Stimuli-responsive, self-assembling nanomaterials hold a great promise to revolutionize medicine and technology. However, current discovery is slow and often serendipitous. Here we report a multiscale modeling study to elucidate the pH-controlled self-assembly of nanofibers from the peptide amphiphiles, palmitoyl-I-A3E4-NH2. The coarse-grained simulations revealed the formation of random-coil based spherical micelles at strong electrostatic repulsion. However, at weak or no electrostatic repulsion, the micelles merge into a nanofiber driven by the β-sheet formation between the peptide segments. The all-atom constant pH molecular dynamics revealed a cooperative transition between random coil and β-sheet in the pH range 6–7, matching the CD data. Interestingly, although the bulk pKa is more than one unit below the transition pH, consistent with the titration data, the highest pKa’s coincide with the transition pH, suggesting that the latter may be tuned by modulating the pKa’s of a few solvent-buried Glu side chains. Together, these data offer, to our best knowledge, the first multiresolution and quantitative view of the pH-dependent self-assembly of nanofibers. The novel protocols and insights gained are expected to advance the computer-aided design and discovery of pH-responsive nanomaterials.

Structural fluctuations of a protein are essential for a protein to function and fold. By using molecular dynamics (MD) simulations of the model α/β protein VA3 in its native state, the coupling between the main-chain (MC) motions [represented by coarsegrained dihedral angles (CGDAs) γ n based on four successive C α atoms (n − 1, n, n þ 1, n þ 2) along the amino acid sequence] and its side-chain (SC) motions [represented by CGDAs δ n formed by the virtual bond joining two consecutive C α atoms (n, n þ 1) and the bonds joining these C α atoms to their respective C β atoms] was analyzed. The motions of SCs (δ n ) and MC (γ n ) over time occur on similar free-energy profiles and were found to be subdiffusive. The fluctuations of the SCs (δ n ) and those of the MC (γ n ) are generally poorly correlated on a ps time-scale with a correlation increasing with time to reach a maximum value at about 10 ns. This maximum value is close to the correlation between the δ n ðtÞ and γ n ðtÞ time-series extracted from the entire duration of the MD runs (400 ns) and varies significantly along the amino acid sequence. High correlations between the SC and MC motions [δðtÞ and γðtÞ time-series] were found only in flexible regions of the protein for a few residues which contribute the most to the slowest collective modes of the molecule. These results are a possible indication of the role of the flexible regions of proteins for the biological function and folding.dihedral principal component analysis | free-energy landscape | power law | subdiffusion T he motions of the side chains and of the backbone of a protein are coupled to each other in protein folding. The removal of the nonpolar side chains from the solvent in protein folding orients the backbone locally (1), and the formation of the backbone hydrogen bonds between residues in the secondary structures induces displacements of their side chains. Therefore, in order to understand protein folding, it is necessary to understand how the motions of the side chains are propagated to the backbone and vice versa. As a prerequisite, it is necessary to understand how the motions of the side chains are coupled to those of the main chain in the native state of a protein. To address this question, five 80 ns all-atom molecular dynamics (MD) simulations of a 46-residue α/β model protein VA3 (PDB: 1ED0) (2) in its native state were analyzed. Protein VA3 was chosen here because it is highly homologous to the well-studied protein crambin, but unlike crambin (3), it is soluble in water (2).To express the correlation between the main-chain and the side-chain motions quantitatively, two coarse-grained dihedral angles (CGDAs) were defined for each residue n (Fig. S1A). The angles characterizing the fluctuations of the main chain are the CGDAs γ n (4-6) formed by the virtual bonds joining four consecutive C α atoms (n − 1, n, n þ 1 and n þ 2) along the amino acid sequence with 2 ≤ n ≤ N − 2 and N being the number of residues (Fig. S1A). The angles γ n are coordinates used to describe large changes o...

