Stacked endoplasmic reticulum sheets are connected by helicoidal membrane motifs.

The endoplasmic reticulum (ER) often forms stacked membrane sheets, an arrangement that is likely required to accommodate a maximum of membrane-bound polysomes for secretory protein synthesis. How sheets are stacked is unknown. Here, we used improved staining and automated ultrathin sectioning electron microscopy methods to analyze stacked ER sheets in neuronal cells and secretory salivary gland cells of mice. Our results show that stacked ER sheets form a continuous membrane system in which the sheets are connected by twisted membrane surfaces with helical edges of left- or right-handedness. The three-dimensional structure of tightly stacked ER sheets resembles a parking garage, in which the different levels are connected by helicoidal ramps. A theoretical model explains the experimental observations and indicates that the structure corresponds to a minimum of elastic energy of sheet edges and surfaces. The structure allows the dense packing of ER sheets in the restricted space of a cell.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells.

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

Polysomally protected viruses.

It is conceivable that an RNA virus could use a polysome, that is, a string of ribosomes covering the RNA strand, to protect the genetic material from degradation inside a host cell. This paper discusses how such a virus might operate, and how its presence might be detected by ribosome profiling. There are two possible forms for such apolysomally protected virus, depending upon whether just the forward strand or both the forward and complementary strands can be encased by ribosomes (these will be termed type 1 and type 2, respectively). It is argued that in the type 2 case the viral RNA would evolve anambigrammaticproperty, whereby the viral genes are free of stop codons in a reverse reading frame (with forward and reverse codons aligned). Recent observations of ribosome profiles of ambigrammatic narnavirus sequences are consistent with our predictions for the type 2 case.

A minimal model for household-based testing and tracing in epidemics.

In a previous work (Huberet al.2020Phys. Biol.17065010), we discussed virus transmission dynamics modified by a uniform clustering of contacts in the population: close contacts within households and more distant contacts between households. In this paper, we discuss testing and tracing in such a stratified population. We propose a minimal tracing strategy consisting of random testing of the entire population plus full testing of the households of those persons found positive. We provide estimates of testing frequency for this strategy to work.

A minimal model for household effects in epidemics.

Shelter-in-place and other confinement strategies implemented in the current COVID-19 pandemic have created stratified patterns of contacts between people: close contacts within households and more distant contacts between the households. The epidemic transmission dynamics is significantly modified as a consequence. We introduce a minimal model that incorporates these household effects in the framework of mean-field theory and numerical simulations. We show that the reproduction number R 0 depends on the household size in a surprising way: linearly for relatively small households, and as a square root of size for larger households. We discuss the implications of the findings for the lockdown, test, tracing, and isolation policies.

Terasaki spiral ramps and intracellular diffusion.

The sheet-like endoplasmic reticulum (ER) of eukaryotic cells has been found to be riddled with spiral dislocations, known as 'Terasaki ramps', in the vicinity of which the doubled bilayer membranes which make up ER sheets can be approximately modeled by helicoids. Here we analyze diffusion on a surface with locally helicoidal topological dislocations, and use the results to argue that the Terasaki ramps facilitate a highly efficient transport of water-soluble molecules both within the lumen of the endoplasmic reticulum, and in the adjacent cytoplasmic space.

Terasaki spiral ramps in the rough endoplasmic reticulum.

We present a model describing the morphology as well as the assembly of "Terasaki ramps," the recently discovered helicoidal connections linking adjacent sheets of the rough endoplasmic reticulum (ER). The fundamental unit is a localized symmetric double-ramped "parking garage" formed by two separated gently pitched, approximately helicoidal, ramps of opposite chiralities. This geometry is stabilized by a short-range repulsive interaction between ramps associated with bending energy which opposes the long-range attraction associated with tension. The ramp inner boundaries are themselves stabilized by the condensation of membrane-shaping proteins along their length. A mechanism for parking garage self-assembly is proposed involving the nucleation of dipoles at the center of tubular three-way junctions within the smooth ER. Our predictions are compared with the experimental data.

Iterative feature removal yields highly discriminative pathways.

BACKGROUND: We introduce Iterative Feature Removal (IFR) as an unbiased approach for selecting features with diagnostic capacity from large data sets. The algorithm is based on recently developed tools in machine learning that are driven by sparse feature selection goals. When applied to genomic data, our method is designed to identify genes that can provide deeper insight into complex interactions while remaining directly connected to diagnostic utility. We contrast this approach with the search for a minimal best set of discriminative genes, which can provide only an incomplete picture of the biological complexity. RESULTS: Microarray data sets typically contain far more features (genes) than samples. For this type of data, we demonstrate that there are many equivalently-predictive subsets of genes. We iteratively train a classifier using features identified via a sparse support vector machine. At each iteration, we remove all the features that were previously selected. We found that we could iterate many times before a sustained drop in accuracy occurs, with each iteration removing approximately 30 genes from consideration. The classification accuracy on test data remains essentially flat even as hundreds of top-genes are removed.Our method identifies sets of genes that are highly predictive, even when comprised of genes that individually are not. Through automated and manual analysis of the selected genes, we demonstrate that the selected features expose relevant pathways that other approaches would have missed. CONCLUSIONS: Our results challenge the paradigm of using feature selection techniques to design parsimonious classifiers from microarray and similar high-dimensional, small-sample-size data sets. The fact that there are many subsets of genes that work equally well to classify the data provides a strong counter-result to the notion that there is a small number of "top genes" that should be used to build classifiers. In our results, the best classifiers were formed using genes with limited univariate power, thus illustrating that deeper mining of features using multivariate techniques is important.

