Salt-Dependent Self-Association of Trinucleotide Repeat RNA Sequences

Repeat RNA sequences self-associate to form condensates. Simulations of a coarse-grained single-interaction site model for (CAG)n (n = 30 and 31) show that the salt-dependent free energy gap, ΔGS, between the ground (perfect hairpin) and the excited state (slipped hairpin (SH) with one CAG overhang) of the monomer for (n even) is the primary factor that determines the rates and yield of self-assembly. For odd n, the free energy (GS) of the ground state, which is an SH, is used to predict the self-association kinetics. As the monovalent salt concentration, CS, increases, ΔGS and GS increase, which decreases the rates of dimer formation. In contrast, ΔGS for shuffled sequences, with the same length and sequence composition as (CAG)31, is larger, which suppresses their propensities to aggregate. Although demonstrated explicitly for (CAG) polymers, the finding of inverse correlation between the free energy gap and RNA aggregation is general.

Competition between Stacking and Divalent Cation-Mediated Electrostatic Interactions Determines the Conformations of Short DNA Sequences

Interplay between divalent cations (Mg2+ and Ca2+) and single-stranded DNA (ssDNA) and double-stranded DNA (dsDNA), as well as stacking interactions, is important in nucleosome stability and phase separation in nucleic acids. Quantitative techniques accounting for ion-DNA interactions are needed to obtain insights into these and related problems. Toward this end, we created a sequence-dependent computational TIS-ION model that explicitly accounts for monovalent and divalent ions. Simulations of the rigid 24 base-pair (bp) dsDNA and flexible ssDNA sequences, dT30 and dA30, with varying amounts of the divalent cations show that the calculated excess number of ions around the dsDNA and ssDNA agree quantitatively with ion-counting experiments. Using an ensemble of all-atom structures generated from coarse-grained simulations, we calculated the small-angle X-ray scattering profiles, which are in excellent agreement with experiments. Although ion-counting experiments mask the differences between Mg2+ and Ca2+, we find that Mg2+ binds to the minor grooves and phosphate groups, whereas Ca2+ binds specifically to the minor groove. Both Mg2+ and Ca2+ exhibit a tendency to bind to the minor groove of DNA as opposed to the major groove. The dA30 conformations are dominated by stacking interactions, resulting in structures with considerable helical order. The near cancellation of the favorable stacking and unfavorable electrostatic interactions leads to dT30 populating an ensemble of heterogeneous conformations. The successful applications of the TIS-ION model are poised to confront many problems in DNA biophysics.

Structural basis for the preservation of a subset of topologically associating domains in interphase chromosomes upon cohesin depletion

Compartment formation in interphase chromosomes is a result of spatial segregation between euchromatin and heterochromatin on a few megabase pairs (Mbp) scale. On the sub-Mbp scales, topologically associating domains (TADs) appear as interacting domains along the diagonal in the ensemble averaged Hi-C contact map. Hi-C experiments showed that most of the TADs vanish upon deleting cohesin, while the compartment structure is maintained, and perhaps even enhanced. However, closer inspection of the data reveals that a non-negligible fraction of TADs is preserved (P-TADs) after cohesin loss. Imaging experiments show that, at the single-cell level, TAD-like structures are present even without cohesin. To provide a structural basis for these findings, we first used polymer simulations to show that certain TADs with epigenetic switches across their boundaries survive after depletion of loops. More importantly, the three-dimensional structures show that many of the P-TADs have sharp physical boundaries. Informed by the simulations, we analyzed the Hi-C maps (with and without cohesin) in mouse liver and human colorectal carcinoma cell lines, which affirmed that epigenetic switches and physical boundaries (calculated using the predicted 3D structures using the data-driven HIPPS method that uses Hi-C as the input) explain the origin of the P-TADs. Single-cell structures display TAD-like features in the absence of cohesin that are remarkably similar to the findings in imaging experiments. Some P-TADs, with physical boundaries, are relevant to the retention of enhancer-promoter/promoter-promoter interactions. Overall, our study shows that preservation of a subset of TADs upon removing cohesin is a robust phenomenon that is valid across multiple cell lines.

Transcription-induced active forces suppress chromatin motion

The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.

Conformational fluctuations and phases in fused in sarcoma (FUS) low-complexity domain

The well-known phenomenon of phase separation in synthetic polymers and proteins has become a major topic in biophysics because it has been invoked as a mechanism of compartment formation in cells, without the need for membranes. Most of the coacervates (or condensates) are composed of Intrinsically Disordered Proteins (IDPs) or regions that are structureless, often in interaction with RNA and DNA. One of the more intriguing IDPs is the 526-residue RNA-binding protein, Fused in Sarcoma (FUS), whose monomer conformations and condensates exhibit unusual behavior that are sensitive to solution conditions. By focussing principally on the N-terminus low-complexity domain (FUS-LC comprising residues 1-214) and other truncations, we rationalize the findings of solid-state NMR experiments, which show that FUS-LC adopts a non-polymorphic fibril structure (core-1) involving residues 39-95, flanked by fuzzy coats on both the N- and C-terminal ends. An alternate structure (core-2), whose free energy is comparable to core-1, emerges only in the truncated construct (residues 110-214). Both core-1 and core-2 fibrils are stabilized by a Tyrosine ladder as well as hydrophilic interactions. The morphologies (gels, fibrils, and glass-like) adopted by FUS seem to vary greatly, depending on the experimental conditions. The effect of phosphorylation is site-specific. Simulations show that phosphorylation of residues within the fibril has a greater destabilization effect than residues that are outside the fibril region, which accords well with experiments. Many of the peculiarities associated with FUS may also be shared by other IDPs, such as TDP43 and hnRNPA2. We outline a number of problems for which there is no clear molecular explanation.

