Quantitative understanding of the kinetics of fibril formation and the molecular mechanism of transition from monomers to fibrils is needed to obtain insights into the growth of amyloid fibrils and more generally self-assembly multisubunit protein complexes. Significant advances using computations of protein aggregation in a number of systems have established generic and sequence-specific aspects of the early steps in oligomer formation. Theoretical considerations, which view oligomer and fibril growth as diffusion in a complex energy landscape, and computational studies, involving minimal lattice and coarse-grained models, have revealed general principles governing the transition from monomeric protein to ordered fibrillar aggregates. Detailed atomistic calculations have explored the early stages of the protein aggregation pathway for a number of amyloidogenic proteins, most notably amyloid β- (Aβ-) protein and fragments from proteins linked to various diseases. These computational studies have provided insights into the role of sequence, role of water, and specific interatomic interactions underlying the thermodynamics and dynamics of elementary kinetic steps in the aggregation pathway. Novel methods are beginning to illustrate the structural basis for the production of Aβ-peptides through interactions with secretases in the presence of membranes. We show that a variety of theoretical approaches, ranging from scaling arguments to minimal models to atomistic simulations, are needed as a complement to experimental studies probing the principles governing protein aggregation.

This review summarizes the synthetic methods to sulphated polysaccharides, describes their compositional and structural diversity in regards to activity, and showcases their biomedical applications.

An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochromecis studied by using two theoretical approaches. One approach is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach, which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements. Both methods result in similar estimates of the VER time (subpicoseconds) for a CD stretching mode in the protein at room temperature. The theoretical predictions are in accord with previous experimental data. A perspective on directions for the detailed study of time scales and mechanisms of VER in proteins is presented.

Generalized Monte Carlo and molecular dynamics algorithms which provide enhanced sampling of the phase space in the calculation of equilibrium thermodynamic properties is presented. The algorithm samples trial moves from a generalized statistical distribution derived from a modification of the Gibbs–Shannon entropy proposed by Tsallis. Results for a one-dimensional model potential demonstrate that the algorithm leads to a greatly enhanced rate of barrier crossing and convergence in the calculation of equilibrium averages. Comparison is made with standard Metropolis Monte Carlo and the J-walking algorithm of Franz, Freeman and Doll. Application to a 13-atom Lennard-Jones cluster demonstrates the ease with which the algorithm may be applied to complex molecular systems.