Propensity to form amyloid fibrils is encoded as excitations in the free energy landscape of monomeric proteins

Protein aggregation, linked to many of diseases, is initiated when monomers access rogue conformations that are poised to form amyloid fibrils. We show, using simulations of src SH3 domain, that mechanical force enhances the population of the aggregation prone ($N^*$) states, which are rarely populated under force free native conditions, but are encoded in the spectrum of native fluctuations. The folding phase diagrams of SH3 as a function of denaturant concentration ($[C]$), mechanical force ($f$), and temperature exhibit an apparent two-state behavior, without revealing the presence of the elusive $N^*$ states. Interestingly, the phase boundaries separating the folded and unfolded states at all [C] and $f$ fall on a master curve, which can can be quantitatively described using an analogy to superconductors in a magnetic field. The free energy profiles as a function of the molecular extension ($R$), which are accessible in pulling experiments, ($R$), reveal the presence of a native-like $N^*$ with a disordered solvent-exposed amino terminal $\beta$-strand. The structure of the $N^*$ state is identical to that found in Fyn SH3 by NMR dispersion experiments. We show that the time scale for fibril formation can be estimated from the population of the $N^*$ state, determined by the free energy gap separating the native structure and the $N^*$ state, a finding that can be used to assess fibril forming tendencies of proteins. The structures of the $N^*$ state are used to show that oligomer formation and likely route to fibrils occur by a domain-swap mechanism in SH3 domain.Comment: 12 pages, 8 figures, 9 supplementary figures (on 5 more pages), 2 supplementary movies (on youtube

Unraveling the complexity of biological processes from protein native dynamics to cell motility

This dissertation consists of two major parts. Both are dedicated to studying biological molecular processes with computer simulations, but differ in the scale of the studied processes. In one project we investigated the dynamics of cellular organelles involved in cell motility -- the filopodia. The other project is zooming in to the scale of single molecule, elucidating the organization of protein molecule native state. Some motile cells use special fingerlike probes of their environment for guiding their motion called filopodia. They are bundles of parallel actin filaments protruding from the cell body and enveloped by cell's membrane. They are highly dynamic, constantly growing an retracting, randomly, or in response to the change in the environment. These dynamics are governed by the cell's regulatory proteins and by external chemical cues or mechanical obstacles. The previous models predicted that a filopodium grows to a stationary length of about 1 micron with miniscule fluctuations around. (i) We found that capping proteins (they attach to the barbed ends of actin filaments and stop polymerization) can induce macroscopic oscillation of filopodial length -- the growth-retraction cycles. The retraction can be complete. This is the first model that predicts finite lifetimes for filopodia. The lifetimes are consistent with experimental observations. (ii) In the model, however, the maximal filopodial lengths of several microns are still limited by the diffusional transport of actin monomers to the filopodial tip and are far below experimentally observed lengths of up to 100 microns. Assuming the obvious solution for the problem of slow transport in cell, the molecular motors, that are known to be present inside filopodia, we found that a naive addition of motors does not increase the lengths much. In order to have an efficient active transport, two rules must be observed: the motors should not sequester the cargo and the rails for motors should be kept from being clogged by motors. Protein Ena/VASP that is known to be actively transported to the filopodial tip by molecular motors may be a way to fight sequestration. On the scale of a single macromolecule we studied the organization of protein native state. It is not a single structure, but an ensemble of constantly interconverting conformations. It is essential for a deep insight into protein functioning to know thermodynamics of these substates and dynamical regime of their exploration. (i) In all-atom MD simulations we constructed a 2D free energy surface for a protein Trp-cage and using the FES for Brownian dynamics investigated the nature of dynamical behavior of Trp-cage in its native state. We found that the dynamical regime is borderline between liquid and supercooled liquid. (ii) We developed a general technique for calculating free energy difference between two polymer conformations in explicit solvent simulations and used the Trp-cage 2D FES for testing of this technique, revealing remarkable accuracy and computation efficiency

High Resolution Approach to the Native State Ensemble Kinetics and Thermodynamics

Many biologically interesting functions such as allosteric switching or protein-ligand binding are determined by the kinetics and mechanisms of transitions between various conformational substates of the native basin of globular proteins. To advance our understanding of these processes, we constructed a two-dimensional free energy surface (FES) of the native basin of a small globular protein, Trp-cage. The corresponding order parameters were defined using two native substructures of Trp-cage. These calculations were based on extensive explicit water all-atom molecular dynamics simulations. Using the obtained two-dimensional FES, we studied the transition kinetics between two Trp-cage conformations, finding that switching process shows a borderline behavior between diffusive and weakly-activated dynamics. The transition is well-characterized kinetically as a biexponential process. We also introduced a new one-dimensional reaction coordinate for the conformational transition, finding reasonable qualitative agreement with the two-dimensional kinetics results. We investigated the distribution of all the 38 native nuclear magnetic resonance structures on the obtained FES, analyzing interactions that stabilize specific low-energy conformations. Finally, we constructed a FES for the same system but with simple dielectric model of water instead of explicit water, finding that the results were surprisingly similar in a small region centered on the native conformations. The dissimilarities between the explicit and implicit model on the larger-scale point to the important role of water in mediating interactions between amino acid residues

Bayesian and Frequentist Semantics for Common Variations of Differential Privacy: Applications to the 2020 Census

The purpose of this paper is to guide interpretation of the semantic privacy guarantees for some of the major variations of differential privacy, which include pure, approximate, R\'enyi, zero-concentrated, and $f$ differential privacy. We interpret privacy-loss accounting parameters, frequentist semantics, and Bayesian semantics (including new results). The driving application is the interpretation of the confidentiality protections for the 2020 Census Public Law 94-171 Redistricting Data Summary File released August 12, 2021, which, for the first time, were produced with formal privacy guarantees

IMPROVEMENT OF WORKING CONDITIONS IN RURAL AREAS THROUGH THE FORMATION OF INFRASTRUCTURE FOR AGRICULTURAL SERVICES

Relevance of the study. The infrastructure of rural settlements has a significant impact on the quality of life of the rural population and, as a result, on the development of the infrastructure of the agro-industrial complex. Objective. The purpose of this study is to develop scientific and methodological provisions for improving the infrastructure of agricultural services. Materials and methods. The research methodology includes bibliographic analysis, as well as analysis of statistical data. To identify the most significant factors for ordinary agricultural workers, the method of expert assessments is used. Results. Studies have been conducted on the agro-industrial complex organizations of the Altai Territory. The main part of the article identifies external and internal factors that determine the quality of working conditions in agriculture. Using the method of expert assessments, the most significant factors for ordinary agricultural workers were identified. In order to introduce digitalization in the agro-industrial complex, software and hardware unmanned complexes designed to perform certain functions in crop production are considered. Digital solutions designed to perform the functions of interaction with suppliers, consumers and transportation of agricultural products are described. The issues of environmental safety of workplaces in the agro-industrial complex are considered. Conclusion. It is revealed that in order to effectively develop the infrastructure of rural settlements as a tool to improve the quality of life of the rural population, it is necessary to abandon the policy of maximum coverage in favor of a policy of concentrating efforts on a certain territory on the basis of a comprehensive plan covering all spheres of society and involving sectoral authorities in its implementation within a single project