A Simple Charged Three-Body Problem

The dynamics of a simple model of three charged bodies interacting under an inverse square electrostatic force is presented. The model may be viewed as an alternative to the pendulum, the standard model of a periodically forced and damped nonlinear oscillator

Survey of variation in human transcription factors reveals prevalent DNA binding changes

Published in final edited form as: Science. 2016 Mar 25; 351(6280): 1450–1454. Published online 2016 Mar 24. doi: 10.1126/science.aad2257Sequencing of exomes and genomes has revealed abundant genetic variation affecting the coding sequences of human transcription factors (TFs), but the consequences of such variation remain largely unexplored. We developed a computational, structure-based approach to evaluate TF variants for their impact on DNA binding activity and used universal protein-binding microarrays to assay sequence-specific DNA binding activity across 41 reference and 117 variant alleles found in individuals of diverse ancestries and families with Mendelian diseases. We found 77 variants in 28 genes that affect DNA binding affinity or specificity and identified thousands of rare alleles likely to alter the DNA binding activity of human sequence-specific TFs. Our results suggest that most individuals have unique repertoires of TF DNA binding activities, which may contribute to phenotypic variation.National Institutes of Health; NHGRI R01 HG003985; P50 HG004233; A*STAR National Science Scholarship; National Science Foundatio

Determining the Underlying Distributions of Change in Free Energy Change for Pathogenic and Benign Protein Mutations

A mutation in a patient's genome can affect a protein in that patient’s body, resulting in either no change in the health of the patient or a disease experienced by the patient. Assigning terminology, the mutations can therefore be referred to as benign or pathogenic, respectively. When these benign or pathogenic mutations occur, there is an associated change in change in free energy (ΔΔG) when the protein folds, which essentially means the act of the protein folding can become more or less stabilizing. The questions we were interested in are the following: are pathogenic protein mutations stabilizing or destabilizing when compared to benign protein mutations and is there a difference between ΔΔG distributions for benign and pathogenic mutations. In order to analyze the distribution of the ΔΔG’s, we looked at both data from a previous study and data obtained from an extensive literature search for pathogenic mutations found in patients who exhibit a disease. We found that there appears to be a statistical difference between the distribution of benign ΔΔG’s and pathogenic ΔΔG’s when organizing proteins by general function and that pathogenic mutations appear to be more destabilizing than benign mutations. Furthermore, pathogenic distributions appear better described by two gaussians, or a bimodal distribution, whereas benign distributions are adequately described by a single gaussian. Pathogenic distributions also appear to have greater range and variance. While the causes are not yet entirely understood, these results can play a role in understanding what, if any, role ΔΔG has on the pathogenicity of a mutation and could be one day used alongside other methods to generate a model that can help predict the pathogenicity of an arbitrary mutation.http://deepblue.lib.umich.edu/bitstream/2027.42/176952/1/Honors_Capstone_Protein_Mutation_Distributions_Report_-_Jorden_Thompson.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/176952/2/Honors_Capstone_Protein_Mutation_Distributions_poster_-_Jorden_Thompson.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/176952/3/Honors_Capstone_Protein_Mutation_Distributions_methyltransferase_mutations_-_Jorden_Thompson.xlsxhttp://deepblue.lib.umich.edu/bitstream/2027.42/176952/4/Honors_Capstone_Protein_Mutation_Distributions_transporter_mutations_-_Jorden_Thompson.xls

Circuit topology predicts pathogenicity of missense mutations

The contact topology of a protein determines important aspects of the folding process. The topological measure of contact order has been shown to be predictive of the rate of folding. Circuit topology is emerging as another fundamental descriptor of biomolecular structure, with predicted effects on the folding rate. We analyze the residue‐based circuit topological environments of 21 K mutations labeled as pathogenic or benign. Multiple statistical lines of reasoning support the conclusion that the number of contacts in two specific circuit topological arrangements, namely inverse parallel and cross relations, with contacts involving the mutated residue have discriminatory value in determining the pathogenicity of human variants. We investigate how results vary with residue type and according to whether the gene is essential. We further explore the relationship to a number of structural features and find that circuit topology provides nonredundant information on protein structures and pathogenicity of mutations. Results may have implications for the polymer physics of protein folding and suggest that “local” topological information, including residue‐based circuit topology and residue contact order, could be useful in improving state‐of‐the‐art machine learning algorithms for pathogenicity prediction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/174789/1/prot26342.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/174789/2/prot26342-sup-0001-Supinfo1.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/174789/3/prot26342_am.pd

