The proteome is a terminal electron acceptor.

Microbial metabolism is impressively flexible, enabling growth even when available nutrients differ greatly from biomass in redox state. E. coli, for example, rearranges its physiology to grow on reduced and oxidized carbon sources through several forms of fermentation and respiration. To understand the limits on and evolutionary consequences of metabolic flexibility, we developed a mathematical model coupling redox chemistry with principles of cellular resource allocation. Our integrated model clarifies key phenomena, including demonstrating that autotrophs grow slower than heterotrophs because of constraints imposed by intracellular production of reduced carbon. Our model further indicates that growth is improved by adapting the redox state of biomass to nutrients, revealing an unexpected mode of evolution where proteins accumulate mutations benefiting organismal redox balance.

Dissecting endogeneous genetic circuits from first principles.

For the vast majority of genes in sequenced genomes, there is limited understanding of how they are regulated. Without such knowledge, it is not possible to perform a quantitative theory-experiment dialogue on how such genes give rise to physiological and evolutionary adaptation. One category of high-throughput experiments used to understand the sequence-phenotype relationship of the transcriptome is massively parallel reporter assays (MPRAs). However, to improve the versatility and scalability of MPRA pipelines, we need a "theory of the experiment" to help us better understand the impact of various biological and experimental parameters on the interpretation of experimental data. These parameters include binding site copy number, where a large number of specific binding sites may titrate away transcription factors, as well as the presence of overlapping binding sites, which may affect analysis of the degree of mutual dependence between mutations in the regulatory region and expression levels. Here, we develop a computational pipeline that makes it possible to systematically explore how each biological and experimental parameter controls measured MPRA data. Specifically, we use equilibrium statistical mechanics in conjunction with predictive base-pair resolution energy matrices to predict expression levels of genes with mutated regulatory sequences and subsequently use mutual information to interpret synthetic MPRA data including recovering the expected binding sites. Our simulations reveal important effects of the parameters on MPRA data and we demonstrate our ability to optimize MPRA experimental designs with the goal of generating thermodynamic models of the transcriptome with base-pair specificity. Further, this approach makes it possible to carefully examine the mapping between mutations in binding sites and their corresponding expression profiles, a tool useful not only for better designing MPRAs, but also for exploring regulatory evolution.

Dissecting endogeneous genetic circuits from first principles.

For the vast majority of genes in sequenced genomes, there is limited understanding of how they are regulated. Without such knowledge, it is not possible to perform a quantitative theory-experiment dialogue on how such genes give rise to physiological and evolutionary adaptation. One category of high-throughput experiments used to understand the sequence-phenotype relationship of the transcriptome is massively parallel reporter assays (MPRAs). However, to improve the versatility and scalability of MPRA pipelines, we need a "theory of the experiment" to help us better understand the impact of various biological and experimental parameters on the interpretation of experimental data. These parameters include binding site copy number, where a large number of specific binding sites may titrate away transcription factors, as well as the presence of overlapping binding sites, which may affect analysis of the degree of mutual dependence between mutations in the regulatory region and expression levels. Here, we develop a computational pipeline that makes it possible to systematically explore how each biological and experimental parameter controls measured MPRA data. Specifically, we use equilibrium statistical mechanics in conjunction with predictive base-pair resolution energy matrices to predict expression levels of genes with mutated regulatory sequences and subsequently use mutual information to interpret synthetic MPRA data including recovering the expected binding sites. Our simulations reveal important effects of the parameters on MPRA data and we demonstrate our ability to optimize MPRA experimental designs with the goal of generating thermodynamic models of the transcriptome with base-pair specificity. Further, this approach makes it possible to carefully examine the mapping between mutations in binding sites and their corresponding expression profiles, a tool useful not only for better designing MPRAs, but also for exploring regulatory evolution.

Wildebeest herds on rolling hills: Flocking on arbitrary curved surfaces.

