selectable genetic variation through mutation. We provide evidence for these concepts using examples from different taxa, but focus on experimental data on large-scale DNA sequencing that expose between-group genetic variation after bidirectional selection on honeybees, Apis mellifera.

Introduction Intravenous lipid emulsions (ILE) have been credited for successful resuscitation in drug intoxication cases where other cardiac life-support methods have failed. However, inter-individual variability can function as a confounder that challenges our ability to define the scope of efficacy for lipid interventions, particularly as relevant data are scarce. To address this challenge, we developed a quantitative systems pharmacology model to predict outcome variability and shed light on causal mechanisms in a virtual population of rats subjected to bupivacaine toxicity and ILE intervention. Materials and Methods We combined a physiologically based pharmacokinetic–pharmacodynamic model with data from a small study in Sprague-Dawley rats to characterize individual-specific cardiac responses to lipid infusion. We used the resulting individual parameter estimates to posit a population distribution of responses to lipid infusion. On that basis, we constructed a large virtual population of rats ( N  = 10,000) undergoing lipid therapy following bupivacaine cardiotoxicity. Results Using unsupervised clustering to assign resuscitation endpoints, our simulations predicted that treatment with a 30% lipid emulsion increases bupivacaine median lethal dose (LD 50 ) by 46% when compared with a simulated control fluid. Prior experimental findings indicated an LD 50 increase of 48%. Causal analysis of the population data suggested that muscle accumulation rather than liver accumulation of bupivacaine drives survival outcomes. Conclusion Our results represent a successful prediction of complex, dynamic physiological outcomes over a virtual population. Despite being informed by very limited data, our mechanistic model predicted a plausible range of treatment outcomes that accurately predicts changes in LD 50 when extrapolated to putatively toxic doses of bupivacaine. Furthermore, causal analysis of the predicted survival outcomes indicated a critical synergy between scavenging and direct cardiotonic mechanisms of ILE action.