A global view of T cell metabolism in systemic lupus erythematosus.

Impaired metabolism is recognized as an important contributor to pathogenicity of T cells in Systemic Lupus Erythematosus (SLE). Over the last two decades, we have acquired significant knowledge about the signaling and transcriptomic programs related to metabolic rewiring in healthy and SLE T cells. However, our understanding of metabolic network activity derives largely from studying metabolic pathways in isolation. Here, we argue that enzymatic activities are necessarily coupled through mass and energy balance constraints with in-built network-wide dependencies and compensation mechanisms. Therefore, metabolic rewiring of T cells in SLE must be understood in the context of the entire network, including changes in metabolic demands such as shifts in biomass composition and cytokine secretion rates as well as changes in uptake/excretion rates of multiple nutrients and waste products. As a way forward, we suggest cell physiology experiments and integration of orthogonal metabolic measurements through computational modeling towards a comprehensive understanding of T cell metabolism in lupus.

The ability to sense the environment is heterogeneously distributed in cell populations.

Channel capacity of signaling networks quantifies their fidelity in sensing extracellular inputs. Low estimates of channel capacities for several mammalian signaling networks suggest that cells can barely detect the presence/absence of environmental signals. However, given the extensive heterogeneity and temporal stability of cell state variables, we hypothesize that the sensing ability itself may depend on the state of the cells. In this work, we present an information-theoretic framework to quantify the distribution of sensing abilities from single-cell data. Using data on two mammalian pathways, we show that sensing abilities are widely distributed in the population and most cells achieve better resolution of inputs compared to an 'average cell'. We verify these predictions using live-cell imaging data on the IGFR/FoxO pathway. Importantly, we identify cell state variables that correlate with cells' sensing abilities. This information-theoretic framework will significantly improve our understanding of how cells sense in their environment.

Designing host-associated microbiomes using the consumer/resource model.

A key step towards rational microbiome engineering is the in silico sampling of realistic microbial communities that correspond to desired host phenotypes, and vice versa. This remains challenging due to a lack of generative models that simultaneously model compositions of host-associated microbiomes and host phenotypes. To that end, we present a machine learning model based on the consumer/resource (C/R) framework. In the model, variation in microbial ecosystem composition arises due to differences in the availability of effective resources (latent variables) while species' resource preferences remain conserved. Variation in the same latent variables is used to model phenotypic variation across hosts. In silico microbiomes generated by our model accurately reproduce universal and dataset-specific statistics of bacterial communities. The model allows us to address two salient questions in microbiome design: (1) which host phenotypes maximally constrain the composition of the host-associated microbiome? and (2) what are plausible microbiome compositions corresponding to user-specified host phenotypes? Thus, our model aids the design and analysis of microbial communities associated with host phenotypes of interest.

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.

The ability to sense the environment is heterogeneously distributed in cell populations.

Channel capacity of signaling networks quantifies their fidelity in sensing extracellular inputs. Low estimates of channel capacities for several mammalian signaling networks suggest that cells can barely detect the presence/absence of environmental signals. However, given the extensive heterogeneity and temporal stability of cell state variables, we hypothesize that the sensing ability itself may depend on the state of the cells. In this work, we present an information theoretic framework to quantify the distribution of sensing abilities from single cell data. Using data on two mammalian pathways, we show that sensing abilities are widely distributed in the population and most cells achieve better resolution of inputs compared to an " average cell ". We verify these predictions using live cell imaging data on the IGFR/FoxO pathway. Importantly, we identify cell state variables that correlate with cells' sensing abilities. This information theoretic framework will significantly improve our understanding of how cells sense in their environment.

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.

Reverse Plasticity Underlies Rapid Evolution by Clonal Selection within Populations of Fibroblasts Propagated on a Novel Soft Substrate.