The collective behavior of active agents, whether herds of wildebeest or microscopic actin filaments propelled by molecular motors, is an exciting frontier in biological and soft matter physics. Almost three decades ago, Toner and Tu developed a continuum theory of the collective action of flocks, or herds, that helped launch the modern field of active matter. One challenge faced when applying continuum active matter theories to living phenomena is the complex geometric structure of biological environments. Both macroscopic and microscopic herds move on asymmetric curved surfaces, like undulating grass plains or the surface layers of cells or embryos, which can render problems analytically intractable. In this paper, we present a formulation of the Toner-Tu flocking theory that uses the finite element method to solve the governing equations on arbitrary curved surfaces. First, we test the developed formalism and its numerical implementation in channel flow with scattering obstacles and on cylindrical and spherical surfaces, comparing our results to analytical solutions. We then progress to surfaces with arbitrary curvature, moving beyond previously accessible problems to explore herding behavior on a variety of landscapes. This approach allows the investigation of transients and dynamic solutions not revealed by analytic methods. It also enables versatile incorporation of new geometries and boundary conditions and efficient sweeps of parameter space. Looking forward, the paper presented here lays the groundwork for a dialogue between Toner-Tu theory and data on collective motion in biologically relevant geometries, from drone footage of migrating animal herds to movies of microscopic cytoskeletal flows within cells.

High Fidelity Pressure Wires Provide Accurate Validation of Non-Invasive Central Blood Pressure and Pulse Wave Velocity Measurements.

Central blood pressure (cBP) is known to be a better predictor of the damage caused by hypertension in comparison with peripheral blood pressure. During cardiac catheterization, we measured cBP in the ascending aorta with a fluid-filled guiding catheter (FF) in 75 patients and with a high-fidelity micromanometer tipped wire (FFR) in 20 patients. The wire was withdrawn into the brachial artery and aorto-brachial pulse wave velocity (abPWV) was calculated from the length of the pullback and the time delay between the ascending aorta and the brachial artery pulse waves by gating to the R-wave of the ECG for both measurements. In 23 patients, a cuff was inflated around the calf and an aorta-tibial pulse wave velocity (atPWV) was calculated from the distance between the cuff around the leg and the axillary notch and the time delay between the ascending aorta and the tibial pulse waves. Brachial BP was measured non-invasively and cBP was estimated using a new suprasystolic oscillometric technology. The mean differences between invasively measured cBP by FFR and non-invasive estimation were -0.4 ± 5.7 mmHg and by FF 5.4 ± 9.4 mmHg in 52 patients. Diastolic and mean cBP were both overestimated by oscillometry, with mean differences of -8.9 ± 5.5 mmHg and -6.4 ± 5.1 mmHg compared with the FFR and -10.6 ± 6.3 mmHg and -5.9 ± 6.2 mmHg with the FF. Non-invasive systolic cBP compared accurately with the high-fidelity FFR measurements, demonstrating a low bias (≤5 mmHg) and high precision (SD ≤ 8 mmHg). These criteria were not met when using the FF measurements. Invasively derived average Ao-brachial abPWV was 7.0 ± 1.4 m/s and that of Ao-tibial atPWV was 9.1 ± 1.8 m/s. Non-invasively estimated PWV based on the reflected wave transit time did not correlate with abPWV or with atPWV. In conclusion, we demonstrate the advantages of a novel method of validation for non-invasive cBP monitoring devices using acknowledged gold standard FFR wire transducers and the possibility to easily measure PWV during coronary angiography with the impact of cardiovascular risk factors.

Flexibility and sensitivity in gene regulation out of equilibrium.

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume bio-chemical energy. How does this dissipation enable cellular behaviors unobtainable in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different levels or achieve outputs with multiple concentration regions of locally-enhanced sensitivity. We systematically dissect how energetically-driving individual transitions within regulatory networks, or pairs of transitions, generates more adjustable and sensitive phenotypic responses. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors-feasibly accessed using biological energy budgets and rates-may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium. Significance Statement: Growing theoretical and experimental evidence demonstrates that cells can (and do) spend biochemical energy while regulating their genes. Here we explore the impact of departing from equilibrium in simple regulatory cycles, and learn that beyond increasing sensitivity, dissipation can unlock more flexible input-output behaviors that are otherwise forbidden without spending energy. These more complex behaviors could enable cells to perform more sophisticated functions using simpler systems than those needed at equilibrium.

