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Intrinsically disordered proteins and regions (IDPs) are involved in vital biological processes. To understand the IDP function, often controlled by conformation, we need to find the link between sequence and conformation. We decode this link by integrating theory, simulation, and machine learning (ML) where sequence-dependent electrostatics is modeled analytically while nonelectrostatic interaction is extracted from simulations for many sequences and subsequently trained using ML. The resulting Hamiltonian, combining physics-based electrostatics and machine-learned nonelectrostatics, accurately predicts sequence-specific global and local measures of conformations beyond the original observable used from the simulation. This is in contrast to traditional ML approaches that train and predict a specific observable, not a Hamiltonian. Our formalism reproduces experimental measurements, predicts multiple conformational features directly from sequence with high throughput that will give insights into IDP design and evolution, and illustrates the broad utility of using physics-based ML to train unknown parts of a Hamiltonian, rather than a specific observable, in combination with known physics. 

Abstract Conformations and dynamics of an intrinsically disordered protein (IDP) depend on its composition of charged and uncharged amino acids, and their specific placement in the protein sequence. In general, the charge (positive or negative) on an amino acid residue in the protein is not a fixed quantity. Each of the ionizable groups can exist in an equilibrated distribution of fully ionized state (monopole) and an ion-pair (dipole) state formed between the ionizing group and its counterion from the background electrolyte solution. The dipole formation (counterion condensation) depends on the protein conformation, which in turn depends on the distribution of charges and dipoles on the molecule. Consequently, effective charges of ionizable groups in the IDP backbone may differ from their chemical charges in isolation—a phenomenon termed charge-regulation. Accounting for the inevitable dipolar interactions, that have so far been ignored, and using a self-consistent procedure, we present a theory of charge-regulation as a function of sequence, temperature, and ionic strength. The theory quantitatively agrees with both charge reduction and salt-dependent conformation data of Prothymosin-alpha and makes several testable predictions. We predict charged groups are less ionized in sequences where opposite charges are well mixed compared to sequences where they are strongly segregated. Emergence of dipolar interactions from charge-regulation allows spontaneous coexistence of two phases having different conformations and charge states, sensitively depending on the charge patterning. These findings highlight sequence dependent charge-regulation and its potential exploitation by biological regulators such as phosphorylation and mutations in controlling protein conformation and function. 

Abstract Effective population size estimates are critical information needed for evolutionary predictions and conservation decisions. This is particularly true for species with social factors that restrict access to breeding or experience repeated fluctuations in population size across generations. We investigated the genomic estimates of effective population size along with diversity, subdivision, and inbreeding from 162,109 minimally filtered and 81,595 statistically neutral and unlinked SNPs genotyped in 437 grey wolf samples from North America collected between 1986 and 2021. We found genetic structure across North America, represented by three distinct demographic histories of western, central, and eastern regions of the continent. Further, grey wolves in the northern Rocky Mountains have lower genomic diversity than wolves of the western Great Lakes and have declined over time. Effective population size estimates revealed the historical signatures of continental efforts of predator extermination, despite a quarter century of recovery efforts. We are the first to provide molecular estimates of effective population size across distinct grey wolf populations in North America, which ranged betweenN_e ~ 275 and 3050 since early 1980s. We provide data that inform managers regarding the status and importance of effective population size estimates for grey wolf conservation, which are on average 5.2–9.3% of census estimates for this species. We show that while grey wolves fall above minimum effective population sizes needed to avoid extinction due to inbreeding depression in the short term, they are below sizes predicted to be necessary to avoid long‐term risk of extinction. 

Cell cycle transitions result from global changes in protein phosphorylation states triggered by cyclin-dependent kinases (CDKs). To understand how this complexity produces an ordered and rapid cellular reorganisation, we generated a high-resolution map of changing phosphosites throughout unperturbed early cell cycles in singleXenopusembryos, derived the emergent principles through systems biology analysis, and tested them by biophysical modelling and biochemical experiments. We found that most dynamic phosphosites share two key characteristics: they occur on highly disordered proteins that localise to membraneless organelles, and are CDK targets. Furthermore, CDK-mediated multisite phosphorylation can switch homotypic interactions of such proteins between favourable and inhibitory modes for biomolecular condensate formation. These results provide insight into the molecular mechanisms and kinetics of mitotic cellular reorganisation. 

If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries $$\pm1$$, then the matrix formed by taking the columns as the eigenvectors is a Hadamard matrix and the graph is said to be Hadamard diagonalizable. In this article, we prove that if $n=8k+4$ the only possible Hadamard diagonalizable graphs are $$K_n$$, $$K_{n/2,n/2}$$, $$2K_{n/2}$$, and $$nK_1$$, and we develop a computational method for determining all graphs diagonalized by a given Hadamard matrix of any order. Using these two tools, we determine and present all Hadamard diagonalizable graphs up to order 36. Note that it is not even known how many Hadamard matrices there are of order 36. 

For many outside the profession, teaching looks simple and straightforward; however, for those working in classrooms, it can be a challenging task. In this paper we argue that teaching is a complex profession that requires both novice and expert educators alike to engage students in sets of activities aimed at transforming their understanding of a subject area. This work requires complex planning, enacting instruction, and reflecting on outcomes. In a moment to moment basis teachers must make decisions and iterate on previously made decisions in order to provide effective opportunities for students to engage with the materials, skills or content to be learned. In this paper, we aim to highlight the complexity of the decision-making process and, in doing so we make the argument that individual teachers’ decisionmaking draws upon a personal epistemic frame which includes factors such as skills, knowledge, identity, values, and epistemology. We provide examples of previous research efforts that have attempted to explore such factors and the limitations, both philosophical and methodological shortcomings of such attempts. Finally, we propose that the use of Quantitative Ethnography and Epistemic Frame Theory provides new opportunities to interrogate teachers’ practices and decision-making as a way to better understand the complexity of teacher work.