Brewing COFFEE: A Sequence-Specific Coarse-Grained Energy Function for Simulations of DNA-Protein Complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription and gene expression to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse-grained Force Field for Energy Estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the self-organized polymer model with side-chains for proteins and the three interaction site model for DNA in a modular fashion, without recalibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a data set of high-resolution crystal structures. The only parameter in COFFEE is the strength (λDNAPRO) of the DNA-protein contact potential. For an optimal choice of λDNAPRO, the crystallographic B-factors for DNA-protein complexes with varying sizes and topologies are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts scattering profiles that are in quantitative agreement with small-angle X-ray scattering experiments, as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which do not alter the balance of electrostatic interactions but affect chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

Scaling regimes for wormlike chains confined to cylindrical surfaces under tension

We compute the free energy of confinement [Formula: see text] for a wormlike chain (WLC), with persistence length [Formula: see text], that is confined to the surface of a cylinder of radius R under an external tension f using a mean field variational approach. For long chains, we analytically determine the behavior of the chain in a variety of regimes, which are demarcated by the interplay of [Formula: see text], the Odijk deflection length ([Formula: see text]), and the Pincus length ([Formula: see text], with [Formula: see text] being the thermal energy). The theory accurately reproduces the Odijk scaling for strongly confined chains at [Formula: see text], with [Formula: see text]. For moderate values of f, the Odijk scaling is discernible only when [Formula: see text] for strongly confined chains. Confinement does not significantly alter the scaling of the mean extension for sufficiently high tension. The theory is used to estimate unwrapping forces for DNA from nucleosomes.

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

Outcomes for patients with EBV-positive PTLD post-allogeneic HCT after failure of rituximab-containing therapy

Epstein-Barr virus-positive (EBV+) post-transplant lymphoproliferative disease (PTLD) is an ultra-rare and aggressive condition that may occur following allogeneic hematopoietic cell transplant (HCT) due to immunosuppression. Approximately half of EBV+ PTLD cases are relapsed or refractory (R/R) to initial rituximab-containing therapy. There are limited treatment options and no standard of care for patients with R/R EBV+ PTLD, and little is known about their treatment history and outcomes. We performed a multinational, multicenter, retrospective chart review of patients with R/R EBV+ PTLD following HCT to describe patients' demographic and disease characteristics, treatment history, and overall survival (OS) from rituximab failure. Among 81 patients who received initial treatment with rituximab as monotherapy (84.0%) or in combination with chemotherapy (16.0%), median time from HCT to PTLD diagnosis was 3.0 months and median OS was 0.7 months. Thirty-six patients received a subsequent line of treatment. The most frequent causes of death were PTLD (56.8%), graft-versus-host disease (13.5%) and treatment-related mortality (10.8%). In multivariate analysis, early PTLD onset and lack of response to initial treatment were associated with mortality. This real-world study demonstrates that the prognosis of patients with R/R EBV+ PTLD following HCT remains poor, highlighting the urgent unmet medical need in this population.

Treatment Patterns and Unmet Need for Patients with Progressive Multiple Sclerosis in the United States: Survey Results from 2016 to 2021

INTRODUCTION

Much of the current literature on treatment patterns and disability progression in multiple sclerosis (MS) does not distinguish between the relapsing-remitting and progressive subtypes (including primary [PPMS] and secondary progressive MS [SPMS]), or between active/nonactive disease. Current treatment options for progressive MS are limited, with only one approved product for PPMS and none specifically for nonactive SPMS. Here we report treatment patterns, disability progression, and unmet needs among patients with active and nonactive PPMS and SPMS.

METHODS

The annual, cross-sectional survey from the Adelphi Disease Specific Program was used to collect physician-reported data on US adult patients with PPMS and SPMS, including active and nonactive disease. Treatment patterns (including the proportion of patients who were untreated with a disease-modifying therapy [DMT]), disability progression, and unmet need are described from 2016 to 2021.

RESULTS

Data were collected for 2067 patients with progressive MS (PPMS, 1583; SPMS, 484). A substantial proportion of patients were untreated across all groups, and this was highest for nonactive PPMS (~ 43%). The proportion of untreated patients generally declined over time but remained high in 2018-2021 (~ 10-38%). Among treated patients, the proportion receiving infusions increased over time to ~ 34-46%, largely driven by ocrelizumab use after approval. Disability progression was reported for most patients (> 50%), including many who were receiving a DMT. Across all disease subtypes, when physicians were asked about the greatest unmet need with current DMTs, they most frequently cited effectiveness (~ 63-87%), and specifically slowing disease progression (~ 32-59%).

CONCLUSIONS

This analysis of physician-reported data reveals that patients with progressive MS, particularly those with nonactive disease, frequently remain untreated or continue to decline despite treatment with available DMTs. Thus there is an enduring need for safe and effective treatments for this underserved population.

Watching ion-driven kinetics of ribozyme folding and misfolding caused by energetic and topological frustration one molecule at a time

Folding of ribozymes into well-defined tertiary structures usually requires divalent cations. How Mg2+ ions direct the folding kinetics has been a long-standing unsolved problem because experiments cannot detect the positions and dynamics of ions. To address this problem, we used molecular simulations to dissect the folding kinetics of the Azoarcus ribozyme by monitoring the path each molecule takes to reach the folded state. We quantitatively establish that Mg2+ binding to specific sites, coupled with counter-ion release of monovalent cations, stimulate the formation of secondary and tertiary structures, leading to diverse pathways that include direct rapid folding and trapping in misfolded structures. In some molecules, key tertiary structural elements form when Mg2+ ions bind to specific RNA sites at the earliest stages of the folding, leading to specific collapse and rapid folding. In others, the formation of non-native base pairs, whose rearrangement is needed to reach the folded state, is the rate-limiting step. Escape from energetic traps, driven by thermal fluctuations, occurs readily. In contrast, the transition to the native state from long-lived topologically trapped native-like metastable states is extremely slow. Specific collapse and formation of energetically or topologically frustrated states occur early in the assembly process.

Brewing COFFEE: A sequence-specific coarse-grained energy function for simulations of DNA-protein complexes

DNA-protein interactions are pervasive in a number of biophysical processes ranging from transcription, gene expression, to chromosome folding. To describe the structural and dynamic properties underlying these processes accurately, it is important to create transferable computational models. Toward this end, we introduce Coarse grained force field for energy estimation, COFFEE, a robust framework for simulating DNA-protein complexes. To brew COFFEE, we integrated the energy function in the Self-Organized Polymer model with Side Chains for proteins and the Three Interaction Site model for DNA in a modular fashion, without re-calibrating any of the parameters in the original force-fields. A unique feature of COFFEE is that it describes sequence-specific DNA-protein interactions using a statistical potential (SP) derived from a dataset of high-resolution crystal structures. The only parameter in COFFEE is the strength (λ D N A P R O ) of the DNA-protein contact potential. For an optimal choice of λ D N A P R O , the crystallographic B-factors for DNA-protein complexes, with varying sizes and topologies, are quantitatively reproduced. Without any further readjustments to the force-field parameters, COFFEE predicts the scattering profiles that are in quantitative agreement with SAXS experiments as well as chemical shifts that are consistent with NMR. We also show that COFFEE accurately describes the salt-induced unraveling of nucleosomes. Strikingly, our nucleosome simulations explain the destabilization effect of ARG to LYS mutations, which does not alter the balance of electrostatic interactions, but affects chemical interactions in subtle ways. The range of applications attests to the transferability of COFFEE, and we anticipate that it would be a promising framework for simulating DNA-protein complexes at the molecular length-scale.