Solvation and Hydrogen Bonding in Alanine- and Glycine-Containing Dipeptides Probed Using Solutionand Solid-State NMR Spectroscopy

The NMR chemical shift is a sensitive reporter of peptide secondary structure and its solvation environment, and it is potentially rich with information about both backbone dihedral angles and hydrogen bonding. We report results from solution- and solid-state 13C and 15N NMR studies of four zwitterionic model dipeptides, l-alanyl-l-alanine, l-alanyl-glycine, glycyl-l-alanine, and glycyl-glycine, in which we attempt to isolate structural and environmental contributions to the chemical shift. We have mapped hydrogen-bonding patterns in the crystalline states of these dipeptides using the published crystal structures and correlated them with 13C and 15N magic angle spinning chemical shift data. To aid in the interpretation of the solvated chemical shifts, we performed ab initio quantum chemical calculations to determine the low-energy conformers and their chemical shifts. Assuming low energy barriers to interconversion between thermally accessible conformers, we compare the Boltzmann-averaged chemical shifts with the experimentally determined solvated-state shifts. The results allow us to correlate the observed differences in chemical shifts between the crystalline and solvated states to changes in conformation and hydrogen bonding that occur upon solvation

Thermal Stabilization of Dihydrofolate Reductase Using Monte Carlo Unfolding Simulations and Its Functional Consequences

<div><p>Design of proteins with desired thermal properties is important for scientific and biotechnological applications. Here we developed a theoretical approach to predict the effect of mutations on protein stability from non-equilibrium unfolding simulations. We establish a relative measure based on apparent simulated melting temperatures that is independent of simulation length and, under certain assumptions, proportional to equilibrium stability, and we justify this theoretical development with extensive simulations and experimental data. Using our new method based on all-atom Monte-Carlo unfolding simulations, we carried out a saturating mutagenesis of Dihydrofolate Reductase (DHFR), a key target of antibiotics and chemotherapeutic drugs. The method predicted more than 500 stabilizing mutations, several of which were selected for detailed computational and experimental analysis. We find a highly significant correlation of <i>r</i> = 0.65–0.68 between predicted and experimentally determined melting temperatures and unfolding denaturant concentrations for WT DHFR and 42 mutants. The correlation between energy of the native state and experimental denaturation temperature was much weaker, indicating the important role of entropy in protein stability. The most stabilizing point mutation was D27F, which is located in the active site of the protein, rendering it inactive. However for the rest of mutations outside of the active site we observed a weak yet statistically significant <i>positive</i> correlation between thermal stability and catalytic activity indicating the lack of a stability-activity tradeoff for DHFR. By combining stabilizing mutations predicted by our method, we created a highly stable catalytically active <i>E</i>. <i>coli</i> DHFR mutant with measured denaturation temperature 7.2°C higher than WT. Prediction results for DHFR and several other proteins indicate that computational approaches based on unfolding simulations are useful as a general technique to discover stabilizing mutations.</p></div

Simulated <i>T</i>_m values, based on RMSD, Total Energy and Contact number.

<p>(A) Scatter plot of <i>T</i>_m (RMSD) vs. <i>T</i>_m (Total energy), with <i>T</i>_m (contact number) represented by color (see color bar to right of plot). The green ball denotes WT and the gold ball denotes the destabilized mutant I155A. The correlation coefficients of simulated <i>T</i>_m between RMSD and total energy, RMSD and Contact number, and Contact number and total energy were 0.68, 0.79 and 0.84, respectively. (B) Histogram of <i>T</i>_m values, determined by averaging the values obtained from RMSD, energy, and contact number. The vertical red line denotes WT <i>T</i>_m.</p

A sample WT DHFR unfolding trajectory at simulation temperature 1.5 (arbitrary simulation units).

<p>In MC simulations, separation of the C-terminal beta hairpin from the rest of the protein (steps 1,000,000 through 1,200,000) is an early event in the unfolding process.</p

Simulation results on non-DHFR proteins.

<p>Error number and error rate describe the number and fraction of mutations not predicted in the correct direction (stabilizing vs. destabilizing)</p><p>Simulation results on non-DHFR proteins.</p