Dimerization of Full-length Aß -42 Peptide: A Comparison of Different Force Fields and Water Models.

Among the two isoforms of amyloid- i.e., Aß-40 and Aß-42, Aß-42 is more toxic due to its increased aggregation propensity. The oligomerization pathways of amyloid-ß may be investigated by studying its dimerization process at an atomic level. Intrinsically disordered proteins (IDPs) lack well-defined structures and are associated with numerous neurodegenerative disorders. Molecular dynamics simulations of these proteins are often limited by the choice of parameters due to inconsistencies in the empirically developed protein force fields and water models. To evaluate the accuracy of recently developed force fields for IDPs, we study the dimerization of full-length Aß-42 in aqueous solution with three different combinations of AMBER force field parameters and water models such as ff14SB/TIP3P, ff19SB/OPC, and ff19SB/TIP3P using classical MD and Umbrella Sampling method. This work may be used as a benchmark to compare the performance of different force fields for the simulations of IDPs.

Effect of caffeine on the aggregation of amyloid-ß-A 3D RISM study.

Alzheimer's disease is a detrimental neurological disorder caused by the formation of amyloid fibrils due to the aggregation of amyloid-ß peptide. The primary therapeutic approaches for treating Alzheimer's disease are targeted to prevent this amyloid fibril formation using potential inhibitor molecules. The discovery of such inhibitor molecules poses a formidable challenge to the design of anti-amyloid drugs. This study investigates the effect of caffeine on dimer formation of the full-length amyloid-ß using a combined approach of all-atom, explicit water molecular dynamics simulations and the three-dimensional reference interaction site model theory. The change in the hydration free energy of amyloid-ß dimer, with and without the inhibitor molecules, is calculated with respect to the monomeric amyloid-ß, where the hydration free energy is decomposed into energetic and entropic components, respectively. Dimerization is accompanied by a positive change in the partial molar volume. Dimer formation is spontaneous, which implies a decrease in the hydration free energy. However, a reverse trend is observed for the dimer with inhibitor molecules. It is observed that the negatively charged residues primarily contribute for the formation of the amyloid-ß dimer. A residue-wise decomposition reveals that hydration/dehydration of the side-chain atoms of the charged amino acid residues primarily contribute to dimerization.

Aggregation propensities of proteins with varying degrees of disorder.

The hydration thermodynamics of a globular protein (AcP), three intrinsically disordered protein regions (1CD3, 1MVF, 1F0R) and a fully disordered protein (α-synuclein) is studied by an approach that combines an all-atom explicit water molecular dynamics simulations and three-dimensional reference interaction site model (3D-RISM) theory. The variation in hydration free energy with percentage disorder of the selected proteins is investigated through its nonelectrostatic and electrostatic components. A decrease in hydration free energy is observed with an increase in percentage disorder, indicating favorable interactions of the disordered proteins with the solvent. This confirms the role of percentage disorder in determining the aggregation propensity of proteins which is measured in terms of the hydration free energy in addition to their respective mean net charge and mean hydrophobicity. The hydration free energy is decoupled into energetic and entropic terms. A residue-wise decomposition analysis of the hydration free energy for the selected proteins is evaluated. The decomposition shows that the disordered regions contribute more than the ordered ones for the intrinsically disordered protein regions. The dominant role of electrostatic interactions is confirmed from the residue-wise decomposition of the hydration free energy. The results depict that the negatively charged residues contribute more to the total hydration free energy for the proteins with negative mean net charge, while the positively charged residues contribute more for proteins with positive mean net charge.

Curvature induced structural changes of the chicken villin headpiece subdomain by single walled carbon nanotubes.

