Lytic and temperate phage naturally coexist in a dynamic population model.

When phage infect their bacterial hosts, they may either lyse the cell and generate a burst of new phage, or lysogenize the bacterium, incorporating the phage genome into it. Phage lysis/lysogeny strategies are assumed to be highly optimized, with the optimal tradeoff depending on environmental conditions. However, in nature, phage of radically different lysis/lysogeny strategies coexist in the same environment, preying on the same bacteria. How can phage preying on the same bacteria coexist if one is more optimal than the other? Here, we address this conundrum within a modeling framework, simulating the population dynamics of communities of phage and their lysogens. We find that coexistence between phage of different lysis/lysogeny strategies is a natural outcome of chaotic population dynamics that arise within sufficiently diverse communities, which ensure no phage is able to absolutely dominate its competitors. Our results further suggest a bet-hedging mechanism at the level of the phage pan-genome, wherein obligate lytic (virulent) strains typically outcompete temperate strains, but also more readily fluctuate to extinction within a local community.

A computational toolbox for the assembly yield of complex and heterogeneous structures.

The self-assembly of complex structures from a set of non-identical building blocks is a hallmark of soft matter and biological systems, including protein complexes, colloidal clusters, and DNA-based assemblies. Predicting the dependence of the equilibrium assembly yield on the concentrations and interaction energies of building blocks is highly challenging, owing to the difficulty of computing the entropic contributions to the free energy of the many structures that compete with the ground state configuration. While these calculations yield well known results for spherically symmetric building blocks, they do not hold when the building blocks have internal rotational degrees of freedom. Here we present an approach for solving this problem that works with arbitrary building blocks, including proteins with known structure and complex colloidal building blocks. Our algorithm combines classical statistical mechanics with recently developed computational tools for automatic differentiation. Automatic differentiation allows efficient evaluation of equilibrium averages over configurations that would otherwise be intractable. We demonstrate the validity of our framework by comparison to molecular dynamics simulations of simple examples, and apply it to calculate the yield curves for known protein complexes and for the assembly of colloidal shells.

RNA structure modulates Cas13 activity and enables mismatch detection.

The RNA-targeting CRISPR nuclease Cas13 has emerged as a powerful tool for applications ranging from nucleic acid detection to transcriptome engineering and RNA imaging1-6. Cas13 is activated by the hybridization of a CRISPR RNA (crRNA) to a complementary single-stranded RNA (ssRNA) protospacer in a target RNA1,7. Though Cas13 is not activated by double-stranded RNA (dsRNA) in vitro, it paradoxically demonstrates robust RNA targeting in environments where the vast majority of RNAs are highly structured2,8. Understanding Cas13's mechanism of binding and activation will be key to improving its ability to detect and perturb RNA; however, the mechanism by which Cas13 binds structured RNAs remains unknown9. Here, we systematically probe the mechanism of LwaCas13a activation in response to RNA structure perturbations using a massively multiplexed screen. We find that there are two distinct sequence-independent modes by which secondary structure affects Cas13 activity: structure in the protospacer region competes with the crRNA and can be disrupted via a strand-displacement mechanism, while structure in the region 3' to the protospacer has an allosteric inhibitory effect. We leverage the kinetic nature of the strand displacement process to improve Cas13-based RNA detection, enhancing mismatch discrimination by up to 50-fold and enabling sequence-agnostic mutation identification at low (<1%) allele frequencies. Our work sets a new standard for CRISPR-based nucleic acid detection and will enable intelligent and secondary-structure-guided target selection while also expanding the range of RNAs available for targeting with Cas13.

Measuring intramolecular connectivity in long RNA molecules using two-dimensional DNA patch-probe arrays.