Structural fluctuations of a protein are essential for the function of native proteins and for protein folding. To understand how the main chain in the native state of a protein fluctuates on different time scales, we examined the rotational correlation functions (RCFs), CðtÞ, of the backbone N-H bonds and of the dihedral angles γ built on four consecutive C α atoms. Using molecular dynamics simulations of a model α∕β protein (VA3) in its native state, we demonstrate that these RCFs decay as stretched exponentials, ln ½CðtÞ≈D α t α with a constant D α and an exponent α (0<α<0.35) varying with the free-energy profiles (FEPs) along the amino acid sequence. The probability distributions of the fluctuations of the main chain computed at short time scale (1 ps) were identical to those computed at large time scale (1 ns) if the time is rescaled by a factor depending on α<1. This self-similar property and the nonexponential decays (α≠1) of the RCFs are described by a rotational diffusion equation with a time-dependent diffusion coefficient DðtÞ¼αD α t α−1 . The present findings agree with observations of subdiffusion (α<1) of fluorescent probes within a protein molecule. The subdiffusion of 15 N-H bonds did not affect the value of the order parameter S 2 extracted from the NMR relaxation data by assuming normal diffusion (α¼1) of 15 N-H bonds on a nanosecond time scale. However, we found that the RCF does not converge to S 2 on the nanosecond time scale for residues with multiple-minima FEPs.anomalous diffusion | model-free approach | power law | free-energy landscape

α-Synuclein (αS) is a major constituent of Lewy bodies, the insoluble aggregates that are the hallmark of one of the most prevalent neurodegenerative disorders, Parkinson's disease (PD). The vast majority of experiments in vitro and in vivo provide extensive evidence that a disordered monomeric form is the predominant state of αS in water solution, and it undergoes a large-scale disorder-to-helix transition upon binding to vesicles of different types. Recently, another form, tetrameric, of αS with a stable helical structure was identified experimentally. It has been shown that a dynamic intracellular population of metastable αS tetramers and monomers coexists normally; and the tetramer plays an essential role in maintaining αS homeostasis. Therefore, it is of interest to know whether the tetramer can serve as a means of preventing or delaying the start of PD. Before answering this very important question, it is, first, necessary to find out, on an atomistic level, a correlation between tetramers and monomers; what mediates tetramer formation and what makes a tetramer stable. We address these questions here by investigating both monomeric and tetrameric forms of αS. In particular, by examining correlations between the motions of the side chains and the main chain, steric parameters along the amino-acid sequence, and one- and two-dimensional free-energy landscapes along the coarse-grained dihedral angles γ and δ and principal components, respectively, in monomeric and tetrameric αS, we were able to shed light on a fundamental relationship between monomers and tetramers, and the key residues involved in mediating formation of a tetramer. Also, the reasons for the stability of tetrameric αS and inability of monomeric αS to fold are elucidated here.

A fundamental open problem in biophysics is how the folded structure of the main chain (MC) of a protein is determined by the physics of the interactions between the side-chains (SCs). All-atom molecular dynamics simulations of a model protein (Trp-cage) revealed that strong correlations between the motions of the SCs and the MC occur transiently at 380 K in unfolded segments of the protein, and during the simulations of the whole amino-acid sequence at 450 K. The high correlation between the SC and MC fluctuations is a fundamental property of the unfolded state and is also relevant to unstructured proteins as Intrinsically Disordered Proteins (IDPs), for which new reaction coordinates are introduced. The presented findings may open a new door as to how functions of IDPs are related to conformations, which play a crucial role in neurodegenerative diseases.

Molecular dynamics (MD) simulations and far-infrared (far-IR) spectroscopy were combined to study peptide binding by the second PDZ domain (PDZ1) of MAGI1, which has been identified as an important target for the Human Papilloma Virus. PDZ1 recognizes and binds to the C-terminal end of the E6 protein from high-risk Human Papilloma Virus. The far-IR spectra of two forms of the protein, an unbound APO form and a HOLO form (where the PDZ1 is bound to an 11-residue peptide derived from the C terminus of HPV16 E6), were obtained. MD simulations were used to determine the most representative structure of each form and these were used to compute their respective IR spectra by normal mode analysis. Far-UV circular dichroism spectroscopy was used to confirm the secondary structure content and the stability through temperature-dependent studies. Both the experimental and calculated far-IR spectra showed a red shift of the low-frequency peaks upon peptide binding. The calculations show that this is coincident with an increased number of hydrogen bonds formed as the peptide augments the protein β-sheet. We further identified the contribution of surface-bound water molecules to bands in the far-IR and, through the calculations, identified potential pathways for allosteric communication. Together, these results demonstrate the utility of combining far-IR experiments and MD studies to study peptide binding by proteins.