Motor processivity and speed determine structure and dynamics of microtubule-motor assemblies.

Active matter systems can generate highly ordered structures, avoiding equilibrium through the consumption of energy by individual constituents. How the microscopic parameters that characterize the active agents are translated to the observed mesoscopic properties of the assembly has remained an open question. These active systems are prevalent in living matter; for example, in cells, the cytoskeleton is organized into structures such as the mitotic spindle through the coordinated activity of many motor proteins walking along microtubules. Here, we investigate how the microscopic motor-microtubule interactions affect the coherent structures formed in a reconstituted motor-microtubule system. This question is of deeper evolutionary significance as we suspect motor and microtubule type contribute to the shape and size of resulting structures. We explore key parameters experimentally and theoretically, using a variety of motors with different speeds, processivities, and directionalities. We demonstrate that aster size depends on the motor used to create the aster, and develop a model for the distribution of motors and microtubules in steady-state asters that depends on parameters related to motor speed and processivity. Further, we show that network contraction rates scale linearly with the single-motor speed in quasi-one-dimensional contraction experiments. In all, this theoretical and experimental work helps elucidate how microscopic motor properties are translated to the much larger scale of collective motor-microtubule assemblies.

Modeling and mechanical perturbations reveal how spatially regulated anchorage gives rise to spatially distinct mechanics across the mammalian spindle.

During cell division, the spindle generates force to move chromosomes. In mammals, microtubule bundles called kinetochore-fibers (k-fibers) attach to and segregate chromosomes. To do so, k-fibers must be robustly anchored to the dynamic spindle. We previously developed microneedle manipulation to mechanically challenge k-fiber anchorage, and observed spatially distinct response features revealing the presence of heterogeneous anchorage (Suresh et al., 2020). How anchorage is precisely spatially regulated, and what forces are necessary and sufficient to recapitulate the k-fiber's response to force remain unclear. Here, we develop a coarse-grained k-fiber model and combine with manipulation experiments to infer underlying anchorage using shape analysis. By systematically testing different anchorage schemes, we find that forces solely at k-fiber ends are sufficient to recapitulate unmanipulated k-fiber shapes, but not manipulated ones for which lateral anchorage over a 3 µm length scale near chromosomes is also essential. Such anchorage robustly preserves k-fiber orientation near chromosomes while allowing pivoting around poles. Anchorage over a shorter length scale cannot robustly restrict pivoting near chromosomes, while anchorage throughout the spindle obstructs pivoting at poles. Together, this work reveals how spatially regulated anchorage gives rise to spatially distinct mechanics in the mammalian spindle, which we propose are key for function.

Anthroponumbers.org: A quantitative database of human impacts on Planet Earth.

The Human Impacts Database (www.anthroponumbers.org) is a curated, searchable resource housing quantitative data relating to the diverse anthropogenic impacts on our planet, with topics ranging from sea-level rise to livestock populations, greenhouse gas emissions, fertilizer use, and beyond. Each entry in the database reports a quantitative value (or a time series of values) along with clear referencing of the primary source, the method of measurement or estimation, an assessment of uncertainty, and links to the underlying data, as well as a permanent identifier called a Human Impacts ID (HuID). While there are other databases that house some of these values, they are typically focused on a single topic area, like energy usage or greenhouse gas emissions. The Human Impacts Database facilitates access to carefully curated data, acting as a quantitative resource pertaining to the myriad ways in which humans have an impact on the Earth, for practicing scientists, the general public, and those involved in education for sustainable development alike. We outline the structure of the database, describe our curation procedures, and use this database to generate a graphical summary of the current state of human impacts on the Earth, illustrating both their numerical values and their intimate interconnections.

MCRL: using a reference library to compress a metagenome into a non-redundant list of sequences, considering viruses as a case study.

