Proteinlerde pertürbasyon-tepki ve gürültü dinamiği ve biyomoleküler simülasyonlarda temsil öğrenme

Molecular Dynamics simulations, the standard tool for analyzing biomolecules, provide detailed and accurate characterizations but at the expense of tremendous computational cost. A variety of more efficient computational methods have been developed in order to enable the understanding of practical systems of interest. This thesis contributes to this body of work by adapting and repurposing tools from electrical circuit analysis for analyzing the perturbation-response and noise dynamics of proteins, and by applying dimensionality reduction techniques from machine learning for identifying and extracting the essential features of biomolecules from large amounts of simulation data. The interactions of proteins with ligands are determined by their dynamic characteristics as opposed to only static, time-invariant processes. Inspired by a frequency domain analysis technique from electronic circuit design, we propose a novel computational technique that can be used to analyze small scale functional protein motions as well as interactions with ligands directly in the frequency domain. It can be considered as a generalization of previously proposed static perturbation-response methods, where the frequency of the perturbation becomes the key. We show that the frequency of the perturbation may be an important factor in protein dynamics. Furthermore, we introduce several novel frequency dependent metrics in order to characterize response behavior. Allostery-a phenomenon in which the binding of a ligand induces alterations in the activity of remote functional sites-can be conceptually viewed as point-to-point telecommunication in a networked communication medium, where a signal (ligand) arriving at the input (binding site) propagates through the network (interconnected and interacting atoms) to reach the output (remote functional site). The reliable transmission of the signal to distal points occurs despite all the disturbances (noise) affecting the protein. Based on this point of view, we propose a computational frequency-domain framework to characterize the displacements and the fluctuations in a region within the protein, originating from the ligand excitation at the binding site and noise, respectively. We characterize the displacements in the presence of the ligand, and the fluctuations in its absence. In the former case, the effect of the ligand is modeled as an external dynamic oscillatory force excitation, whereas in the latter, the sole source of fluctuations is the noise arising from the interactions with the surrounding medium that is further shaped by the internal protein network dynamics. We introduce the excitation frequency as a key factor in a Signal-to-Noise ratio (SNR) based analysis, where SNR is defined as the ratio of the displacements stemming from only the ligand to the fluctuations due to noise alone. We then employ an information-theoretic (communication) channel capacity analysis that extends the SNR based characterization by providing a route for discovering new allosteric regions. Extracting insight from the enormous quantity of data generated from molecular simulations requires the identification of a small number of collective variables whose corresponding low-dimensional free-energy landscape retains the essential features of the underlying system. Data-driven techniques provide a systematic route to constructing this landscape, without the need for extensive a priori intuition into the relevant driving forces. In particular, autoencoders are powerful tools for dimensionality reduction, as they naturally force an information bottleneck and, thereby, a low-dimensional embedding of the essential features. While variational autoencoders ensure continuity of the embedding by assuming a unimodal Gaussian prior, this is at odds with the multi-basin free-energy landscapes that typically arise from the identification of meaningful collective variables. In this work, we incorporate this physical intuition into the prior by employing a Gaussian mixture variational autoencoder (GMVAE), which encourages the separation of metastable states within the embedding. The GMVAE performs dimensionality reduction and clustering within a single unified framework, and is capable of identifying the inherent dimensionality of the input data, in terms of the number of Gaussians required to categorize the data. The resulting embeddings also provide representations for constructing Markov state models, highlighting the transferability of the dimensionality reduction from static equilibrium properties to dynamics.