Observe without disturbing: tracer particles sense local stresses in cell collectives without affecting the cancer cell dynamics

Measurements of local stresses on the cancer cells (CCs), inferred by embedding inert compressible tracer particles (TPs) in a growing multicellular spheroid (MCS), show that pressure decreases monotonically as the distance from the core of the MCS increases. How faithfully do the TPs report the local stresses in the CCs is an important question because pressure buildup in the MCS is dynamically generated due to CC division, which implies that the CC dynamics should be minimally altered by the TPs. Here using theory and simulations, we show that although the TP dynamics is unusual, exhibiting sub-diffusive behavior on times less than the CC division times and hyper-diffusive dynamics in the long-time limit, they do not affect the long-time CC dynamics. The CC pressure profile within the MCS, which decays from a high value at the core to the periphery, is almost identical with and without the TPs. That the TPs have a small effect on the local stresses in the MCS implies that they are reasonale reporters of the CC microenvironment.

Odd-even disparity in the population of slipped hairpins in RNA repeat sequences with implications for phase separation

Low-complexity nucleotide repeat sequences, which are implicated in several neurological disorders, undergo liquid-liquid phase separation (LLPS) provided the number of repeat units, n, exceeds a critical value. Here, we establish a link between the folding landscapes of the monomers of trinucleotide repeats and their propensity to self-associate. Simulations using a coarse-grained Self-Organized Polymer (SOP) model for (CAG)n repeats in monovalent salt solutions reproduce experimentally measured melting temperatures, which are available only for small n. By extending the simulations to large n, we show that the free-energy gap, ΔGS, between the ground state (GS) and slipped hairpin (SH) states is a predictor of aggregation propensity. The GS for even n is a perfect hairpin (PH), whereas it is a SH when n is odd. The value of ΔGS (zero for odd n) is larger for even n than for odd n. As a result, the rate of dimer formation is slower in (CAG)30 relative to (CAG)31, thus linking ΔGS to RNA-RNA association. The yield of the dimer decreases dramatically, compared to the wild type, in mutant sequences in which the population of the SH decreases substantially. Association between RNA chains is preceded by a transition to the SH even if the GS is a PH. The finding that the excitation spectrum-which depends on the exact sequence, n, and ionic conditions-is a predictor of self-association should also hold for other RNAs (mRNA for example) that undergo LLPS.

Allosteric communication between ACE2 active site and binding interface with SARS-CoV-2

SARS-CoV-2, the virus causing COVID-19, initiates cell invasion by deploying a receptor binding domain (RBD) to recognize the host transmembrane peptidase angiotensin-converting enzyme 2 (ACE2). Numerous experimental and theoretical studies have adopted high-throughput and structure-guided approaches to (i) understand how the RBD recognizes ACE2, (ii) rationalize, and (iii) predict the effect of viral mutations on the binding affinity. Here, we investigate the allosteric signal triggered by the dissociation of the ACE2-RBD complex. To this end, we construct an Elastic Network Model (ENM), and we use the Structural Perturbation Method (SPM). Our key result is that complex dissociation opens the ACE2 substrate-binding cleft located away from the interface and that fluctuations of the ACE2 binding cleft are facilitated by RBD binding. These and other observations provide a structural and dynamical basis for the influence of SARS-CoV-2 on ACE2 enzymatic activity. In addition, we identify a conserved glycine (G502 in SARS-CoV-2) as a key participant in complex disassembly.

Conformational Fluctuations and Phases in Fused in Sarcoma (FUS) Low-Complexity Domain

The well known phenomenon of phase separation in synthetic polymers and proteins has become a major topic in biophysics because it has been invoked as a mechanism of compartment formation in cells, without the need for membranes. Most of the coacervates (or condensates) are composed of Intrinsically Disordered Proteins (IDPs) or regions that are structureless, often in interaction with RNA and DNA. One of the more intriguing IDPs is the 526-residue RNA binding protein, Fused In Sarcoma (FUS), whose monomer conformations and condensates exhibit unusual behavior that are sensitive to solution conditions. By focussing principally on the N-terminus low complexity domain (FUS-LC comprising residues 1-214) and other truncations, we rationalize the findings of solid state NMR experiments, which show that FUS-LC adopts a non-polymorphic fibril (core-1) involving residues 39-95, flanked by fuzzy coats on both the N- and C- terminal ends. An alternate structure (core-2), whose free energy is comparable to core-1, emerges only in the truncated construct (residues 110-214). Both core-1 and core-2 fibrils are stabilized by a Tyrosine ladder as well as hydrophilic interactions. The morphologies (gels, fibrils, and glass-like behavior) adopted by FUS seem to vary greatly, depending on the experimental conditions. The effect of phosphorylation is site specific and affects the stability of the fibril depending on the sites that are phosphorylated. Many of the peculiarities associated with FUS may also be shared by other IDPs, such as TDP43 and hnRNPA2. We outline a number of problems for which there is no clear molecular understanding.

Entropic Contribution of ACE2 Glycans to RBD Binding

The spike protein in the virus SARS-CoV-2 (the causative agent of COVID-19) recognizes the host cell by binding to the peptidase domain (PD) of the extracellular enzyme Angiotensin-Converting Enzyme 2 (ACE2). A variety of carbohydrates could be attached to the six asparagines in the PD, resulting in a heterogeneous population of ACE2 glycoforms. Experiments have shown that the binding affinity of glycosylated and deglycosylated ACE2 to the virus is virtually identical. In most cases, the reduction in glycan size correlates with stronger binding, which suggests that volume exclusion, and hence entropic forces, determine the binding affinity. Here, we quantitatively test the entropy-based hypothesis by developing a lattice model for the complex between ACE2 and the SARS-CoV-2 spike protein Receptor-Binding Domain (RBD). Glycans are treated as branched polymers with only volume exclusion, which we justify using all atom molecular dynamics simulations in explicit water. We show that the experimentally measured changes in the ACE2-RBD dissociation constants for a variety of engineered ACE2 glycoforms are in reasonable agreement with our theory, thus supporting our hypothesis. However, a quantitative recovery of all the experimental data could require weak attractive interactions.