MOTIVATION: Metagenomes offer a glimpse into the total genomic diversity contained within a sample. Currently, however, there is no straightforward way to obtain a non-redundant list of all putative homologs of a set of reference sequences present in a metagenome. RESULTS: To address this problem, we developed a novel clustering approach called 'metagenomic clustering by reference library' (MCRL), where a reference library containing a set of reference genes is clustered with respect to an assembled metagenome. According to our proposed approach, reference genes homologous to similar sets of metagenomic sequences, termed 'signatures', are iteratively clustered in a greedy fashion, retaining at each step the reference genes yielding the lowest E values, and terminating when signatures of remaining reference genes have a minimal overlap. The outcome of this computation is a non-redundant list of reference genes homologous to minimally overlapping sets of contigs, representing potential candidates for gene families present in the metagenome. Unlike metagenomic clustering methods, there is no need for contigs to overlap to be associated with a cluster, enabling MCRL to draw on more information encoded in the metagenome when computing tentative gene families. We demonstrate how MCRL can be used to extract candidate viral gene families from an oral metagenome and an oral virome that otherwise could not be determined using standard approaches. We evaluate the sensitivity, accuracy and robustness of our proposed method for the viral case study and compare it with existing analysis approaches. AVAILABILITY AND IMPLEMENTATION: https://github.com/a-tadmor/MCRL. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Fundamental limits on the rate of bacterial growth and their influence on proteomic composition.

Despite abundant measurements of bacterial growth rate, cell size, and protein content, we lack a rigorous understanding of what sets the scale of these quantities and when protein abundances should (or should not) depend on growth rate. Here, we estimate the basic requirements and physical constraints on steady-state growth by considering key processes in cellular physiology across a collection of Escherichia coli proteomic data covering ≈4,000 proteins and 36 growth rates. Our analysis suggests that cells are predominantly tuned for the task of cell doubling across a continuum of growth rates; specific processes do not limit growth rate or dictate cell size. We present a model of proteomic regulation as a function of nutrient supply that reconciles observed interdependences between protein synthesis, cell size, and growth rate and propose that a theoretical inability to parallelize ribosomal synthesis places a firm limit on the achievable growth rate. A record of this paper's transparent peer review process is included in the supplemental information.

Schrödinger's What Is Life? at 75.

2019 marked the 75th anniversary of the publication of Erwin Schrödinger's What Is Life?, a short book described by Roger Penrose in his preface to a reprint of this classic as "among the most influential scientific writings of the 20th century." In this article, I review the long argument made by Schrödinger as he mused on how the laws of physics could help us understand "the events in space and time which take place within the spatial boundary of a living organism." Though Schrödinger's book is often hailed for its influence on some of the titans who founded molecular biology, this article takes a different tack. Instead of exploring the way the book touched biologists such as James Watson and Francis Crick, as well as its critical reception by others such as Linus Pauling and Max Perutz, I argue that Schrödinger's classic is a timeless manifesto, rather than a dated historical curiosity. What Is Life? is full of timely outlooks and approaches to understanding the mysterious living world that includes and surrounds us and can instead be viewed as a call to arms to tackle the great unanswered challenges in the study of living matter that remain for 21st century science.

The total number and mass of SARS-CoV-2 virions.

Quantitatively describing the time course of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection within an infected individual is important for understanding the current global pandemic and possible ways to combat it. Here we integrate the best current knowledge about the typical viral load of SARS-CoV-2 in bodily fluids and host tissues to estimate the total number and mass of SARS-CoV-2 virions in an infected person. We estimate that each infected person carries 109 to 1011 virions during peak infection, with a total mass in the range of 1 µg to 100 µg, which curiously implies that all SARS-CoV-2 virions currently circulating within human hosts have a collective mass of only 0.1 kg to 10 kg. We combine our estimates with the available literature on host immune response and viral mutation rates to demonstrate how antibodies markedly outnumber the spike proteins, and the genetic diversity of virions in an infected host covers all possible single nucleotide substitutions.

Multiplexed characterization of rationally designed promoter architectures deconstructs combinatorial logic for IPTG-inducible systems.