We describe a simple method to infer intramolecular connections in a population of long RNA molecules in vitro. First we add DNA oligonucleotide "patches" that perturb the RNA connections, then we use a microarray containing a complete set of DNA oligonucleotide "probes" to record where perturbations occur. The pattern of perturbations reveals couplings between different regions of the RNA sequence, from which we infer connections as well as their prevalences in the population. We validate this patch-probe method using the 1,058-nucleotide RNA genome of satellite tobacco mosaic virus (STMV), which has previously been shown to have multiple long-range connections. Our results not only indicate long duplexes that agree with previous structures but also reveal the prevalence of competing connections. Together, these results suggest that globally-folded and locally-folded structures coexist in solution. We show that the prevalence of connections changes when pseudouridine, an important component of natural and synthetic RNA molecules, is substituted for uridine in STMV RNA.

Nucleic Acid Structure Prediction Including Pseudoknots Through Direct Enumeration of States: A User's Guide to the LandscapeFold Algorithm.

Here we detail the LandscapeFold secondary structure prediction algorithm and how it is used. The algorithm was previously described and tested in (Kimchi O et al., Biophys J 117(3):520-532, 2019), though it was not named there. The algorithm directly enumerates all possible secondary structures into which up to two RNA or single-stranded DNA sequences can fold. It uses a polymer physics model to estimate the configurational entropy of structures including complex pseudoknots. We detail each of these steps and ways in which the user can adjust the algorithm as desired. The code is available on the GitHub repository https://github.com/ofer-kimchi/LandscapeFold .

Uncovering the mechanism for aggregation in repeat expanded RNA reveals a reentrant transition.

RNA molecules aggregate under certain conditions. The resulting condensates are implicated in human neurological disorders, and can potentially be designed towards specified bulk properties in vitro. However, the mechanism for aggregation-including how aggregation properties change with sequence and environmental conditions-remains poorly understood. To address this challenge, we introduce an analytical framework based on multimer enumeration. Our approach reveals the driving force for aggregation to be the increased configurational entropy associated with the multiplicity of ways to form bonds in the aggregate. Our model uncovers rich phase behavior, including a sequence-dependent reentrant phase transition, and repeat parity-dependent aggregation. We validate our results by comparison to a complete computational enumeration of the landscape, and to previously published molecular dynamics simulations. Our work unifies and extends published results, both explaining the behavior of CAG-repeat RNA aggregates implicated in Huntington's disease, and enabling the rational design of programmable RNA condensates.

Self-assembly-based posttranslational protein oscillators.

Recent advances in synthetic posttranslational protein circuits are substantially impacting the landscape of cellular engineering and offer several advantages compared to traditional gene circuits. However, engineering dynamic phenomena such as oscillations in protein-level circuits remains an outstanding challenge. Few examples of biological posttranslational oscillators are known, necessitating theoretical progress to determine realizable oscillators. We construct mathematical models for two posttranslational oscillators, using few components that interact only through reversible binding and phosphorylation/dephosphorylation reactions. Our designed oscillators rely on the self-assembly of two protein species into multimeric functional enzymes that respectively inhibit and enhance this self-assembly. We limit our analysis to within experimental constraints, finding (i) significant portions of the restricted parameter space yielding oscillations and (ii) that oscillation periods can be tuned by several orders of magnitude using recent advances in computational protein design. Our work paves the way for the rational design and realization of protein-based dynamic systems.

Sequence analysis of SARS-CoV-2 genome reveals features important for vaccine design.

As the SARS-CoV-2 pandemic is rapidly progressing, the need for the development of an effective vaccine is critical. A promising approach for vaccine development is to generate, through codon pair deoptimization, an attenuated virus. This approach carries the advantage that it only requires limited knowledge specific to the virus in question, other than its genome sequence. Therefore, it is well suited for emerging viruses, for which we may not have extensive data. We performed comprehensive in silico analyses of several features of SARS-CoV-2 genomic sequence (e.g., codon usage, codon pair usage, dinucleotide/junction dinucleotide usage, RNA structure around the frameshift region) in comparison with other members of the coronaviridae family of viruses, the overall human genome, and the transcriptome of specific human tissues such as lung, which are primarily targeted by the virus. Our analysis identified the spike (S) and nucleocapsid (N) proteins as promising targets for deoptimization and suggests a roadmap for SARS-CoV-2 vaccine development, which can be generalizable to other viruses.

