Molecular Mechanics Study of Protein Folding and Protein-Ligand Binding

In this dissertation, molecular dynamics (MD) simulations were applied to study the effect of single point mutations on protein folding free energy and the protein-ligand binding in the bifunctional protein dihydrofolate reductase-thymidylate synthase (TS-DHFR) in plasmodium falciparum (pf). The main goal of current computational studies is to have a deeper understanding of factors related to protein folding stability and protein-ligand binding. Chapter two aims to seek solutions for improving the accuracy of predicting changes of folding free energy upon single point mutations in proteins. While the importance of conformational sampling was adequately addressed, the diverse dielectric properties of proteins were also taken into consideration in this study. Through developing a three-dielectric-constant model and broadening conformational sampling, a method for predicting the effect of point mutations on protein folding free energy is described, and factors of affecting the prediction accuracy are addressed in this chapter. The following two chapters focus on the binding process and domain-domain interactions in the bifunctional protein pfDHFR-TS. This protein usually plays as the target of antimalarial drugs, but the drug resistance in this protein has caused lots of problems. In chapter three, the mechanism of the development of drug resistance was investigated. This study indicated that the accumulation of mutations in pfDHFR caused obvious changes of conformation and interactions among residues in the binding pocket, which further weakened the binding affinity between pfDHFR and the inhibitor drug. Furthermore, the high rigidity and significantly weakened communications among key residues in the protein binding pocket were exhibited in the pfDHFR quadruple mutant. The rigid binding site was associated with the failure of conformational reorganization upon the binding of pyrimethamine in the quadruple mutant. Chapter four investigated the effect of the N-terminus in pfDHFR-TS on enzyme activity and domain-domain communications. This is the first computational study that focuses on the full-length pfDHFR-TS dimer. This study provided computational evidence to support that remote mutations could disturb the interactions and conformations of the binding site through disrupting dynamic motions in pfDHFR-TS

Quantitative model checking of continuous-time Markov chains against timed automata specifications

We study the following problem: given a continuous-time Markov chain (CTMC) C, and a linear real-time property provided as a deterministic timed automaton (DTA) A, what is the probability of the set of paths of C that are\ud accepted by A (C satisfies A)? It is shown that this set of paths is measurable and computing its probability can be reduced to computing the reachability probability in a piecewise deterministic Markov process (PDP). The reachability probability is characterized as the least solution of a system of integral equations and is shown to be approximated by solving a system of partial differential equations. For the special case of single-clock DTA, the system of integral equations can be transformed into a system of linear equations where the coefficients are solutions of ordinary differential equations

On the complexity of computing maximum entropy for Markovian Models

We investigate the complexity of computing entropy of various Markovian models including Markov Chains (MCs), Interval Markov Chains (IMCs) and Markov Decision Processes (MDPs). We consider both entropy and entropy rate for general MCs, and study two algorithmic questions, i.e., entropy approximation problem and entropy threshold problem. The former asks for an approximation of the entropy/entropy rate within a given precision, whereas the latter aims to decide whether they exceed a given threshold. We give polynomial-time algorithms for the approximation problem, and show the threshold problem is in P CH3 (hence in PSPACE) and in P assuming some number-theoretic conjectures. Furthermore, we study both questions for IMCs and MDPs where we aim to maximise the entropy/entropy rate among an infinite family of MCs associated with the given model. We give various conditional decidability results for the threshold problem, and show the approximation problem is solvable in polynomial-time via convex programming

Effects of Different Grazing Intensities on Grasshopper Communities in \u3cem\u3eStipa breviflora\u3c/em\u3e Desert Steppe

As a common method of grassland management, grazing plays an important role in grassland conservation. Grasshoppers and large herbivores are integral parts of grassland biodiversity and food webs. However, to some extent there is still room for further research on how grasshoppers cope with grazing by large herbivores. A field grazing experiment in Stipa breviflora desert steppe in Inner Mongolia, China to investigate the effects of sheep grazing intensity on the abundance and richness of locust population and community. The grazing experiment started in 2004, and the grasshopper population and community were investigated in 2021. The results showed that: Grazing results in the change of dominant species of grasshopper in desert steppe from the C.abbreviatus to the O.asiaticus. Grazing intensity increases the abundance of dominant species, thus increasing the risk of grasshopper outbreaks. Our results suggest that light grazing by sheep is a beneficial management practice to maintain locust species diversity, but at the same time keep the abundance lo

RMSE-ELM: Recursive Model based Selective Ensemble of Extreme Learning Machines for Robustness Improvement

Extreme learning machine (ELM) as an emerging branch of shallow networks has shown its excellent generalization and fast learning speed. However, for blended data, the robustness of ELM is weak because its weights and biases of hidden nodes are set randomly. Moreover, the noisy data exert a negative effect. To solve this problem, a new framework called RMSE-ELM is proposed in this paper. It is a two-layer recursive model. In the first layer, the framework trains lots of ELMs in different groups concurrently, then employs selective ensemble to pick out an optimal set of ELMs in each group, which can be merged into a large group of ELMs called candidate pool. In the second layer, selective ensemble is recursively used on candidate pool to acquire the final ensemble. In the experiments, we apply UCI blended datasets to confirm the robustness of our new approach in two key aspects (mean square error and standard deviation). The space complexity of our method is increased to some degree, but the results have shown that RMSE-ELM significantly improves robustness with slightly computational time compared with representative methods (ELM, OP-ELM, GASEN-ELM, GASEN-BP and E-GASEN). It becomes a potential framework to solve robustness issue of ELM for high-dimensional blended data in the future.Comment: Accepted for publication in Mathematical Problems in Engineering, 09/22/201

Two Kinds Hybrid Power Mean Involving Two-Term Exponential Sums and Dedekind Sums

The main purpose of this article is using the analytic mathods and the quadratic residual transformation technique, and properties of Dedekind sums to study the calculating problem of two kinds hybrid power mean involving the two-term exponential sums and Dedekind sums, and give two asymptotic formulas for it. This work is a generalization for existing conclusions