How many bits of information can be transferred between residues in a protein and how fast?

Time resolved Raman and infrared spectroscopy experiments show the basic features of information transfer between residues in proteins. Here, we present the theoretical basis of information transfer using a simple elastic net model and recently developed entropy transfer concept in proteins. Mutual information between two residues is a measure of communication in proteins which shows the maximum amount of information that may be transferred between two residues. However, it does not explain the actual amount of transfer nor the transfer rate of information between residues. For this, dynamic equations of the system are needed. We used the Schreiber theory of information transfer and the Gaussian network Model of proteins, together with the solution of the Langevin equation, to quantify allosteric information transfer. Results of the model are in perfect agreement with ultraviolet resonance Raman measurements. Analysis of the allosteric protein Human NAD-dependent isocitrate dehydrogenase shows that a multitude of paths contribute collectively to information transfer. While the peak values of information transferred are small relative to information content of residues, considering the estimated transfer rates, which are in the order of megabits per second, sustained transfer during the activity time-span of proteins may be significant.

Gaussian Network Model Revisited: Effects of Mutation and Ligand Binding on Protein Behavior

The coarse-grained Gaussian Network model, GNM, considers only the alpha carbons of the folded protein. Therefore it is not directly applicable to the study of mutation or ligand binding problems where atomic detail is required. This shortcoming is improved by including the local effect of heavy atoms in the neighborhood of each alpha carbon into the Kirchoff Adjacency Matrix. The presence of other atoms in the coordination shell of each alpha carbon diminishes the magnitude of fluctuations of that alpha carbon. But more importantly, it changes the graph-like connectivity structure, i.e., the Kirchoff Adjacency Matrix of the whole system which introduces amino acid specific and position specific information into the classical coarse-grained GNM which was originally modelled in analogy with phantom network theory of rubber elasticity. With this modification, it is now possible to make predictions on the effects of mutation and ligand binding on residue fluctuations and their pair-correlations. We refer to the new model as all-atom GNM. Using examples from published data we show that the all-atom GNM applied to in silico mutated proteins and to their laboratory mutated structures gives similar results. Thus, loss and gain of correlations, which may be related to loss and gain of function, may be studied by using simple in silico mutations only.

Meta-analytic Gaussian Network Aggregation

A growing number of publications focus on estimating Gaussian graphical models (GGM, networks of partial correlation coefficients). At the same time, generalizibility and replicability of these highly parameterized models are debated, and sample sizes typically found in datasets may not be sufficient for estimating the underlying network structure. In addition, while recent work emerged that aims to compare networks based on different samples, these studies do not take potential cross-study heterogeneity into account. To this end, this paper introduces methods for estimating GGMs by aggregating over multiple datasets. We first introduce a general maximum likelihood estimation modeling framework in which all discussed models are embedded. This modeling framework is subsequently used to introduce meta-analytic Gaussian network aggregation (MAGNA). We discuss two variants: fixed-effects MAGNA, in which heterogeneity across studies is not taken into account, and random-effects MAGNA, which models sample correlations and takes heterogeneity into account. We assess the performance of MAGNA in large-scale simulation studies. Finally, we exemplify the method using four datasets of post-traumatic stress disorder (PTSD) symptoms, and summarize findings from a larger meta-analysis of PTSD symptom.

Multi-objective topology optimization of magnetic couplers for wireless power transfer

In this paper, the multi-objective topology optimizations of wireless power transfer (WPT) devices with two different coil geometries are proposed for obtaining the designs with good balance between transfer efficiency and safety. For this purpose, the proposed method adopts the normalized Gaussian network (NGnet) and Non-dominated Sorting Genetic Algorithm II (NSGA-II). In addition, the optimization under the different constraint on ferrite volume is carried out to verify its influence on optimization results. It has been shown that the proposed method successfully provides the Pareto solution to the design problem of the WPT device.

Synchronous and Asynchronous Response in Dynamically Perturbed Proteins

We developed a Dynamic Gaussian Network Model to study perturbation and response in proteins. The model is based on the solution of the Langevin equation in the presence of noise and perturbation. A residue is perturbed periodically with a given frequency and the response of other residues is determined in terms of a storage and loss modulus of the protein. The amount of work lost upon periodic perturbation and the residues that contribute significantly to the lost work is determined. The model shows that perturbation introduces new dynamic correlations into the system with time delayed synchronous and asynchronous components. Residues whose perturbation induces large correlations in the protein and those that do not lead to correlations may be identified. The model is used to investigate the dynamic modulation of nanobodies. Despite its simplicity, the model explains several features of perturbation and response such as the role of loops and linkers in perturbation, dispersion of work of perturbation, and information transfer through preexisting pathways, all shown to be important factors in allostery.