Microcanonical thermostatistics of coarse-grained proteins with amyloidogenic propensity

A density of states-based approach to determine temperature-dependent aggregation rates

Here, we establish an approach to determine temperature-dependent aggregation rates in terms of thermostatistical quantities, which can be obtained directly from flat-histogram and statistical temperature algorithms considering the density of states of the system. Our approach is validated through simulations of an Ising-like model with anisotropically interacting particles at temperatures close to its first-order phase transition. Quantitative comparisons between the numerically obtained forward and reverse rates to approximate analytical expressions corroborate its use as a model-independent approach.

On the origin of the negative energy-related contribution to the elastic modulus of rubber-like gels

We consider a coarse-grained polymer model in order to investigate the origin of a recently discovered negative energy-related contribution to the elastic modulus G(T) of rubber-like gels. From this model, we are able to compute an exact expression for the free energy of the system, which allows us to evaluate a stress-strain relationship that displays a non-trivial dependence on the temperature T. We validate our approach through comparisons between the theoretical results and the experimental data obtained for tetra-PEG hydrogels, which indicate that, although simple, the present model works well to describe the experiments. Importantly, our approach unveiled aspects of the experimental analysis which turned out to be different from the conventional entropic and energetic analysis broadly used in the literature. Also, in contrast to the linear dependence predicted by the traditional, i.e., purely entropic, models, our results suggest that the general expression of the elastic modulus should be of the form [Formula: see text], with w(T) being a temperature-dependent correction factor that could be related to the interaction between the chains in the network and the solvent. Accordingly, the correction factor allows the expression found for the elastic modulus to describe both rubber and rubber-like gels.

Microcanonical insights into the physicochemical stability of the coformulation of insulin with amylin analogues

Injections of insulin are the main treatment for diabetes, but in the long run this therapy can induce serious drawbacks. This has inspired new drugs able to decrease insulin requirements. For instance, human amylin (hIAPP) is a small hormone cosecreted by pancreatic β-cells with insulin to which is a synergistic partner. However, the high amyloidogenicity of hIAPP precluded it as a therapeutics and led to the design of pramlintide (sIAPP), a chimeric analogue with substitutions (A25P, S28P, and S29P) inherited from the aggregation-resistant rat isoform (rIAPP). Despite sIAPP advantages, it still shares with hIAPP a poorly soluble profile at physiological pH that hampers its mixture with insulin. Recent improvements, as charge-enhanced mutants, have been proposed. For instance, sIAPP⁺ was screened in silico by purely microcanonical thermostatistical methods and adds to sIAPP an S20R mutation to uplift its solubility. This suggests that such physically inspired computational approach may also be auspicious on devising effective coformulations of insulin with amylin analogues. In this seminal attempt, we make comparative multicanonical simulations of regular acting human insulin coformulated with hIAPP, sIAPP, or sIAPP⁺. To assess the respective physicochemical stabilities against aggregation, we characterize the structural-phase transitions through the microcanonical thermodynamic formalism and evaluate their time lags using the classical nucleation theory. These results are then correlated with estimates of solvation free energies, modeled by the Poisson-Boltzmann equation, and structural propensities. Experimental essays are compared to our simulations and support our methodology.

PathMolD-AB: Spatiotemporal pathways of protein folding using parallel molecular dynamics with a coarse-grained model

Solving the protein folding problem (PFP) is one of the grand challenges still open in computational biophysics. Globular proteins are believed to evolve from initial configurations through folding pathways connecting several thermodynamically accessible states in a free energy landscape until reaching its minimum, inhabited by the stable native structures. Despite its huge computational burden, molecular dynamics (MD) is the leading approach in the PFP studies by preserving the Newtonian temporal evolution in the canonical ensemble. Non-trivial improvements are provided by highly parallel implementations of MD in cost-effective GPUs, concomitant to multiscale descriptions of proteins by coarse-grained minimalist models. In this vein, we present the PathMolD-AB framework, a comprehensive software package for massively parallel MD simulations using the canonical ensemble, structural analysis, and visualization of the folding pathways using the minimalist AB-model. It has, also, a tool to compare the results with proteins re-scaled from the PDB. We simulate and analyze, as case studies, the folding of four proteins: 13FIBO, 2GB1, 1PLC and 5ANZ, with 13, 55, 99 and 223 amino acids, respectively. The datasets generated from simulations correspond to the MD evolution of 3500 folding pathways, encompassing 35×106 states, which contains the spatial amino acid positions, the protein free energies and radii of gyration at each time step. Results indicate that the speedup of our approach grows logarithmically with the protein length and, therefore, it is suited for most of the proteins in the PDB. The predicted structures simulated by PathMolD-AB were similar to the re-scaled biological structures, indicating that it is promising for the study of the PFP study.

Be positive: optimizing pramlintide from microcanonical analysis of amylin isoforms

Amylin, or human islet amyloid polypeptide (hIAPP), is a 37-residue hormone synergistic to insulin and co-secreted with it by β-cells in the pancreas. The deposition of its cytotoxic amyloid fibrils is strongly related to the progression of Type II diabetes (T2D) and islet graft failures. Notably, isoforms from some mammalian species, such as rats (rIAPP) and porcine (pIAPP), present a few key mutations preventing aggregation. This has lead to biotechnological development of drugs for adjunct therapies of T2D, such as pramlintide, a variant of hIAPP inspired by rIAPP whose proline substitutions have β-strand fibril-breaking properties. Ideally, such a drug should be formulated with insulin and co-administered, but this has been prevented by a poor solubility profile at the appropriate pH. Hopefully, this could be improved with appropriate point mutations, increasing the molecular net charge. Despite experimental progress, preliminary screening during rational drug design can greatly benefit from thermodynamic insight derived from molecular simulations. So we introduce microcanonical thermostatistics analysis of multicanonical (MUCA) simulations of wild-type amylin isoforms as a systematic assessment of protein thermostability. As a consequence of this comprehensive investigation, the most suitable single-point mutations able to optimize pramlintide are located among the wild-type amylin isoforms. In particular, we find that aggregation inhibition and increased solubility are inherited by pramlintide through further S20R substitution typical of pIAPP. Thus, we provide a consistent thermostatistical methodology to aid the design of improved adjunct therapies for T2D according to current clinical knowledge.

Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations

Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.

Breakout character of islet amyloid polypeptide hydrophobic mutations at the onset of type-2 diabetes

Toxic fibrillar aggregates of islet amyloid polypeptide (IAPP) appear as the physical outcome of a peptidic phase transition signaling the onset of type-2 diabetes mellitus in different mammalian species. In particular, experimentally verified mutations on the amyloidogenic segment 20-29 in humans, cats, and rats are highly correlated with the molecular aggregation propensities. Through a microcanonical analysis of the aggregation of IAPP_{20-29} isoforms, we show that a minimalist one-bead hydrophobic-polar continuum model for protein interactions properly quantifies those propensities from free-energy barriers. Our results highlight the central role of sequence-dependent hydrophobic mutations on hot spots for stabilization, and thus for the engineering, of such biological peptides.