Structural changes in chromosomes driven by multiple condensin motors during mitosis

We create a computational framework that utilizes loop extrusion (LE) by multiple condensin I/II motors to predict changes in chromosome organization during mitosis. The theory accurately reproduces the experimental contact probability profiles for the mitotic chromosomes in HeLa and DT40 cells. The LE rate is smaller at the start of mitosis and increases as the cells approach metaphase. Condensin II-mediated mean loop size is about six times larger than loops because of condensin I. The loops, which overlap each other, are stapled to a central dynamically changing helical scaffold formed by the motors during the LE process. A polymer physics-based data-driven method that uses the Hi-C contact map as the only input shows that the helix is characterized as random helix perversions (RHPs) in which the handedness changes randomly along the scaffold. The theoretical predictions, which are testable using imaging experiments, do not contain any parameters.

Energy landscapes of Aβ monomers are sculpted in accordance with Ostwald's rule of stages

The transition from a disordered to an assembly-competent monomeric state (N*) in amyloidogenic sequences is a crucial event in the aggregation cascade. Using a well-calibrated model for intrinsically disordered proteins (IDPs), we show that the N* states, which bear considerable resemblance to the polymorphic fibril structures found in experiments, not only appear as excitations in the free energy landscapes of Aβ40 and Aβ42, but also initiate the aggregation cascade. For Aβ42, the transitions to the different N* states are in accord with Ostwald's rule of stages, with the least stable structures forming ahead of thermodynamically favored ones. The Aβ40 and Aβ42 monomer landscapes exhibit different extents of local frustration, which we show have profound implications in dictating subsequent self-assembly. Using kinetic transition networks, we illustrate that the most favored dimerization routes proceed via N* states. We argue that Ostwald's rule also holds for the aggregation of fused in sarcoma and polyglutamine proteins.

Expert Consensus on the Characteristics of Patients with Epstein-Barr Virus-Positive Post-Transplant Lymphoproliferative Disease (EBV+ PTLD) for Whom Standard-Dose Chemotherapy May be Inappropriate: A Modified Delphi Study

INTRODUCTION

Following hematopoietic stem cell transplantation or solid organ transplantation, patients are at risk of developing Epstein-Barr virus-positive post-transplant lymphoproliferative disease (EBV⁺ PTLD), which is an ultra-rare and potentially lethal hematologic malignancy. Common treatments for EBV⁺ PTLD include rituximab alone or combined with chemotherapy. Given specific considerations for this population, including severity of the underlying condition requiring transplant, the rigors of the transplant procedure, as well as risks to the transplanted organ, there is a group of patients with EBV⁺ PTLD for whom chemotherapy may be inappropriate; however, there is limited information characterizing these patients. This study aimed to reach expert consensus on the key characteristics of patients for whom chemotherapy may be inappropriate in a real-world setting.

METHODS

A two-round modified Delphi study was conducted to reach consensus among clinicians with expertise treating EBV⁺ PTLD. Articles identified in a targeted literature review guided the development of round 1 and 2 topics and related statements. The consensus threshold for round 1 statements was 75.0%. If consensus was achieved in round 1, the statement was not discussed further in round 2. The consensus thresholds for round 2 were moderate (62.5-75.0%), strong (87.5%), or complete (100.0%).

RESULTS

The panel was composed of a total of eight clinicians (seven hematologists/hemato-oncologists) from six European countries. The panel generated a final list of 43 consensus recommendations on the following topics: terminology used to describe patients for whom chemotherapy may be inappropriate; demographic characteristics; organ transplant characteristics; comorbidities that preclude the use of chemotherapy; EBV⁺ PTLD characteristics; and factors related to treatment-related mortality and morbidity.

CONCLUSIONS

This modified Delphi panel successfully achieved consensus on key topics and statements that characterized patients with EBV⁺ PTLD for whom chemotherapy may be inappropriate. These recommendations will inform clinicians and aid in the treatment of EBV⁺ PTLD.

A maximum-entropy model to predict 3D structural ensembles of chromatin from pairwise distances with applications to interphase chromosomes and structural variants

The principles that govern the organization of genomes, which are needed for an understanding of how chromosomes are packaged and function in eukaryotic cells, could be deciphered if the three-dimensional (3D) structures are known. Recently, single-cell imaging techniques have been developed to determine the 3D coordinates of genomic loci in vivo. Here, we introduce a computational method (Distance Matrix to Ensemble of Structures, DIMES), based on the maximum entropy principle, with experimental pairwise distances between loci as constraints, to generate a unique ensemble of 3D chromatin structures. Using the ensemble of structures, we quantitatively account for the distribution of pairwise distances, three-body co-localization, and higher-order interactions. The DIMES method can be applied to both small and chromosome-scale imaging data to quantify the extent of heterogeneity and fluctuations in the shapes across various length scales. We develop a perturbation method in conjunction with DIMES to predict the changes in 3D structures from structural variations. Our method also reveals quantitative differences between the 3D structures inferred from Hi-C and those measured in imaging experiments. Finally, the physical interpretation of the parameters extracted from DIMES provides insights into the origin of phase separation between euchromatin and heterochromatin domains.

TMAO Destabilizes RNA Secondary Structure via Direct Hydrogen Bond Interactions

Trimethylamine N-oxide (TMAO) is an osmolyte that accumulates in cells in response to osmotic stress. TMAO stabilizes proteins by the entropic stabilization mechanism, which pictures TMAO as a nanocrowder that predominantly destabilizes the unfolded state. However, the mechanism of action of TMAO on RNA is much less understood. Here, we use all-atom molecular dynamics simulations to investigate how TMAO interacts with a 12-nt RNA hairpin with a high melting temperature, and an 8-nt RNA hairpin, which has a relatively fluid native basin in the absence of TMAO. The use of the two hairpins with different free energy of stabilization allows us to probe the origin of the destabilization effect of TMAO on RNA molecules without the possibility of forming tertiary interactions. We generated multiple trajectories using all-atom molecular dynamics (MD) simulations in explicit water by employing AMBER and CHARMM force fields, both in the absence and presence of TMAO. We observed qualitatively similar RNA-TMAO interaction profiles from the simulations using the two force fields. TMAO hydrogen bond interactions are largely depleted around the paired RNA bases and ribose sugars. In contrast, we show that the oxygen atom in TMAO, the hydrogen bond acceptor, preferentially interacts with the hydrogen bond donors in the solvent exposed bases, such as those in the stem-loop and the destabilized base stacks in the unfolded state, especially in the marginally stable 8-nt RNA hairpin. The predicted destabilization mechanism through TMAO-RNA hydrogen bond interactions could be tested using two-dimensional IR spectroscopy. Since TMAO does not significantly interact with the hydroxyl group of the ribose sugars, we predict that similar results must also hold for DNA.