Mechanical properties such as substrate stiffness are a ubiquitous feature of a cell's environment. Many types of animal cells exhibit canonical phenotypic plasticity when grown on substrates of differing stiffness, in vitro and in vivo. Whether such plasticity is a multivariate optimum due to hundreds of millions of years of animal evolution, or instead is a compromise between conflicting selective demands, is unknown. We addressed these questions by means of experimental evolution of populations of mouse fibroblasts propagated for approximately 90 cell generations on soft or stiff substrates. The ancestral cells grow twice as fast on stiff substrate as on soft substrate and exhibit the canonical phenotypic plasticity. Soft-selected lines derived from a genetically diverse ancestral population increased growth rate on soft substrate to the ancestral level on stiff substrate and evolved the same multivariate phenotype. The pattern of plasticity in the soft-selected lines was opposite of the ancestral pattern, suggesting that reverse plasticity underlies the observed rapid evolution. Conversely, growth rate and phenotypes did not change in selected lines derived from clonal cells. Overall, our results suggest that the changes were the result of genetic evolution and not phenotypic plasticity per se. Whole-transcriptome analysis revealed consistent differentiation between ancestral and soft-selected populations, and that both emergent phenotypes and gene expression tended to revert in the soft-selected lines. However, the selected populations appear to have achieved the same phenotypic outcome by means of at least two distinct transcriptional architectures related to mechanotransduction and proliferation.

The biphasic and age-dependent impact of klotho on hallmarks of aging and skeletal muscle function.

Aging is accompanied by disrupted information flow, resulting from accumulation of molecular mistakes. These mistakes ultimately give rise to debilitating disorders including skeletal muscle wasting, or sarcopenia. To derive a global metric of growing 'disorderliness' of aging muscle, we employed a statistical physics approach to estimate the state parameter, entropy, as a function of genes associated with hallmarks of aging. Escalating network entropy reached an inflection point at old age, while structural and functional alterations progressed into oldest-old age. To probe the potential for restoration of molecular 'order' and reversal of the sarcopenic phenotype, we systemically overexpressed the longevity protein, Klotho, via AAV. Klotho overexpression modulated genes representing all hallmarks of aging in old and oldest-old mice, but pathway enrichment revealed directions of changes were, for many genes, age-dependent. Functional improvements were also age-dependent. Klotho improved strength in old mice, but failed to induce benefits beyond the entropic tipping point.

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.

Building Markov state models using optimal transport theory.

Markov State Models (MSMs) describe the rates and routes in conformational dynamics of biomolecules. Computational estimation of MSMs can be expensive because molecular simulations are slow to find and sample the rare transient events. We describe here an efficient approximate way to determine MSM rate matrices by combining maximum caliber (maximizing path entropies) with optimal transport theory (minimizing some path cost function, as when routing trucks on transportation networks) to patch together transient dynamical information from multiple non-equilibrium simulations. We give toy examples.

Perspective: Maximum caliber is a general variational principle for dynamical systems.

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.

Caliber Corrected Markov Modeling (C2M2): Correcting Equilibrium Markov Models.

Rate processes are often modeled using Markov State Models (MSMs). Suppose you know a prior MSM and then learn that your prediction of some particular observable rate is wrong. What is the best way to correct the whole MSM? For example, molecular dynamics simulations of protein folding may sample many microstates, possibly giving correct pathways through them while also giving the wrong overall folding rate when compared to experiment. Here, we describe Caliber Corrected Markov Modeling (C2M2), an approach based on the principle of maximum entropy for updating a Markov model by imposing state- and trajectory-based constraints. We show that such corrections are equivalent to asserting position-dependent diffusion coefficients in continuous-time continuous-space Markov processes modeled by a Smoluchowski equation. We derive the functional form of the diffusion coefficient explicitly in terms of the trajectory-based constraints. We illustrate with examples of 2D particle diffusion and an overdamped harmonic oscillator.

Mini-grand canonical ensemble: Chemical potential in the solvation shell.

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent bath. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.