Configurational entropy is an intrinsic driver of tissue structural heterogeneity.

Tissues comprise ordered arrangements of cells that can be surprisingly disordered in their details. How the properties of single cells and their microenvironment contribute to the balance between order and disorder at the tissue-scale remains poorly understood. Here, we address this question using the self-organization of human mammary organoids as a model. We find that organoids behave like a dynamic structural ensemble at the steady state. We apply a maximum entropy formalism to derive the ensemble distribution from three measurable parameters - the degeneracy of structural states, interfacial energy, and tissue activity (the energy associated with positional fluctuations). We link these parameters with the molecular and microenvironmental factors that control them to precisely engineer the ensemble across multiple conditions. Our analysis reveals that the entropy associated with structural degeneracy sets a theoretical limit to tissue order and provides new insight for tissue engineering, development, and our understanding of disease progression.

Epinephrine modulates BCAM/Lu and ICAM-4 expression on the sickle cell trait red blood cell membrane.

Collapse and sudden death in physical training are the most serious complications of sickle cell trait (SCT). There is evidence that erythrocytes in SCT patients aggregate during strenuous exercise, likely because of adhesive interactions with the extracellular matrix (ECM) and endothelial cells, and because of their irregular viscoelastic properties. This results in inflammation, blood flow impairment, and vaso-occlusive events. However, the exact role of stress conditions and how they lead to these complications is virtually unknown. Using single-molecule atomic force microscopy experiments, we found that epinephrine, a hormone that is secreted under stressful conditions, increases both the frequency and strength of adhesion events between basal cell adhesion molecule (BCAM/Lu) and ECM laminin, and between intercellular adhesion molecule-4 (ICAM-4) and endothelial α(v)ß(3), compared with nonstimulated SCT erythrocytes. Increases in adhesion frequency provide significant evidence of the role of epinephrine in BCAM/Lu-laminin and ICAM-4-α(v)ß(3) bonding, and suggest mechanisms of vaso-occlusion during physical exertion in SCT.

Optimal filling of shapes.

We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of N disks as N→∞. We note an analogy with energy landscapes.

A high-resolution flux-matrix model describes the spread of diseases in a spatial network and the effect of mitigation strategies.

Propagation of an epidemic across a spatial network of communities is described by a variant of the SIR model accompanied by an intercommunity infectivity matrix. This matrix is estimated from fluxes between communities, obtained from cell-phone tracking data recorded in the USA between March 2020 and February 2021. We apply this model to the SARS-CoV-2 pandemic by fitting just one global parameter representing the frequency of interaction between individuals. We find that the predicted infections agree reasonably well with the reported cases. We clearly see the effect of "shelter-in-place" policies introduced at the onset of the pandemic. Interestingly, a model with uniform transmission rates produces similar results, suggesting that the epidemic transmission was deeply influenced by air travel. We then study the effect of alternative mitigation policies, in particular restricting long-range travel. We find that this policy is successful in decreasing the epidemic size and slowing down the spread, but less effective than the shelter-in-place policy. This policy can result in a pulled wave of infections. We express its velocity and characterize the shape of the traveling front as a function of the epidemiological parameters. Finally, we discuss a policy of selectively constraining travel based on an edge-betweenness criterion.

Forces and torques on rotating spirochete flagella.

Spirochetes are a unique group of motile bacteria that are distinguished by their helical or flat-wave shapes and the location of their flagella, which reside within the tiny space between the bacterial cell wall and the outer membrane (the periplasm). In Borrelia burgdorferi, rotation of the flagella produces cellular undulations that drive swimming. How these shape changes arise due to the forces and torques that act between the flagella and the cell body is unknown. It is possible that resistive forces come from friction or from fluid drag, depending on whether or not the flagella are in contact with the cell wall. Here, we consider both of these cases. By analyzing the motion of an elastic flagellum rotating in the periplasmic space, we show that the flagella are most likely separated from the bacterial cell wall by a lubricating layer of fluid. This analysis then provides drag coefficients for rotation and sliding of a flagellum within the periplasm.

Polymorphism of genetic ambigrams.

