Perceptron learning of pairwise contact energies for proteins incorporating the amino acid environment

Advanced computational approaches to understand protein aggregation

Protein aggregation is a widespread phenomenon implicated in debilitating diseases like Alzheimer's, Parkinson's, and cataracts, presenting complex hurdles for the field of molecular biology. In this review, we explore the evolving realm of computational methods and bioinformatics tools that have revolutionized our comprehension of protein aggregation. Beginning with a discussion of the multifaceted challenges associated with understanding this process and emphasizing the critical need for precise predictive tools, we highlight how computational techniques have become indispensable for understanding protein aggregation. We focus on molecular simulations, notably molecular dynamics (MD) simulations, spanning from atomistic to coarse-grained levels, which have emerged as pivotal tools in unraveling the complex dynamics governing protein aggregation in diseases such as cataracts, Alzheimer's, and Parkinson's. MD simulations provide microscopic insights into protein interactions and the subtleties of aggregation pathways, with advanced techniques like replica exchange molecular dynamics, Metadynamics (MetaD), and umbrella sampling enhancing our understanding by probing intricate energy landscapes and transition states. We delve into specific applications of MD simulations, elucidating the chaperone mechanism underlying cataract formation using Markov state modeling and the intricate pathways and interactions driving the toxic aggregate formation in Alzheimer's and Parkinson's disease. Transitioning we highlight how computational techniques, including bioinformatics, sequence analysis, structural data, machine learning algorithms, and artificial intelligence have become indispensable for predicting protein aggregation propensity and locating aggregation-prone regions within protein sequences. Throughout our exploration, we underscore the symbiotic relationship between computational approaches and empirical data, which has paved the way for potential therapeutic strategies against protein aggregation-related diseases. In conclusion, this review offers a comprehensive overview of advanced computational methodologies and bioinformatics tools that have catalyzed breakthroughs in unraveling the molecular basis of protein aggregation, with significant implications for clinical interventions, standing at the intersection of computational biology and experimental research.

Uncovering symmetry-breaking vector and reliability order for assigning secondary structures of proteins from atomic NMR chemical shifts in amino acids

Unravelling the complex correlation between chemical shifts of (13) C (α), (13) C (β), (13) C', (1) H (α), (15) N, (1) H ( N ) atoms in amino acids of proteins from NMR experiment and local structural environments of amino acids facilitates the assignment of secondary structures of proteins. This is an important impetus for both determining the three-dimensional structure and understanding the biological function of proteins. The previous empirical correlation scores which relate chemical shifts of (13) C (α), (13) C (β), (13) C', (1) H (α), (15) N, (1) H ( N ) atoms to secondary structures resulted in progresses toward assigning secondary structures of proteins. However, the physical-mathematical framework for these was elusive partly due to both the limited and orthogonal exploration of higher-dimensional chemical shifts of hetero-nucleus and the lack of physical-mathematical understanding underlying those correlation scores. Here we present a simple multi-dimensional hetero-nuclear chemical shift score function (MDHN-CSSF) which captures systematically the salient feature of such complex correlations without any references to a random coil state of proteins. We uncover the symmetry-breaking vector and its reliability order not only for distinguishing different secondary structures of proteins but also for capturing the delicate sensitivity interplayed among chemical shifts of (13) C (α), (13) C (β), (13) C', (1) H (α), (15) N, (1) H ( N ) atoms simultaneously, which then provides a straightforward framework toward assigning secondary structures of proteins. MDHN-CSSF could correctly assign secondary structures of training (validating) proteins with the favourable (comparable) Q3 scores in comparison with those from the previous correlation scores. MDHN-CSSF provides a simple and robust strategy for the systematic assignment of secondary structures of proteins and would facilitate the de novo determination of three-dimensional structures of proteins.

Extending the PRIME model for protein aggregation to all 20 amino acids

We extend PRIME, an intermediate-resolution protein model previously used in simulations of the aggregation of polyalanine and polyglutamine, to the description of the geometry and energetics of peptides containing all 20 amino acid residues. The 20 amino acid side chains are classified into 14 groups according to their hydrophobicity, polarity, size, charge, and potential for side chain hydrogen bonding. The parameters for extended PRIME, called PRIME 20, include hydrogen-bonding energies, side chain interaction range and energy, and excluded volume. The parameters are obtained by applying a perceptron-learning algorithm and a modified stochastic learning algorithm that optimizes the energy gap between 711 known native states from the PDB and decoy structures generated by gapless threading. The number of independent pair interaction parameters is chosen to be small enough to be physically meaningful yet large enough to give reasonably accurate results in discriminating decoys from native structures. The most physically meaningful results are obtained with 19 energy parameters.

Learning rate and attractor size of the single-layer perceptron

We study the simplest possible order one single-layer perceptron with two inputs, using the delta rule with online learning, in order to derive closed form expressions for the mean convergence rates. We investigate the rate of convergence in weight space of the weight vectors corresponding to each of the 14 out of 16 linearly separable rules. These vectors follow zigzagging lines through the piecewise constant vector field to their respective attractors. Based on our studies, we conclude that a single-layer perceptron with N inputs will converge in an average number of steps given by an Nth order polynomial in t/l, where t is the threshold, and l is the size of the initial weight distribution. Exact values for these averages are provided for the five linearly separable classes with N=2. We also demonstrate that the learning rate is determined by the attractor size, and that the attractors of a single-layer perceptron with N inputs partition RN plus sign in circle RN.