We present a predictive scheme connecting the topological structure of highly branched entangled polymers, with industrial-level complexity, to the emergent viscoelasticity of the polymer melt. The ...scheme is able to calculate the linear and nonlinear viscoelasticity of a stochastically branched "high-pressure free radical" polymer melt as a function of the chemical kinetics of its formation. The method combines numerical simulation of polymerization with the tube/ entanglement physics of polymer dynamics extended to fully nonlinear response. We compare calculations for a series of low-density polyethylenes with experiments on structural and viscoelastic properties. The method provides a window onto the molecular processes responsible for the optimized rheology of these melts, connecting fundamental science to process in complex flow, and opens up the in silico design of new materials.
Silk is one of the most intriguing examples of biomolecular self-assembly, yet little is understood of molecular mechanisms behind the flow behavior generating these complex high-performance fibers. ...This work applies the polymer physics of entangled solution rheology to present a first microphysical understanding of silk in the linear viscoelastic regime. We show that silk solutions can be approximated as reptating polymers with “sticky” calcium bridges whose strength can be controlled through the potassium concentration. This approach provides a new window into critical microstructural parameters, in particular identifying the mechanism by which potassium and calcium ions are recruited as a powerful viscosity control in silk. Our model constitutes a viable starting point to understand not only the “flow-induced self-assembly” of silk fibers but also a broader range of phenomena in the emergent field of material-focused synthetic biology.
The COVID-19 pandemic caused by the novel coronavirus SARS-CoV-2 has no publicly available vaccine or antiviral drugs at the time of writing. An attractive coronavirus drug target is the main ...protease (M
, also known as 3CL
) because of its vital role in the viral cycle. A significant body of work has been focused on finding inhibitors which bind and block the active site of the main protease, but little has been done to address potential non-competitive inhibition, targeting regions other than the active site, partly because the fundamental biophysics of such allosteric control is still poorly understood. In this work, we construct an elastic network model (ENM) of the SARS-CoV-2 M
homodimer protein and analyse its dynamics and thermodynamics. We found a rich and heterogeneous dynamical structure, including allosterically correlated motions between the homodimeric protease's active sites. Exhaustive 1-point and 2-point mutation scans of the ENM and their effect on fluctuation free energies confirm previously experimentally identified bioactive residues, but also suggest several new candidate regions that are distant from the active site, yet control the protease function. Our results suggest new dynamically driven control regions as possible candidates for non-competitive inhibiting binding sites in the protease, which may assist the development of current fragment-based binding screens. The results also provide new insights into the active biophysical research field of protein fluctuation allostery and its underpinning dynamical structure.
We examine the contrast between mechanisms for allosteric signaling that involve structural change, and those that do not, from the perspective of allosteric pathways. In particular we treat in ...detail the case of fluctuation-allostery by which amplitude modulation of the thermal fluctuations of the elastic normal modes conveys the allosteric signal, and address the question of what an allosteric pathway means in this case. We find that a perturbation theory of thermal elastic solids and nonperturbative approach (by super-coarse-graining elasticity into internal bending modes) have opposite signatures in their structure of correlated pathways. We illustrate the effect from analysis of previous results from GlxR of Corynebacterium glutamicum, an example of the CRP/FNR transcription family of allosteric homodimers. We find that the visibility of both correlated pathways and disconnected sites of correlated motion in this protein suggests that mechanisms of local elastic stretch and bend are recruited for the purpose of creating and controlling allosteric cooperativity.
We present a tube model for the Brownian dynamics of associating polymers in extensional flow. In linear response, the model confirms the analytical predictions for the sticky diffusivity by ...Leibler-Rubinstein-Colby theory. Although a single-mode Doi-Edwards-Marrucci-Grizzuti approximation accurately describes the transient stretching of the polymers above a "sticky" Weissenberg number (product of the strain rate with the sticky-Rouse time), the preaveraged model fails to capture a remarkable development of a power law distribution of stretch in steady-state extensional flow: while the mean stretch is finite, the fluctuations in stretch may diverge. We present an analytical model that shows how strong stochastic forcing drives the long tail of the distribution, gives rise to rare events of reaching a threshold stretch, and constitutes a framework within which nucleation rates of flow-induced crystallization may be understood in systems of associating polymers under flow. The model also exemplifies a wide class of driven systems possessing strong, and scaling, fluctuations.
