BIOMOLECULAR FUNCTION FROM STRUCTURAL SNAPSHOTS

Biological molecules can assume a continuous range of conformations during function. Near equilibrium, the Boltzmann relation connects a particular conformation\u27s free energy to the conformation\u27s occupation probability, thus giving rise to one or more energy landscapes. Biomolecular function proceeds along minimum-energy pathways on such landscapes. Consequently, a comprehensive understanding of biomolecular function often involves the determination of the free-energy landscapes and the identification of functionally relevant minimum-energy conformational paths on these landscapes. Specific techniques are necessary to determine continuous conformational spectra and identify functionally relevant conformational trajectories from a collection of raw single-particle snapshots from, e.g. cryogenic electron microscopy (cryo-EM) or X-ray diffraction. To assess the capability of different algorithms to recover conformational landscapes, we:• Measure, compare, and benchmark the performance of four leading data-analytical approaches to determine the accuracy with which energy landscapes are recovered from simulated cryo-EM data. Our simulated data are derived from projection directions along the great circle, emanating from a known energy landscape. • Demonstrate the ability to recover a biomolecule\u27s energy landscapes and functional pathways of biomolecules extracted from collections of cryo-EM snapshots. Structural biology applications in drug discovery and molecular medicine highlight the importance of the free-energy landscapes of the biomolecules more crucial than ever. Recently several data-driven machine learning algorithms have emerged to extract energy landscapes and functionally relevant continuous conformational pathways from single-particle data (Dashti et al., 2014; Dashti et al., 2020; Mashayekhi,et al., 2022). In a benchmarking study, the performance of several advanced data-analytical algorithms was critically assessed (Dsouza et al., 2023). In this dissertation, we have benchmarked the performance of four leading algorithms in extracting energy landscapes and functional pathways from single-particle cryo-EM snapshots. In addition, we have significantly improved the performance of the ManifoldEM algorithm, which has demonstrated the highest performance. Our contributions can be summarized as follows.: • Expert user supervision is required in one of the main steps of the ManifoldEM framework wherein the algorithm needs to propagate the conformational information through all angular space. We have succeeded in introducing an automated approach, which eliminates the need for user involvement. • The quality of the energy landscapes extracted by ManifoldEM from cryo-EM data has been improved, as the accuracy scores demonstrate this improvement. These measures have substantially enhanced ManifoldEM’s ability to recover the conformational motions of biomolecules by extracting the energy landscape from cryo-EM data.In line with the primary goal of our research, we aimed to extend the automated method across the entire angular sphere rather than a great circle. During this endeavor, we encountered challenges, particularly with some projection directions not following the proposed model. Through methodological adjustments and sampling optimization, we improved the projection direction\u27s conformity to the model. However, a small subset of Projection directions (5 %) remained challenging. We also recommended the use of specific methodologies, namely feature extraction and edge detection algorithms, to enhance the precision in quantifying image differentiation, a crucial component of our automated model. we also suggested that integrating different techniques might potentially resolve challenges associated with certain projection directions. We also applied ManifoldEM to experimental cryo-EM images of the SARS-CoV-2 spike protein in complex with the ACE2 receptor. By introducing several improvements, such as the incorporation of an adaptive mask and cosine curve fitting, we enhanced the framework\u27s output quality. This enhancement can be quantified by observing the removal of the artifact from the energy landscape, especially if the post-enhancement landscape differs from the artifact-affected one. These modifications, specifically aimed at addressing challenges from Nonlinear Laplacian Spectral Analysis (NLSA) (Giannakis et al., 2012), are intended for application in upcoming cryo-EM studies utilizing ManifoldEM. In the closing sections of this dissertation, a summary and a projection of future research directions are provided. While initial automated methods have been explored, there remains room for refinement. We have offered numerous methodological suggestions oriented toward addressing solutions to the challenge of conformational information propagation. Key methodologies discussed include Manifold Alignment, Canonical Correlation Analysis, and Multi-View Diffusion Maps. These recommendations are aimed to inform and guide subsequent developments in the ManifoldEM suite

Population analysis of neural data -- developments in statistical methods and related computational models

A key goal of neuroscience is to understand how the remarkable computational abilities of our brain emerge as a result of interconnected neuronal populations. Recently, advances in technologies for recording neural activity have increased the number of simultaneously recorded neurons by orders of magnitude, and these technologies are becoming more widely adopted. At the same time, massive increases in computational power and improved algorithms have enabled advanced statistical analyses of neural population activity and promoted our understanding of population coding. Nevertheless, there are many unanswered emerging questions, when it comes to analyzing and interpreting neural recordings. There are two major parts to this study. First, we consider an issue of increasing importance: that many in vivo recordings are now made by calcium-dependent fluorescent imaging, which only indirectly reports neural activity. We compare measurements of extracellular single units with fluorescence changes extracted from single neurons (often used as a proxy for spike rates), both recorded from cortical neural populations of behaving mice. We perform identical analyses at the single cell level and population level, and compare the results, uncovering a number of differences, or biases. We propose a phenomenological model to transform spike trains into synthetic imaging data and test whether the transformation explains the biases found. We discover that the slow temporal dynamics of calcium imaging obscure rapid changes in neuronal selectivity and disperse dynamic features in time. As a result, spike rate modulation that is locked to temporally localized events can appear as a more sequence-like pattern of activity in the imaging data. In addition, calcium imaging is more sensitive to increases rather than decreases in spike rate, leading to biased estimates of neural selectivity. These biases need to be considered when interpreting calcium imaging data. The second part of this work embarks on a challenging yet fruitful study of latent variable analysis of simultaneously recorded neural activity in a decision-making task. To connect the neural dynamics in different stages of a decision-making task, we developed a time-varying latent dynamics system model that uncovers neural dynamics shared by neurons in a local decision-making circuit. The shared neural activity supports the dynamics of choice generation and memory in a fashion akin to drift diffusion models, and robustly maintains a decision signal in the post-decision period. Importantly, we find that error trials follow similar dynamics to those of correct trials, but their dynamics are separated in shared neural activity space, proving a more correct early decoding estimation of an animal's success or failure at a given trial. Overall, the shared neural activity dynamics can predict multiple measures of behavioral variability including performance, reaction time, and trial correctness, and therefore are a useful summary of the neural representation. Such an approach can be readily applied to study complex dynamics in other neural systems. In summary, this dissertation represents an important step towards developing model-based analysis of neuronal dynamics and understanding population codes in large-scale neural data

Two-Manifold Problems with Applications to Nonlinear System Identification

<p>Recently, there has been much interest in spectral approaches to learning manifolds— so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space, and discuss when two-manifold problems are useful. Finally, we demonstrate that solving a two-manifold problem can aid in learning a nonlinear dynamical system from limited data.</p