Residue-Dependent Transition Temperatures and Denaturant Midpoints in the Folding of a Multidomain Protein

As a consequence of the finite size of globular proteins, it is expected that there should be dispersions in the global melting temperature (T_m) and the denaturation midpoint (C_m). Thermodynamic considerations dictate that the dispersions, ΔT_m in T_m, and ΔC_m in C_m, should decrease with N, the number of residues in the protein. We performed coarse-grained simulations of the self-organized polymer (SOP) model of the multidomain protein adenylate kinase (ADK) with N = 214 in order to calculate thermal and denaturation unfolding titration curves. The results show that ΔT_m/T_m and ΔC_m/C_m are nonzero and follow the previously established ( Phys. Rev. Lett. 2004, 93, 268107) thermodynamic 1/N scaling for proteins accurately. For ADK, the dispersions are small (≈0.004), which implies that the melting temperature is more or less unique, which is unlike in BBL (N = 40) where ΔT_m/T_m ≈ 0.03.

Friends in need: How chaperonins recognize and remodel proteins that require folding assistance

Chaperonins are biological nanomachines that help newly translated proteins to fold by rescuing them from kinetically trapped misfolded states. Protein folding assistance by the chaperonin machinery is obligatory in vivo for a subset of proteins in the bacterial proteome. Chaperonins are large oligomeric complexes, with unusual seven fold symmetry (group I) or eight/nine fold symmetry (group II), that form double-ring constructs, enclosing a central cavity that serves as the folding chamber. Dramatic large-scale conformational changes, that take place during ATP-driven cycles, allow chaperonins to bind misfolded proteins, encapsulate them into the expanded cavity and release them back into the cellular environment, regardless of whether they are folded or not. The theory associated with the iterative annealing mechanism, which incorporated the conformational free energy landscape description of protein folding, quantitatively explains most, if not all, the available data. Misfolded conformations are associated with low energy minima in a rugged energy landscape. Random disruptions of these low energy conformations result in higher free energy, less folded, conformations that can stochastically partition into the native state. Two distinct mechanisms of annealing action have been described. Group I chaperonins (GroEL homologues in eubacteria and endosymbiotic organelles), recognize a large number of misfolded proteins non-specifically and operate through highly coordinated cooperative motions. By contrast, the less well understood group II chaperonins (CCT in Eukarya and thermosome/TF55 in Archaea), assist a selected set of substrate proteins. Sequential conformational changes within a CCT ring are observed, perhaps promoting domain-by-domain substrate folding. Chaperonins are implicated in bacterial infection, autoimmune disease, as well as protein aggregation and degradation diseases. Understanding the chaperonin mechanism and the specific proteins they rescue during the cell cycle is important not only for the fundamental aspect of protein folding in the cellular environment, but also for effective therapeutic strategies.

Adhesion strength between cells regulate nonmonotonic growth by a biomechanical feedback mechanism

We determine how intercellular interactions and mechanical pressure experienced by single cells regulate cell proliferation using a minimal computational model for three-dimensional multicellular spheroid (MCS) growth. We discover that emergent spatial variations in the cell division rate, depending on the location of the cells either at the core or periphery within the MCS, is regulated by intercellular adhesion strength (fad). Varying fad results in nonmonotonic proliferation of cells in the MCS. A biomechanical feedback mechanism coupling the fad and microenvironment-dependent pressure fluctuations relative to a threshold value (pc) determines the onset of a dormant phase, and explains the nonmonotonic proliferation response. Increasing fad from low values enhances cell proliferation because pressure on individual cells is smaller compared with pc. However, at high fad, cells readily become dormant and cannot rearrange effectively in spacetime, leading to arrested cell proliferation. Utilizing our theoretical predictions, we explain experimental data on the impact of adhesion strength on cell proliferation and find good agreement. Our work, which shows that proliferation is regulated by pressure-adhesion feedback mechanism, may be a general feature of multicellular growth.

Differences in ion-RNA binding modes due to charge density variations explain the stability of RNA in monovalent salts

The stability of RNA increases as the charge density of the alkali metal cations increases. The molecular mechanism for this phenomenon remains elusive. To fill this gap, we performed all-atom molecular dynamics pulling simulations of HIV-1 trans-activation response RNA. We first established that the free energy landscape obtained in the simulations is in excellent agreement with the single-molecule optical tweezer experiments. The origin of the stronger stability in sodium compared to potassium is found to be due to the differences in the charge density-related binding modes. The smaller hydrated sodium ion preferentially binds to the highly charged phosphates that have high surface area. In contrast, the larger potassium ions interact with the major grooves. As a result, more cations condense around phosphate groups in the case of sodium ions, leading to the reduction of electrostatic repulsion. Because the proposed mechanism is generic, we predict that the same conclusions are valid for divalent alkaline earth metal cations.

Chromatin dynamics controls epigenetic domain formation

In multicellular organisms, nucleosomes carry epigenetic information that defines distinct patterns of gene expression, which are inherited over multiple generations. The enhanced capacity for information storage arises by nucleosome modifications, which are triggered by enzymes. Modified nucleosomes can transfer the mark to others that are in proximity by a positive-feedback (modification begets modification) mechanism. We created a generic polymer model, referred to as 3DSpreader, in which each bead, representing a nucleosome, stochastically switches between unmodified (U) and modified (M) states depending on the states of the neighbors. Modification begins at a specific nucleation site (NS) that is permanently in the M state, and could spread to other loci that is dictated by chromatin dynamics. Transfer of marks among the non-nucleation loci occurs stochastically as chromatin evolves in time. If the spreading rate is slower than the chromatin relaxation rate, which is biologically pertinent, then finite-sized domains form, driven by contacts between nucleosomes through a three-dimensional looping mechanism. Surprisingly, simulations based on the 3DSpreader model result in finite bounded domains that arise without the need for any boundary elements. Maintenance of spatially and temporally stable domains requires the presence of the NS, whose removal eliminates finite-sized modified domains. The theoretical predictions are in excellent agreement with experimental data for H3K9me3 spreading in mouse embryonic stem cells.