Double synonyms in the genetic code can be used as a tool to test competing hypotheses regarding ambigrammatic narnavirus genomes. Applying the analysis to recent observations of Culex narnavirus 1 and Zhejiang mosquito virus 3 ambigrammatic viruses indicates that the open reading frame on the complementary strand of the segment coding for RNA-dependent RNA polymerase does not code for a functional protein. Culex narnavirus 1 has been shown to possess a second segment, also ambigrammatic, termed 'Robin'. We find a comparable segment for Zhejiang mosquito virus 3, a moderately diverged relative of Culex narnavirus 1. Our analysis of Robin polymorphisms suggests that its reverse open reading frame also does not code for a functional protein. We make a hypothesis about its role.

A random-walk-based epidemiological model.

Random walkers on a two-dimensional square lattice are used to explore the spatio-temporal growth of an epidemic. We have found that a simple random-walk system generates non-trivial dynamics compared with traditional well-mixed models. Phase diagrams characterizing the long-term behaviors of the epidemics are calculated numerically. The functional dependence of the basic reproductive number [Formula: see text] on the model's defining parameters reveals the role of spatial fluctuations and leads to a novel expression for [Formula: see text]. Special attention is given to simulations of inter-regional transmission of the contagion. The scaling of the epidemic with respect to space and time scales is studied in detail in the critical region, which is shown to be compatible with the directed-percolation universality class.

Persistent features of intermittent transcription.

Single-cell RNA sequencing is a powerful tool for exploring gene expression heterogeneity, but the results may be obscured by technical noise inherent in the experimental procedure. Here we introduce a novel parametrisation of sc-RNA data, giving estimates of the probability of activation of a gene and its peak transcription rate, which are agnostic about the mechanism underlying the fluctuations in the counts. Applying this approach to single cell mRNA counts across different tissues of adult mice, we find that peak transcription levels are approximately constant across different tissue types, in contrast to the gene expression probabilities which are, for many genes, markedly different. Many genes are only observed in a small fraction of cells. An investigation of correlation between genes activities shows that this is primarily due to temporal intermittency of transcription, rather than some genes being expressed in specialised cell types. Both the probability of activation and the peak transcription rate have a very wide ranges of values, with a probability density function well approximated by a power law. Taken together, our results indicate that the peak rate of transcription is a persistent property of a gene, and that differences in gene expression are modulated by temporal intermittency of the transcription.

The tethered infinitesimal tori and spheres algorithm: a versatile calculator for axisymmetric problems in equilibrium membrane mechanics.

Constrained minimization of energy functionals is a central part, and usually the difficult part, of solving problems in the equilibrium mechanics of biological and biomimetic membranes. The inherent difficulties of the conventional variational-calculus approach prevents the numerical calculation involved from being made routine in the analyses of experimental results. We have developed a simulated annealing-based computational technique for routinizing the task of constrained minimization of energy functionals governing whole, or small patches of whole, fluid membranes with axisymmetry, spherical topology, and no domains of inhomogeneity. In this article, we describe the essential principles of the technique and apply it to five examples to demonstrate its versatility. It gives membrane shapes that are automatically stable to axisymmetric perturbations. Presently, it can account for constraints on 1), the membrane area or the effective membrane tension; 2), the enclosed volume or the effective pressure difference across the membrane thickness; and 3), the axial end-to-end distance or the applied axial point force.

An exploration of ambigrammatic sequences in narnaviruses.

Narnaviruses have been described as positive-sense RNA viruses with a remarkably simple genome of ~3 kb, encoding only a highly conserved RNA-dependent RNA polymerase (RdRp). Many narnaviruses, however, are 'ambigrammatic' and harbour an additional uninterrupted open reading frame (ORF) covering almost the entire length of the reverse complement strand. No function has been described for this ORF, yet the absence of stops is conserved across diverse narnaviruses, and in every case the codons in the reverse ORF and the RdRp are aligned. The >3 kb ORF overlap on opposite strands, unprecedented among RNA viruses, motivates an exploration of the constraints imposed or alleviated by the codon alignment. Here, we show that only when the codon frames are aligned can all stop codons be eliminated from the reverse strand by synonymous single-nucleotide substitutions in the RdRp gene, suggesting a mechanism for de novo gene creation within a strongly conserved amino-acid sequence. It will be fascinating to explore what implications this coding strategy has for other aspects of narnavirus biology. Beyond narnaviruses, our rapidly expanding catalogue of viral diversity may yet reveal additional examples of this broadly-extensible principle for ambigrammatic-sequence development.

Vesicle shape, molecular tilt, and the suppression of necks.

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of +2 are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.

Aggregation-fragmentation-diffusion model for trail dynamics.

We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine to form a larger one, and also one trail may split into two. In addition, trails move diffusively. The model is defined by two parameters which quantify the fragmentation rate and the fragment size. In the long-time limit, the system reaches a steady state, and our focus is the limiting distribution of trail weights. We find that the density of trail weight has power-law tail P(w)∼w^{-γ} for small weight w. We obtain the exponent γ analytically and find that it varies continuously with the two model parameters. The exponent γ can be positive or negative, so that in one range of parameters small-weight trails are abundant and in the complementary range they are rare.