GENERALIST: A latent space based generative model for protein sequence families.

Generative models of protein sequence families are an important tool in the repertoire of protein scientists and engineers alike. However, state-of-the-art generative approaches face inference, accuracy, and overfitting- related obstacles when modeling moderately sized to large proteins and/or protein families with low sequence coverage. Here, we present a simple to learn, tunable, and accurate generative model, GENERALIST: GENERAtive nonLInear tenSor-factorizaTion for protein sequences. GENERALIST accurately captures several high order summary statistics of amino acid covariation. GENERALIST also predicts conservative local optimal sequences which are likely to fold in stable 3D structure. Importantly, unlike current methods, the density of sequences in GENERALIST-modeled sequence ensembles closely resembles the corresponding natural ensembles. Finally, GENERALIST embeds protein sequences in an informative latent space. GENERALIST will be an important tool to study protein sequence variability.

EMBED: Essential MicroBiomE Dynamics, a dimensionality reduction approach for longitudinal microbiome studies.

Dimensionality reduction offers unique insights into high-dimensional microbiome dynamics by leveraging collective abundance fluctuations of multiple bacteria driven by similar ecological perturbations. However, methods providing lower-dimensional representations of microbiome dynamics both at the community and individual taxa levels are not currently available. To that end, we present EMBED: Essential MicroBiomE Dynamics, a probabilistic nonlinear tensor factorization approach. Like normal mode analysis in structural biophysics, EMBED infers ecological normal modes (ECNs), which represent the unique orthogonal modes capturing the collective behavior of microbial communities. Using multiple real and synthetic datasets, we show that a very small number of ECNs can accurately approximate microbiome dynamics. Inferred ECNs reflect specific ecological behaviors, providing natural templates along which the dynamics of individual bacteria may be partitioned. Moreover, the multi-subject treatment in EMBED systematically identifies subject-specific and universal abundance dynamics that are not detected by traditional approaches. Collectively, these results highlight the utility of EMBED as a versatile dimensionality reduction tool for studies of microbiome dynamics.

Cancer cells depend on environmental lipids for proliferation when electron acceptors are limited.

Production of oxidized biomass, which requires regeneration of the cofactor NAD+, can be a proliferation bottleneck that is influenced by environmental conditions. However, a comprehensive quantitative understanding of metabolic processes that may be affected by NAD+ deficiency is currently missing. Here, we show that de novo lipid biosynthesis can impose a substantial NAD+ consumption cost in proliferating cancer cells. When electron acceptors are limited, environmental lipids become crucial for proliferation because NAD+ is required to generate precursors for fatty acid biosynthesis. We find that both oxidative and even net reductive pathways for lipogenic citrate synthesis are gated by reactions that depend on NAD+ availability. We also show that access to acetate can relieve lipid auxotrophy by bypassing the NAD+ consuming reactions. Gene expression analysis demonstrates that lipid biosynthesis strongly anti-correlates with expression of hypoxia markers across tumor types. Overall, our results define a requirement for oxidative metabolism to support biosynthetic reactions and provide a mechanistic explanation for cancer cell dependence on lipid uptake in electron acceptor-limited conditions, such as hypoxia.

SiGMoiD: A super-statistical generative model for binary data.

In modern computational biology, there is great interest in building probabilistic models to describe collections of a large number of co-varying binary variables. However, current approaches to build generative models rely on modelers' identification of constraints and are computationally expensive to infer when the number of variables is large (N~100). Here, we address both these issues with Super-statistical Generative Model for binary Data (SiGMoiD). SiGMoiD is a maximum entropy-based framework where we imagine the data as arising from super-statistical system; individual binary variables in a given sample are coupled to the same 'bath' whose intensive variables vary from sample to sample. Importantly, unlike standard maximum entropy approaches where modeler specifies the constraints, the SiGMoiD algorithm infers them directly from the data. Due to this optimal choice of constraints, SiGMoiD allows us to model collections of a very large number (N>1000) of binary variables. Finally, SiGMoiD offers a reduced dimensional description of the data, allowing us to identify clusters of similar data points as well as binary variables. We illustrate the versatility of SiGMoiD using multiple datasets spanning several time- and length-scales.

Macroecological dynamics of gut microbiota.