Sequence analysis of SARS-CoV-2 genome reveals features important for vaccine design.

As the SARS-CoV-2 pandemic is rapidly progressing, the need for the development of an effective vaccine is critical. A promising approach for vaccine development is to generate, through codon pair deoptimization, an attenuated virus. This approach carries the advantage that it only requires limited knowledge specific to the virus in question, other than its genome sequence. Therefore, it is well suited for emerging viruses for which we may not have extensive data. We performed comprehensive in silico analyses of several features of SARS-CoV-2 genomic sequence (e.g., codon usage, codon pair usage, dinucleotide/junction dinucleotide usage, RNA structure around the frameshift region) in comparison with other members of the coronaviridae family of viruses, the overall human genome, and the transcriptome of specific human tissues such as lung, which are primarily targeted by the virus. Our analysis identified the spike (S) and nucleocapsid (N) proteins as promising targets for deoptimization and suggests a roadmap for SARS-CoV-2 vaccine development, which can be generalizable to other viruses.

A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots.

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past 40 years. Although many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges arising from two main factors: 1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots, and 2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model that can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities-over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of ∼80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model's parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark data set of RNA structures of ≤80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.

Ion channels can be allosterically regulated by membrane domains near a de-mixing critical point.

Ion channels are embedded in the plasma membrane, a compositionally diverse two-dimensional liquid that has the potential to exert profound influence on their function. Recent experiments suggest that this membrane is poised close to an Ising critical point, below which cell-derived plasma membrane vesicles phase separate into coexisting liquid phases. Related critical points have long been the focus of study in simplified physical systems, but their potential roles in biological function have been underexplored. Here we apply both exact and stochastic techniques to the lattice Ising model to study several ramifications of proximity to criticality for idealized lattice channels, whose function is coupled through boundary interactions to critical fluctuations of membrane composition. Because of diverging susceptibilities of system properties to thermodynamic parameters near a critical point, such a lattice channel's activity becomes strongly influenced by perturbations that affect the critical temperature of the underlying Ising model. In addition, its kinetics acquire a range of time scales from its surrounding membrane, naturally leading to non-Markovian dynamics. Our model may help to unify existing experimental results relating the effects of small-molecule perturbations on membrane properties and ion channel function. We also suggest ways in which the role of this mechanism in regulating real ion channels and other membrane-bound proteins could be tested in the future.

Paracrine regulation of glucagon secretion: the ß/α/δ model.

The regulation of glucagon secretion in the pancreatic α-cell is not well understood. It has been proposed that glucose suppresses glucagon secretion either directly through an intrinsic mechanism within the α-cell or indirectly through an extrinsic mechanism. Previously, we described a mathematical model for isolated pancreatic α-cells and used it to investigate possible intrinsic mechanisms of regulating glucagon secretion. We demonstrated that glucose can suppress glucagon secretion through both ATP-dependent potassium channels (KATP) and a store-operated current (SOC). We have now developed an islet model that combines previously published mathematical models of α- and ß-cells with a new model of δ-cells and use it to explore the effects of insulin and somatostatin on glucagon secretion. We show that the model can reproduce experimental observations that the inhibitory effect of glucose remains even when paracrine modulators are no longer acting on the α-cell. We demonstrate how paracrine interactions can either synchronize α- and δ-cells to produce pulsatile oscillations in glucagon and somatostatin secretion or fail to do so. The model can also account for the paradoxical observation that glucagon can be out of phase with insulin, whereas α-cell calcium is in phase with insulin. We conclude that both paracrine interactions and the α-cell's intrinsic mechanisms are needed to explain the response of glucagon secretion to glucose.