Carbon nanotubes (CNTs) are identified as potential candidates for drug and biomolecular loading and delivery. CNTs of different chiralities have different diameters, which may significantly affect their abilities to interact with different types of biomolecules. Herein, we employ classical molecular dynamics simulation to provide insight into the curvature-dependent interactions between a model protein, chicken villin headpiece subdomain (HP36), with CNTs having chiralities (8,8), (12,12), and (20,20). It is revealed that, with increasing radii, the protein encounters more aromatic carbon atoms on the surface of the CNT, leading to its increasing strength of adsorption. However, the extent of adsorption has a limiting magnitude, after which an increase in the radius of the nanotube has practically no effect on the extent of adsorption. Spontaneous encapsulation of the protein was demonstrated using a (28,28) CNT, where the protein is found to undergo insignificant structural perturbation. Finally, steered molecular dynamics simulations have been performed to mimic the force-induced release of the protein from within the nanotube cavity. It has been identified that a minimum force of ∼300 pN and a minimum velocity of 4 Šns-1 are required to release the protein from the CNT at 300 K. Any external force below the critical magnitude and inducing velocity less than 4 Šns-1 allows the translocation of the protein through the inner surface of the CNT; however, before being released, the protein undergoes unfolding, thereby losing the secondary structure and biological activity.

Intrinsic viscosity and dielectric relaxation of ring polymers in dilute solutions.

The absence of chain ends makes ring polymers distinctly different from their linear analogues. The intrinsic viscosity, complex viscosity and the dielectric relaxation of ring polymers are investigated within the tenets of the optimized Rouse-Zimm theory. The distance dependent excluded volume interactions (EVIs) are obtained from Flory's mean field theory. The hydrodynamic interactions (HIs) between the pairs of monomers are estimated using the preaveraged Oseen tensor. The intrinsic viscosity of linear and ring polymers both with and without EVI are compared as a function of ring size. A monotonically increasing trend of the intrinsic viscosity is observed in both cases. The intrinsic viscosity of both linear and ring polymers both with and without EVI show a very good agreement with the experimental results of polystyrene over a wide range of molecular weights in both good and theta solvents, respectively. The fractal dimensions of the ring polymers with EVI lie between that of a random walk and a self-avoiding walk model of linear polymers in three dimensions. The ring size increases with EVI and the effect of EVI is stronger on larger rings than that on smaller rings. The dielectric relaxation follow a connectivity independent universal scaling behavior at low and high frequency regions. The imaginary part of the complex dielectric susceptibility displays a local maxima in the intermediate frequency region, which reveals a structure dependent behavior of the rings. The theoretically calculated dielectric loss of ring polymers with HI matches well with those obtained from experiments.

Relaxation dynamics measure the aggregation propensity of amyloid-ß and its mutants.

Atomistic molecular dynamics simulations are employed to investigate the global and segmental relaxation dynamics of the amyloid-ß protein and its causative and protective mutants. Amyloid-ß exhibits significant global/local dynamics that span a broad range of length and time scales due to its intrinsically disordered nature. The relaxation dynamics of the amyloid-ß protein and its mutants is quantitatively correlated with its experimentally measured aggregation propensity. The protective mutant has slower relaxation dynamics, whereas the causative mutants exhibit faster global dynamics compared with that of the wild-type amyloid-ß. The local dynamics of the amyloid-ß protein or its mutants is governed by a complex interplay of the charge, hydrophobicity, and change in the molecular mass of the mutated residue.

Hydration Thermodynamics of Familial Parkinson's Disease-Linked Mutants of α-Synuclein.

The hydration thermodynamics of different mutants of α-synuclein (α-syn) related to familial Parkinson's disease (PD) is explored using a computational approach that combines both molecular dynamics simulations in water and integral equation theory of molecular liquids. This analysis focuses on the change in conformational entropy, hydration free energy (HFE), and partial molar volume of α-syn upon mutation. The results show that A53T, A30P, E46K, and H50Q mutants aggregate more readily and display increased HFE and less negative interaction volume than the wild-type α-syn. In contrast, an opposite trend is observed for the G51D mutant with a lower experimental aggregation rate. The residuewise decomposition analysis of the HFE highlights that the dehydration/hydration of the hydrophilic residue-rich N- and C-termini of α-syn majorly contributes to the change upon mutation. The hydration shell contributions of different residues to the interaction volume are consistent with its increase/decrease upon mutation. This work shows that both HFE and interaction volume determine the aggregation kinetics of α-syn upon mutation and may serve as an appropriate benchmark for the treatment of PD.