A crucial step towards engineering biological systems is the ability to precisely tune the genetic response to environmental stimuli. In the case of Escherichia coli inducible promoters, our incomplete understanding of the relationship between sequence composition and gene expression hinders our ability to predictably control transcriptional responses. Here, we profile the expression dynamics of 8269 rationally designed, IPTG-inducible promoters that collectively explore the individual and combinatorial effects of RNA polymerase and LacI repressor binding site strengths. We then fit a statistical mechanics model to measured expression that accurately models gene expression and reveals properties of theoretically optimal inducible promoters. Furthermore, we characterize three alternative promoter architectures and show that repositioning binding sites within promoters influences the types of combinatorial effects observed between promoter elements. In total, this approach enables us to deconstruct relationships between inducible promoter elements and discover practical insights for engineering inducible promoters with desirable characteristics.

Reconciling kinetic and thermodynamic models of bacterial transcription.

The study of transcription remains one of the centerpieces of modern biology with implications in settings from development to metabolism to evolution to disease. Precision measurements using a host of different techniques including fluorescence and sequencing readouts have raised the bar for what it means to quantitatively understand transcriptional regulation. In particular our understanding of the simplest genetic circuit is sufficiently refined both experimentally and theoretically that it has become possible to carefully discriminate between different conceptual pictures of how this regulatory system works. This regulatory motif, originally posited by Jacob and Monod in the 1960s, consists of a single transcriptional repressor binding to a promoter site and inhibiting transcription. In this paper, we show how seven distinct models of this so-called simple-repression motif, based both on thermodynamic and kinetic thinking, can be used to derive the predicted levels of gene expression and shed light on the often surprising past success of the thermodynamic models. These different models are then invoked to confront a variety of different data on mean, variance and full gene expression distributions, illustrating the extent to which such models can and cannot be distinguished, and suggesting a two-state model with a distribution of burst sizes as the most potent of the seven for describing the simple-repression motif.

The total number and mass of SARS-CoV-2 virions.

Quantitatively describing the time course of the SARS-CoV-2 infection within an infected individual is important for understanding the current global pandemic and possible ways to combat it. Here we integrate the best current knowledge about the typical viral load of SARS-CoV-2 in bodily fluids and host tissues to estimate the total number and mass of SARS-CoV-2 virions in an infected person. We estimate that each infected person carries 109-1011 virions during peak infection, with a total mass in the range of 1-100 µg, which curiously implies that all SARS-CoV-2 virions currently circulating within human hosts have a collective mass of only 0.1-10 kg. We combine our estimates with the available literature on host immune response and viral mutation rates to demonstrate how antibodies markedly outnumber the spike proteins and the genetic diversity of virions in an infected host covers all possible single nucleotide substitutions.

Proofreading through spatial gradients.

Key enzymatic processes use the nonequilibrium error correction mechanism called kinetic proofreading to enhance their specificity. The applicability of traditional proofreading schemes, however, is limited because they typically require dedicated structural features in the enzyme, such as a nucleotide hydrolysis site or multiple intermediate conformations. Here, we explore an alternative conceptual mechanism that achieves error correction by having substrate binding and subsequent product formation occur at distinct physical locations. The time taken by the enzyme-substrate complex to diffuse from one location to another is leveraged to discard wrong substrates. This mechanism does not have the typical structural requirements, making it easier to overlook in experiments. We discuss how the length scales of molecular gradients dictate proofreading performance, and quantify the limitations imposed by realistic diffusion and reaction rates. Our work broadens the applicability of kinetic proofreading and sets the stage for studying spatial gradients as a possible route to specificity.

First-principles prediction of the information processing capacity of a simple genetic circuit.

Given the stochastic nature of gene expression, genetically identical cells exposed to the same environmental inputs will produce different outputs. This heterogeneity has been hypothesized to have consequences for how cells are able to survive in changing environments. Recent work has explored the use of information theory as a framework to understand the accuracy with which cells can ascertain the state of their surroundings. Yet the predictive power of these approaches is limited and has not been rigorously tested using precision measurements. To that end, we generate a minimal model for a simple genetic circuit in which all parameter values for the model come from independently published data sets. We then predict the information processing capacity of the genetic circuit for a suite of biophysical parameters such as protein copy number and protein-DNA affinity. We compare these parameter-free predictions with an experimental determination of protein expression distributions and the resulting information processing capacity of E. coli cells. We find that our minimal model captures the scaling of the cell-to-cell variability in the data and the inferred information processing capacity of our simple genetic circuit up to a systematic deviation.