Mechanical feedback controls the emergence of dynamical memory in growing tissue monolayers

The growth of a tissue, which depends on cell–cell interactions and biologically relevant processes such as cell division and apoptosis, is regulated by a mechanical feedback mechanism. We account for these effects in a minimal two-dimensional model in order to investigate the consequences of mechanical feedback, which is controlled by a critical pressure, p c. A cell can only grow and divide if its pressure, due to interaction with its neighbors, is less than p c. Because temperature is not a relevant variable, the cell dynamics is driven by self-generated active forces (SGAFs) that arise due to cell division. We show that even in the absence of intercellular interactions, cells undergo diffusive behavior. The SGAF-driven diffusion is indistinguishable from the well-known dynamics of a free Brownian particle at a fixed finite temperature. When intercellular interactions are taken into account, we find persistent temporal correlations in the force–force autocorrelation function (FAF) that extends over a timescale of several cell division times. The time-dependence of the FAF reveals memory effects, which increases as p c increases. The observed non-Markovian effects emerge due to the interplay of cell division and mechanical feedback and are inherently a non-equilibrium phenomenon.

Cooperativity and Folding Kinetics in a Multidomain Protein with Interwoven Chain Topology

Although a large percentage of eukaryotic proteomes consist of proteins with multiple domains, not much is known about their assembly mechanism, especially those with intricate native state architectures. Some have a complex topology in which the structural elements along the sequence are interwoven in such a manner that the domains cannot be separated by cutting at any location along the sequence. Such proteins are multiply connected multidomain proteins (MMPs) with the three-domain (NMP, LID, and CORE) phosphotransferase enzyme adenylate kinase (ADK) being an example. We devised a coarse-grained model to simulate ADK folding initiated by changing either the temperature or guanidinium chloride (GdmCl) concentration. The simulations reproduce the experimentally measured melting temperatures (associated with two equilibrium transitions), FRET efficiency as a function of GdmCl concentration, and the folding times quantitatively. Although the NMP domain orders independently, cooperative interactions between the LID and the CORE domains are required for complete assembly of the enzyme. Kinetic simulations show that, on the collapse time scale, multiple interconnected metastable states are populated, attesting to the folding heterogeneity. The network of kinetically connected states reveals that the CORE domain folds only after the NMP and LID domains, reflecting the interwoven nature of the chain topology.

Role of water-bridged interactions in metal ion coupled protein allostery

Allosteric communication between distant parts of proteins controls many cellular functions, in which metal ions are widely utilized as effectors to trigger the allosteric cascade. Due to the involvement of strong coordination interactions, the energy landscape dictating the metal ion binding is intrinsically rugged. How metal ions achieve fast binding by overcoming the landscape ruggedness and thereby efficiently mediate protein allostery is elusive. By performing molecular dynamics simulations for the Ca²⁺ binding mediated allostery of the calmodulin (CaM) domains, each containing two Ca²⁺ binding helix-loop-helix motifs (EF-hands), we revealed the key role of water-bridged interactions in Ca²⁺ binding and protein allostery. The bridging water molecules between Ca²⁺ and binding residue reduces the ruggedness of ligand exchange landscape by acting as a lubricant, facilitating the Ca²⁺ coupled protein allostery. Calcium-induced rotation of the helices in the EF-hands, with the hydrophobic core serving as the pivot, leads to exposure of hydrophobic sites for target binding. Intriguingly, despite being structurally similar, the response of the two symmetrically arranged EF-hands upon Ca²⁺ binding is asymmetric. Breakage of symmetry is needed for efficient allosteric communication between the EF-hands. The key roles that water molecules play in driving allosteric transitions are likely to be general in other metal ion mediated protein allostery.

Natural proteins often utilize allostery in executing a variety of functions. Metal ions are typical cofactors to trigger the allosteric cascade. In this work, using the Ca²⁺ sensor protein calmodulin as the model system, we revealed crucial roles of water-bridged interactions in the metal ion coupled protein allostery. The coordination of the Ca²⁺ to the binding site involves an intermediate in which the water molecule bridges the Ca²⁺ and the liganding residue. The bridging water reduces the free energy barrier height of ligand exchange, therefore facilitating the ligand exchange and allosteric coupling by acting as a lubricant. We also showed that the response of the two symmetrically arranged EF-hand motifs of CaM domains upon Ca²⁺ binding is asymmetric, which is directly attributed to the differing dehydration process of the Ca²⁺ ions and is needed for efficient allosteric communication.

Condensates in RNA repeat sequences are heterogeneously organized and exhibit reptation dynamics

Although it is known that RNA undergoes liquid-liquid phase separation, the interplay between the molecular driving forces and the emergent features of the condensates, such as their morphologies and dynamic properties, is not well understood. We introduce a coarse-grained model to simulate phase separation of trinucleotide repeat RNAs, which are implicated in neurological disorders. After establishing that the simulations reproduce key experimental findings, we show that once recruited inside the liquid droplets, the monomers transition from hairpin-like structures to extended states. Interactions between the monomers in the condensates result in the formation of an intricate and dense intermolecular network, which severely restrains the fluctuations and mobilities of the RNAs inside large droplets. In the largest densely packed high-viscosity droplets, the mobility of RNA chains is best characterized by reptation, reminiscent of the dynamics in polymer melts. Our work provides a microscopic framework for understanding liquid-liquid phase separation in RNA, which is not easily discernible in current experiments.

Plus and minus ends of microtubules respond asymmetrically to kinesin binding by a long-range directionally driven allosteric mechanism

Although it is known that majority of kinesin motors walk predominantly toward the plus end of microtubules (MTs) in a hand-over-hand manner, the structural origin of the stepping directionality is not understood. To resolve this issue, we modeled the structures of kinesin-1 (Kin1), MT, and the Kin1-MT complex using the elastic network model and calculated the residue-dependent responses to a local perturbation in the constructs. Kin1 binding elicits an asymmetric response that is pronounced in α/β-tubulin dimers in the plus end of the MT. Kin1 opens the clefts of multiple plus end α/β-tubulin dimers, creating binding-competent conformations, which is required for processivity. Reciprocally, MT induces correlations between switches I and II in the motor and enhances fluctuations in adenosine 5'-diphosphate and the residues in the binding pocket. Our findings explain both the directionality of stepping and MT effects on a key step in the catalytic cycle of kinesin.