Hydration Thermodynamics of the N-Terminal FAD Mutants of Amyloid-ß.

The hydration thermodynamics of amyloid-ß (Aß) and its pathogenic familial Alzheimer's disease (FAD) mutants such as A2V, Taiwan (D7H), Tottori (D7N), and English (H6R) and the protective A2T mutant is investigated by a combination of all-atom, explicit water molecular dynamics (MD) simulations and the three-dimensional reference interaction site model (3D-RISM) theory. The change in the hydration free energy on mutation is decomposed into the energetic and entropic components, which comprise electrostatic and nonelectrostatic contributions. An increase in the hydration free energy is observed for A2V, D7H, D7N, and H6R mutations that increase the aggregation propensity of Aß and lead to an early onset of Alzheimer's disease, while a reverse trend is noted for the protective A2T mutation. An antiphase correlation is found between the change in the hydration energy and the internal energy of Aß upon mutation. A residue-wise decomposition analysis shows that the change in the hydration free energy of Aß on mutation is primarily due to the hydration/dehydration of the side-chain atoms of the negatively charged residues. The decrease in the hydration of the negatively charged residues on mutation may decrease the solubility of the mutant, which increases the observed aggregation propensity of the FAD mutants. Results obtained from the theory show an excellent match with the experimentally reported data.

Effect of ligand binding on riboswitch folding: Theory and simulations.

The effect of ligand binding on the conformational transitions of the add A-riboswitch in cellular environments is investigated theoretically within the framework of the generalized Langevin equation combined with steered molecular dynamics simulations. Results for the transition path time distribution provide an estimate of the transit times, which are difficult to determine experimentally. The time for the conformational transitions of the riboswitch aptamer is longer for the ligand bound state as compared to that of the unbound one. The transition path time of the riboswitch follows a counterintuitive trend as it decreases with an increase in the barrier height. The mean transition path time of either transitions of the riboswitch in the ligand bound/unbound state increases with an increase in the complexity of the surrounding environment due to the caging effect. The results of the probability density function, transition path time distribution, and mean transition path time obtained from the theory qualitatively agree with those obtained from the simulations and with earlier experimental and theoretical studies.

Conformations of poly(propylene imine) dendrimers in an ionic liquid at different pH.

The conformational behavior of poly(propylene imine) (PPI) dendrimers at three different solution pH is studied in an ionic liquid (IL) solvent, 1-butyl-3-methylimidazolium chloride ([BMIM]Cl), through molecular dynamics (MD) simulations. The size, shape, density distribution, structure factor, and the scattering intensity are evaluated to probe the conformational transition of dendrimers as a function of pH. The results of the radial atomic and terminal amine group density distribution at low pH indicate a shift in the density towards the periphery of the dendrimers due to the electrostatic repulsion between the charged tertiary amine groups within the dendrimers. The [BMIM] cations are not encapsulated within dendrimers and predominantly reside near the periphery. The extensive back-folding of the outer branches due to the electrostatic repulsion between the solvent cations and the peripheral charged amine groups at neutral and low pH results in a dense compact structure in [BMIM]Cl as compared to that in water, as evident from the results of the structure factor and scattering intensity. The structural analysis in terms of the fractal dimension reveals that the lower generation dendrimers exhibit conformational transition as a function of pH, while the higher generations exhibit a highly compact structure at all solution pH. However, PPI dendrimers at low pH exhibit more free volume as compared to that at high pH, which may be utilized to accommodate specific guest molecules.

Conformational properties of complexes of poly(propylene imine) dendrimers with linear polyelectrolytes in dilute solutions.