The gut microbiota is now widely recognized as a dynamic ecosystem that plays an important role in health and disease. Although current sequencing technologies make it possible to explore how relative abundances of host-associated bacteria change over time, the biological processes governing microbial dynamics remain poorly understood. Therefore, as in other ecological systems, it is important to identify quantitative relationships describing various aspects of gut microbiota dynamics. In the present study, we use multiple high-resolution time series data obtained from humans and mice to demonstrate that, despite their inherent complexity, gut microbiota dynamics can be characterized by several robust scaling relationships. Interestingly, the observed patterns are highly similar to those previously identified across diverse ecological communities and economic systems, including the temporal fluctuations of animal and plant populations and the performance of publicly traded companies. Specifically, we find power-law relationships describing short- and long-term changes in gut microbiota abundances, species residence and return times, and the correlation between the mean and the temporal variance of species abundances. The observed scaling laws are altered in mice receiving different diets and are affected by context-specific perturbations in humans. We use the macroecological relationships to reveal specific bacterial taxa, the dynamics of which are substantially perturbed by dietary and environmental changes. Overall, our results suggest that a quantitative macroecological framework will be important for characterizing and understanding the complex dynamics of diverse microbial communities.

The Maximum Caliber Variational Principle for Nonequilibria.

Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.

Receptor-based mechanism of relative sensing and cell memory in mammalian signaling networks.

Detecting relative rather than absolute changes in extracellular signals enables cells to make decisions in constantly fluctuating environments. It is currently not well understood how mammalian signaling networks store the memories of past stimuli and subsequently use them to compute relative signals, that is perform fold change detection. Using the growth factor-activated PI3K-Akt signaling pathway, we develop here computational and analytical models, and experimentally validate a novel non-transcriptional mechanism of relative sensing in mammalian cells. This mechanism relies on a new form of cellular memory, where cells effectively encode past stimulation levels in the abundance of cognate receptors on the cell surface. The surface receptor abundance is regulated by background signal-dependent receptor endocytosis and down-regulation. We show the robustness and specificity of relative sensing for two physiologically important ligands, epidermal growth factor (EGF) and hepatocyte growth factor (HGF), and across wide ranges of background stimuli. Our results suggest that similar mechanisms of cell memory and fold change detection may be important in diverse signaling cascades and multiple biological contexts.

Maximum Entropy Framework for Predictive Inference of Cell Population Heterogeneity and Responses in Signaling Networks.

Predictive models of signaling networks are essential for understanding cell population heterogeneity and designing rational interventions in disease. However, using computational models to predict heterogeneity of signaling dynamics is often challenging because of the extensive variability of biochemical parameters across cell populations. Here, we describe a maximum entropy-based framework for inference of heterogeneity in dynamics of signaling networks (MERIDIAN). MERIDIAN estimates the joint probability distribution over signaling network parameters that is consistent with experimentally measured cell-to-cell variability of biochemical species. We apply the developed approach to investigate the response heterogeneity in the EGFR/Akt signaling network. Our analysis demonstrates that a significant fraction of cells exhibits high phosphorylated Akt (pAkt) levels hours after EGF stimulation. Our findings also suggest that cells with high EGFR levels predominantly contribute to the subpopulation of cells with high pAkt activity. We also discuss how MERIDIAN can be extended to accommodate various experimental measurements.

Quantifying spatiotemporal variability and noise in absolute microbiota abundances using replicate sampling.

Metagenomic sequencing has enabled detailed investigation of diverse microbial communities, but understanding their spatiotemporal variability remains an important challenge. Here, we present decomposition of variance using replicate sampling (DIVERS), a method based on replicate sampling and spike-in sequencing. The method quantifies the contributions of temporal dynamics, spatial sampling variability, and technical noise to the variances and covariances of absolute bacterial abundances. We applied DIVERS to investigate a high-resolution time series of the human gut microbiome and a spatial survey of a soil bacterial community in Manhattan's Central Park. Our analysis showed that in the gut, technical noise dominated the abundance variability for nearly half of the detected taxa. DIVERS also revealed substantial spatial heterogeneity of gut microbiota, and high temporal covariances of taxa within the Bacteroidetes phylum. In the soil community, spatial variability primarily contributed to abundance fluctuations at short time scales (weeks), while temporal variability dominated at longer time scales (several months).

Introducing User-Prescribed Constraints in Markov Chains for Nonlinear Dimensionality Reduction.

Stochastic kernel-based dimensionality-reduction approaches have become popular in the past decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified by the kernel through row normalization. However, in many cases, it is desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Unfortunately, no systematic framework exists to impose such user-defined constraints. Here, based on our previous work on inference of Markov models, we introduce a path entropy maximization based approach to derive the transition probabilities of Markov chains using a kernel and additional user-specified constraints. We illustrate the usefulness of these Markov chains with examples.