A mathematical model for phenotypic heterogeneity in breast cancer with implications for therapeutic strategies

Inevitably, almost all cancer patients develop resistance to targeted therapy. Intratumour heterogeneity is a major cause of drug resistance. Mathematical models that explain experiments quantitatively are useful in understanding the origin of intratumour heterogeneity, which then could be used to explore scenarios for efficacious therapy. Here, we develop a mathematical model to investigate intratumour heterogeneity in breast cancer by exploiting the observation that HER2+ and HER2- cells could divide symmetrically or asymmetrically. Our predictions for the evolution of cell fractions are in quantitative agreement with single-cell experiments. Remarkably, the colony size of HER2+ cells emerging from a single HER2- cell (or vice versa), which occurs in about four cell doublings, also agrees with experimental results, without tweaking any parameter in the model. The theory explains experimental data on the responses of breast tumours under different treatment protocols. We then used the model to predict that, not only the order of two drugs, but also the treatment period for each drug and the tumour cell plasticity could be manipulated to improve the treatment efficacy. Mathematical models, when integrated with data on patients, make possible exploration of a broad range of parameters readily, which might provide insights in devising effective therapies.

Temperature and Guanidine Hydrochloride Effects on the Folding Thermodynamics of WW Domain and Variants

We used simulations based on an all-atom Go model to calculate the folding temperatures (T_fs) and free energies (ΔGs) of two variants of the WW domain, which is a small all-β-sheet protein. The results, without adjusting any parameter, are in good agreement with experiments, thus validating the simulations. We then used the molecular transfer model to predict the changes in the ΔGs and T_fs as the guanidine hydrochloride concentration is varied. The predictions can be readily tested in experiments.

Theory and simulations of condensin mediated loop extrusion in DNA

Condensation of hundreds of mega-base-pair-long human chromosomes in a small nuclear volume is a spectacular biological phenomenon. This process is driven by the formation of chromosome loops. The ATP consuming motor, condensin, interacts with chromatin segments to actively extrude loops. Motivated by real-time imaging of loop extrusion (LE), we created an analytically solvable model, predicting the LE velocity and step size distribution as a function of external load. The theory fits the available experimental data quantitatively, and suggests that condensin must undergo a large conformational change, induced by ATP binding, bringing distant parts of the motor to proximity. Simulations using a simple model confirm that the motor transitions between an open and a closed state in order to extrude loops by a scrunching mechanism, similar to that proposed in DNA bubble formation during bacterial transcription. Changes in the orientation of the motor domains are transmitted over ~50 nm, connecting the motor head and the hinge, thus providing an allosteric basis for LE.

Effects of Gold Nanoparticles on the Stepping Trajectories of Kinesin

A substantial increase in the temporal resolution of the stepping of dimeric molecular motors is possible by tracking the position of a large gold nanoparticle (GNP) attached to a labeled site on one of the heads. This technique was employed to measure the stepping trajectories of conventional kinesin (Kin1) using the time-dependent position of the GNP as a proxy. The trajectories revealed that the detached head always passes to the right of the head that is tightly bound to the microtubule (MT) during a step. In interpreting the results of such experiments, it is assumed that the GNP does not significantly alter the diffusive motion of the detached head. We used coarse-grained simulations of a system consisting of the MT-Kin1 complex with and without attached GNP to investigate how the stepping trajectories are affected. The two significant findings are: (1) The GNP does not faithfully track the position of the stepping head, and (2) the rightward bias is typically exaggerated by the GNP. Both these findings depend on the precise residue position to which the GNP is attached. Surprisingly, the stepping trajectories of kinesin are not significantly affected if, in addition to the GNP, a 1 μm diameter cargo is attached to the coiled coil. Our simulations suggest the effects of the large probe have to be considered when inferring the stepping mechanisms using GNP tracking experiments.

Sequence Determines the Switch in the Fibril Forming Regions in the Low-Complexity FUS Protein and Its Variants

Residues spanning distinct regions of the low-complexity domain of the RNA-binding protein, Fused in Sarcoma (FUS-LC), form fibril structures with different core morphologies. Solid-state NMR experiments show that the 214-residue FUS-LC forms a fibril with an S-bend (core-1, residues 39-95), while the rest of the protein is disordered. In contrast, the fibrils of the C-terminal variant (FUS-LC-C; residues 111-214) have a U-bend topology (core-2, residues 112-150). Absence of the U-bend in FUS-LC implies that the two fibril cores do not coexist. Computer simulations show that these perplexing findings could be understood in terms of the population of sparsely populated fibril-like excited states in the monomer. The propensity to form core-1 is higher compared to core-2. We predict that core-2 forms only in truncated variants that do not contain the core-1 sequence. At the monomer level, sequence-dependent enthalpic effects determine the relative stabilities of the core-1 and core-2 topologies.

Energy Landscape of Ubiquitin Is Weakly Multidimensional

Single molecule pulling experiments report time-dependent changes in the extension (X) of a biomolecule as a function of the applied force (f). By fitting the data to one-dimensional analytical models of the energy landscape, we can extract the hopping rates between the folded and unfolded states in two-state folders as well as the height and the location of the transition state (TS). Although this approach is remarkably insightful, there are cases for which the energy landscape is multidimensional (catch bonds being the most prominent). To assess if the unfolding energy landscape in small single domain proteins could be one-dimensional, we simulated force-induced unfolding of ubiquitin (Ub) using the coarse-grained self-organized polymer-side chain (SOP-SC) model. Brownian dynamics simulations using the SOP-SC model reveal that the Ub energy landscape is weakly multidimensional (WMD), governed predominantly by a single barrier. The unfolding pathway is confined to a narrow reaction pathway that could be described as diffusion in a quasi-1D X-dependent free energy profile. However, a granular analysis using the P_fold analysis, which does not assume any form for the reaction coordinate, shows that X alone does not account for the height and, more importantly, the location of the TS. The f-dependent TS location moves toward the folded state as f increases, in accord with the Hammond postulate. Our study shows that, in addition to analyzing the f-dependent hopping rates, the transition state ensemble must also be determined without resorting to X as a reaction coordinate to describe the unfolding energy landscapes of single domain proteins, especially if they are only WMD.