This study investigates the conformational properties of complexes of poly(propylene imine) dendrimers with a linear polyelectrolyte (LPE) at neutral pH in an aqueous solution via molecular dynamics simulations. Various conformational properties, such as the atomic density profile, counterion density distribution, charge distribution, cavity volume, and the static structure factor are studied as a function of the charge and chain length of the LPE. The lower generation dendrimer complexes encapsulate the shorter linear PE chains, while the longer PE chains are adsorbed on the dendrimer surface that screen the surface charge and prevent the penetration of the counterions and water molecules. However, the overall charge of the higher generation dendrimers is not neutralized by the charge of the PE chains, which results in chloride counterion penetration within the dendrimers. The adsorption of the PE chains on the dendrimers is also verified from the charge distribution of the dendrimer-PE complexes. The charge on the lower generation dendrimer complexes is overcompensated by the longer PE chains resulting in an overall negative charge on the complexes, while the PE chains do not completely neutralize the charge of the higher generation dendrimers and produce positively charged complexes. The results of the structure factor indicate a conformational transition of the dendrimer-PE complexes from a dense compact structure to an open one with an increase in the PE chain length. This transition is characterized by an increase in the cavity volume in dendrimers with an increase in the PE chain length.

Effect of site-directed point mutations on protein misfolding: A simulation study.

A Monte Carlo simulation based sequence design method is proposed to investigate the role of site-directed point mutations in protein misfolding. Site-directed point mutations are incorporated in the designed sequences of selected proteins. While most mutated sequences correctly fold to their native conformation, some of them stabilize in other nonnative conformations and thus misfold/unfold. The results suggest that a critical number of hydrophobic amino acid residues must be present in the core of the correctly folded proteins, whereas proteins misfold/unfold if this number of hydrophobic residues falls below the critical limit. A protein can accommodate only a particular number of hydrophobic residues at the surface, provided a large number of hydrophilic residues are present at the surface and critical hydrophobicity of the core is preserved. Some surface sites are observed to be equally sensitive toward site-directed point mutations as the core sites. Point mutations with highly polar and charged amino acids increases the misfold/unfold propensity of proteins. Substitution of natural amino acids at sites with different number of nonbonded contacts suggests that both amino acid identity and its respective site-specificity determine the stability of a protein. A clash-match method is developed to calculate the number of matching and clashing interactions in the mutated protein sequences. While misfolded/unfolded sequences have a higher number of clashing and a lower number of matching interactions, the correctly folded sequences have a lower number of clashing and a higher number of matching interactions. These results are valid for different SCOP classes of proteins.

Orientational relaxation of ring polymers in dilute solutions.

The segmental relaxation dynamics of ring polymers in dilute solutions is investigated via optimized Rouse-Zimm theory. To the best of our knowledge, this is the first study that characterizes the orientational relaxation dynamics of ring polymers in dilute solutions. The orientational time autocorrelation functions are governed by two major processes that span a broad range of timescales: (i) local segmental motion at short times, independent of the ring size, and (ii) overall motion of the ring at long times that depends on the limiting ring size. Smaller rings relax faster than larger rings and their respective linear analogues. The hydrodynamic interactions decrease the higher relaxation rates corresponding to the local relaxation modes and increase the smaller relaxation rates which correspond to the collective relaxation modes. The spectral density is independent of frequency in the low frequency regime while it decreases with increasing frequency. Regardless of the ring size, the spin-lattice relaxation rate exhibits a single characteristic maximum as a function of frequency that shifts to a lower value with increasing strength of hydrodynamic interactions.

Salt-bridge dynamics in intrinsically disordered proteins: A trade-off between electrostatic interactions and structural flexibility.