Allostery is a fundamental process by which ligand binding to a protein alters its activity at a distinct site. There is growing evidence that allosteric cooperativity can be communicated by ...modulation of protein dynamics without conformational change. The mechanisms, however, for communicating dynamic fluctuations between sites are debated. We provide a foundational theory for how allostery can occur as a function of low-frequency dynamics without a change in structure. We have generated coarse-grained models that describe the protein backbone motions of the CRP/FNR family transcription factors, CAP of Escherichia coli and GlxR of Corynebacterium glutamicum. The latter we demonstrate as a new exemplar for allostery without conformation change. We observe that binding the first molecule of cAMP ligand is correlated with modulation of the global normal modes and negative cooperativity for binding the second cAMP ligand without a change in mean structure. The theory makes key experimental predictions that are tested through an analysis of variant proteins by structural biology and isothermal calorimetry. Quantifying allostery as a free energy landscape revealed a protein "design space" that identified the inter- and intramolecular regulatory parameters that frame CRP/FNR family allostery. Furthermore, through analyzing CAP variants from diverse species, we demonstrate an evolutionary selection pressure to conserve residues crucial for allosteric control. This finding provides a link between the position of CRP/FNR transcription factors within the allosteric free energy landscapes and evolutionary selection pressures. Our study therefore reveals significant features of the mechanistic basis for allostery. Changes in low-frequency dynamics correlate with allosteric effects on ligand binding without the requirement for a defined spatial pathway. In addition to evolving suitable three-dimensional structures, CRP/FNR family transcription factors have been selected to occupy a dynamic space that fine-tunes biological activity and thus establishes the means to engineer allosteric mechanisms driven by low-frequency dynamics.
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•All-atom MD (aaMD) guide ENM distance and mode cut-offs.•Poor local spatial resolution of mode structure affects even low modes.•Backbone-enhanced ENM fails to capture mode ...dispersion.•Protein–ligand elastic network connectivity is vital for allostery.
The family of coarse-grained models for protein dynamics known as Elastic Network Models (ENMs) require careful choice of parameters to represent well experimental measurements or fully-atomistic simulations. The most basic ENM that represents each protein residue by a node at the position of its C-alpha atom, all connected by springs of equal stiffness, up to a cut-off in distance. Even at this level a choice is required of the optimum cut-off distance and the upper limit of elastic normal modes taken in any sum for physical properties, such as dynamic correlation or allosteric effects on binding. Additionally, backbone-enhanced ENM (BENM) may improve the model by allocating a higher stiffness to springs that connect along the protein backbone. This work reports on the effect of varying these three parameters (distance and mode cutoffs, backbone stiffness) on the dynamical structure of three proteins, Catabolite Activator Protein (CAP), Glutathione S-transferase (GST), and the SARS-CoV-2 Main Protease (M pro ). Our main results are: (1) balancing B-factor and dispersion-relation predictions, a near-universal optimal value of 8.5 Å is advisable for ENMs; (2) inhomogeneity in elasticity brings the first mode containing spatial structure not well-resolved by the ENM typically within the first 20; (3) the BENM only affects modes in the upper third of the distribution, and, additionally to the ENM, is only able to model the dispersion curve better in this vicinity; (4) BENM does not typically affect fluctuation-allostery, which also requires careful treatment of the effector binding to the host protein to capture.
The dynamics of entangled flexible polymers is dominated by physics general to many chemical systems. It is an appealing interdisciplinary field where experimental and theoretical physics can work ...closely with chemistry and chemical engineering. The role of topological interactions is particularly important, and has given rise to a successful theoretical framework: the 'tube model'. Progress over the last 30 years is reviewed in the light of specially-synthesized model materials, an increasing palette of experimental techniques, simulation and both linear and nonlinear rheological response. Our current understanding of a series of processes in entangled dynamics: 'reptation', 'contour length fluctuation' and 'constraint-release' are set in the context of remaining serious challenges. Especial attention is paid to the phenomena associated with polymers of complex topology or 'long chain branching'.
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