Multiscale Coarse-Grained Model for the Stepping of Molecular Motors with Application to Kinesin

Conventional kinesin, a motor protein that transports cargo within cells, walks by taking multiple steps toward the plus end of the microtubule (MT). While significant progress has been made in understanding the details of the walking mechanism of kinesin, there are many unresolved issues. From a computational perspective, a central challenge is the large size of the system, which limits the scope of time scales accessible in standard computer simulations. Here, we create a general multiscale coarse-grained model for motors that enables us to simulate the stepping process of motors on polar tracks (actin and MT) with a focus on kinesin. Our approach greatly shortens the computation times without a significant loss in detail, thus allowing us to better describe the molecular basis of the stepping kinetics. The small number of parameters, which are determined by fitting to experimental data, allows us to develop an accurate method that may be adopted to simulate stepping in other molecular motors. The model enables us to simulate a large number of steps, which was not possible previously. We show in agreement with experiments that due to the docking of the neck linker (NL) of kinesin, sometimes deemed as the power stroke, the space explored diffusively by the tethered head is severely restricted, allowing the step to be completed in tens of microseconds. We predict that increasing the interaction strength between the NL and the motor head, achievable by mutations in the NL, decreases the stepping time but reaches a saturation value. Furthermore, the full three-dimensional dynamics of the cargo are fully resolved in our model, contributing to the predictive power and allowing us to study the important aspects of cargo-motor interactions.

Asymmetry in histone rotation in forced unwrapping and force quench rewrapping in a nucleosome

Single molecule pulling experiments have shown that DNA in the nucleosomes unwraps in two stages from the histone protein core (HPC). The first stage, attributed to the rupture of the outer DNA turn, occurs between 3 and 5 pNs, and is reversible. The inner DNA turn ruptures irreversibly at forces between 9 and 15 pNs (or higher) in the second stage. Molecular simulations using the Self-Organized Polymer model capture the experimental findings. The unwrapping of the outer DNA turn is independent of the pulling direction. The rupture of the DNA inner turn depends on the pulling direction and involves overcoming substantial energetic (most likely electrostatic in origin) and kinetic barriers. They arise because the mechanical force has to generate sufficient torque to rotate the HPC by 180°. On the other hand, during the rewrapping process, HPC rotation is stochastic, with force playing no role. The assembly of the outer DNA wrap upon force quench nearly coincides with the unwrapping process, confirming the reversibility of the outer turn rupture. The asymmetry in HPC rotation during unwrapping and rewrapping explains the observed hysteresis in the stretch-release cycles in experiments. We propose experiments to test the prediction that HPC rotation produces kinetic barriers in the unwrapping process.

Mechanical heterogeneity along single cell-cell junctions is driven by lateral clustering of cadherins during vertebrate axis elongation

Morphogenesis is governed by the interplay of molecular signals and mechanical forces across multiple length scales. The last decade has seen tremendous advances in our understanding of the dynamics of protein localization and turnover at subcellular length scales, and at the other end of the spectrum, of mechanics at tissue-level length scales. Integrating the two remains a challenge, however, because we lack a detailed understanding of the subcellular patterns of mechanical properties of cells within tissues. Here, in the context of the elongating body axis of Xenopus embryos, we combine tools from cell biology and physics to demonstrate that individual cell-cell junctions display finely-patterned local mechanical heterogeneity along their length. We show that such local mechanical patterning is essential for the cell movements of convergent extension and is imparted by locally patterned clustering of a classical cadherin. Finally, the patterning of cadherins and thus local mechanics along cell-cell junctions are controlled by Planar Cell Polarity signaling, a key genetic module for CE that is mutated in diverse human birth defects.

Self-generated persistent random forces drive phase separation in growing tumors

A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Dynamics of cells in the core is glass-like, whereas those in the periphery undergoes diffusive or super-diffusive behavior. Quantification of heterogeneity using the mean square displacement or the self-intermediate scattering function, which involves averaging over the cell population, hides the complexity of the collective movement. Using the t-distributed stochastic neighbor embedding (t-SNE), a popular unsupervised machine learning dimensionality reduction technique, we show that the phase space structure of an evolving colony of cells, driven by cell division and apoptosis, partitions into nearly disjoint sets composed principally of the core and periphery cells. The non-equilibrium phase separation is driven by the differences in the persistence of self-generated active forces induced by cell division. Extensive heterogeneity revealed by t-SNE paves the way toward understanding the origins of intratumor heterogeneity using experimental imaging data.

Random First Order Transition Theory for Glassy Dynamics in a Single Condensed Polymer

The number of compact structures of a single condensed polymer (SCP), with similar free energies, grows exponentially with the degree of polymerization. In analogy with structural glasses (SGs), we expect that at low temperatures chain relaxation should occur by activated transitions between the compact metastable states. By evolving the states of the SCP, linearly coupled to a reference state, we show that, below a dynamical transition temperature (T_{d}), the SCP is trapped in a metastable state leading to slow dynamics. At a lower temperature, T_{K}≠0, the configurational entropy vanishes, resulting in a thermodynamic random first order ideal glass transition. The relaxation time obeys the Vogel-Fulcher-Tamman law, diverging at T=T_{0}≈T_{K}. These findings, accord well with the random first order transition theory, establishing that SCP and SG exhibit similar universal characteristics.

Molecular Transfer Model for pH Effects on Intrinsically Disordered Proteins: Theory and Applications

We present a theoretical method to study how changes in pH shape the heterogeneous conformational ensemble explored by intrinsically disordered proteins (IDPs). The theory is developed in the context of coarse-grained models, which enable a fast, accurate, and extensive exploration of conformational space at a given protonation state. In order to account for pH effects, we generalize the molecular transfer model (MTM), in which conformations are re-weighted using the transfer free energy, which is the free energy necessary for bringing to equilibrium in a new environment a "frozen" conformation of the system. Using the semi-grand ensemble, we derive an exact expression of the transfer free energy, which amounts to the appropriate summation over all the protonation states. Because the exact result is computationally too demanding to be useful for large polyelectrolytes or IDPs, we introduce a mean-field (MF) approximation of the transfer free energy. Using a lattice model, we compare the exact and MF results for the transfer free energy and a variety of observables associated with the model IDP. We find that the precise location of the charged groups (the sequence), and not merely the net charge, determines the structural properties. We demonstrate that some of the limitations previously noted for MF theory in the context of globular proteins are mitigated when disordered polymers are studied. The excellent agreement between the exact and MF results poises us to use the method presented here as a computational tool to study the properties of IDPs and other biological systems as a function of pH.