Intrinsically Disordered Proteins (IDPs) are enriched in charged and polar residues; and, therefore, electrostatic interactions play a predominant role in their dynamics. In order to remain multi-functional and exhibit their characteristic binding promiscuity, they need to retain considerable dynamic flexibility. At the same time, they also need to accommodate a large number of oppositely charged residues, which eventually lead to the formation of salt-bridges, imparting local rigidity. The formation of salt-bridges therefore opposes the desired dynamic flexibility. Hence, there appears to be a meticulous trade-off between the two mechanisms which the current study attempts to unravel. With this objective, we identify and analyze salt-bridges, both as isolated as well as composite ionic bond motifs, in the molecular dynamic trajectories of a set of appropriately chosen IDPs. Time evolved structural properties of these salt-bridges like persistence, associated secondary structural 'order-disorder' transitions, correlated atomic movements, contribution in the overall electrostatic balance of the proteins have been studied in necessary detail. The results suggest that the key to maintain such a trade-off over time is the continuous formation and dissolution of salt-bridges with a wide range of persistence. Also, the continuous dynamic interchange of charged-atom-pairs (coming from a variety of oppositely charged side-chains) in the transient ionic bonds supports a model of dynamic flexibility concomitant with the well characterized stochastic conformational switching in these proteins. The results and conclusions should facilitate the future design of salt-bridges as a mean to further explore the disordered-globular interface in proteins.

Estimating the mean first passage time of protein misfolding.

Most theoretical and experimental studies confirm that proteins fold in the time scale of microseconds to milliseconds, but the kinetics of the protein misfolding remains largely unexplored. The kinetics of unfolding-folding-misfolding equilibrium in proteins is formulated in the analytical framework of the Master equation. The folded, unfolded and the misfolded state are characterized in terms of their respective contacts. The Mean First Passage Time (MFPT) to acquire the misfolded conformation from the native or folded state is derived from this equation with different boundary conditions. The MFPT is found to be practically independent of the length of the protein, the number of native contacts and the rate constant for the misfolded to the folded state. The results obtained from the survival probability are directly correlated to the age of onset and appearance of misfolding diseases in humans.

Role of local and nonlocal interactions in folding and misfolding of globular proteins.

A Monte Carlo simulation based sequence design method is proposed to study the role of the local and the nonlocal interactions with varying secondary structure content in protein folding, misfolding and unfolding. A statistical potential is developed from the compilation of a data set of proteins, which accounts for the respective contribution of local and the nonlocal interactions. Sequences are designed through a combination of positive and negative design by a Monte Carlo simulation in the sequence space. The weights of the local and the nonlocal interactions are tuned appropriately to study the role of the local and the nonlocal interactions in the folding, unfolding and misfolding of the designed sequences. Results suggest that the nonlocal interactions are the primary determinant of protein folding while the local interactions may be required but not always necessary. The nonlocal interactions mainly guide the polypeptide chain to form compact structures but do not differentiate between the native-like conformations, while the local interactions stabilize the target conformation against the native-like competing conformations. The study concludes that the local interactions govern the fold-misfold transition, while the nonlocal interactions regulate the fold-unfold transition of proteins. However, for proteins with predominantly ß-sheet content, the nonlocal interactions control both fold-misfold and fold-unfold transitions.

Globular-disorder transition in proteins: a compromise between hydrophobic and electrostatic interactions?

The charge-hydrophobicity correlation of globular and disordered proteins is explored using a generalized self-consistent field theoretical method combined with Monte Carlo simulations. Globular and disordered protein sequences with varied mean net charge and mean hydrophobicity are designed by theory, while Metropolis Monte Carlo generates a suitable ensemble of conformations. Results imply a transition of the dominant interactions between globular and disordered proteins across the charge-hydrophobicity boundary. It is observed that the charge-hydrophobicity boundary actually represents a trade-off between the repulsive and attractive interactions in a protein sequence. The attractive interactions predominate on the globular side of the boundary, while the repulsive interactions prevail on the disordered side. For globular proteins, core forming hydrophobic interactions are dominant leading to a minimally frustrated native conformation. For disordered proteins, the repulsive electrostatic interactions prevail yielding a minimally frustrated region comprising of an expanded, dynamic conformational ensemble. Thus, protein disorder, like protein folding, satisfies the principle of minimal frustration. All results are compared to real globular and disordered proteins. Thus this algorithm may be useful to probe the conformational characteristics of disordered proteins.

Does lack of secondary structure imply intrinsic disorder in proteins? A sequence analysis.

Intrinsically disordered proteins (IDPs)/protein regions (IDPRs) lack unique three-dimensional structure at the level of secondary and/or tertiary structure and are represented as an ensemble of interchanging conformations. To investigate the role of presence/absence of secondary structures in promoting intrinsic disorder in proteins, a comparative sequence analysis of IDPs, IDPRs and proteins with minimal secondary structures (less than 5%) is required. A sequence analysis reveals proteins with minimal secondary structure content have high mean net positive charge, low mean net hydrophobicity and low sequence complexity. Interestingly, analysis of the relative local electrostatic interactions reveal that an increase in the relative repulsive interactions between amino acids separated by three or four residues lead to either loss of secondary structure or intrinsic disorder. IDPRs show increase in both local negative-negative and positive-positive repulsive interactions. While IDPs show a marked increase in the local negative-negative interactions, proteins with minimal secondary structure depict an increase in the local positive-positive interactions. IDPs and IDPRs are enriched in D, E and Q residues, while proteins with minimal secondary structure are depleted of these residues. Proteins with minimal secondary structures have higher content of G and C, while IDPs and IDPRs are depleted of these residues. These results confirm that proteins with minimal secondary structure have a distinctly different propensity for charge, hydrophobicity, specific amino acids and local electrostatic interactions as compared to IDPs/IDPRs. Thus we conclude that lack of secondary structure may be a necessary but not a sufficient condition for intrinsic disorder in proteins.

Designing pH induced fold switch in proteins.

This work investigates the computational design of a pH induced protein fold switch based on a self-consistent mean-field approach by identifying the ensemble averaged characteristics of sequences that encode a fold switch. The primary challenge to balance the alternative sets of interactions present in both target structures is overcome by simultaneously optimizing two foldability criteria corresponding to two target structures. The change in pH is modeled by altering the residual charge on the amino acids. The energy landscape of the fold switch protein is found to be double funneled. The fold switch sequences stabilize the interactions of the sites with similar relative surface accessibility in both target structures. Fold switch sequences have low sequence complexity and hence lower sequence entropy. The pH induced fold switch is mediated by attractive electrostatic interactions rather than hydrophobic-hydrophobic contacts. This study may provide valuable insights to the design of fold switch proteins.

Effect of excluded volume on the rheology and transport dynamics of randomly hyperbranched polymers.

The rheology and transport dynamics of the randomly hyperbranched polymers with excluded volume interactions are investigated within the tenets of the Rouse-Zimm theory. The excluded volume interactions typically account for an effective co-volume between the nearest non-bonded monomers, modeled through a delta function pseudopotential, while the strength of such interactions is evaluated from the possible geometric orientations of the bonds. The mechanical moduli are primarily determined by the smaller eigenvalues corresponding to the collective modes. These modes with smaller relaxation rates increase with the decrease in the strength of excluded volume interaction parameter, while the local modes with higher relaxation rates remain unaffected. The internal structure of the randomly hyperbranched polymer is reflected in the intermediate frequency regime of the mechanical relaxation moduli, where the characteristic power-law behavior implies the fractal nature of the randomly hyperbranched polymers. The length of this power-law region increases either with the decrease in the strength of excluded volume interactions or with the increase in the number of shells of the randomly hyperbranched polymer, while the numerical values of the power-law exponents are strongly affected by the strength of excluded volume interactions. Intrinsic viscosity increases linearly for lower values of the excluded volume interaction parameters, while depicting a non-linear trend at higher strengths of excluded volume interactions. The randomly hyperbranched polymers are relatively more compact compared to the star polymer but less compact than that of dendrimers with the same number of monomers and same strength of excluded volume interactions. The values of the scaling exponents of the diffusion coefficient increase with decreasing the strength of excluded volume interactions. The scaling exponents of the diffusion coefficient of randomly hyperbranched polymers calculated with excluded volume exactly match with the earlier experimental results for hyperbranched polyglycidols in poly(vinyl alcohol) solutions.