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The topology of biological polymers such as proteins and nucleic acids is an important aspect of their 3D structure. Recently, two applications of topology to molecular chains have emerged as important theoretical developments that are beginning to find utility in heteropolymer characterization and design: namely, circuit topology (CT) and knot theory. Here, we review the application of these two theories to protein, RNA, and DNA/genome structure, focusing on connections to conventional 3D structural information and relevance to function and highlighting recent experimental findings. We conclude with a discussion of recent applications to molecular origami and engineering.

Sequencing 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 Human Genome Research Institute (U.S.) (Grant R01 HG003985)

Automated audio processing systems, such as the Language Environment Analysis (LENA) system, are useful tools for understanding developmental language behaviors for clinical and basic research purposes. However, it is still unclear how accurate they may be in comparison to the traditional gold standard of evaluation by trained human listeners. In our study, human coders identified starts and ends of communicative vocalizations of children and adults from sampled audio in day-long LENA recordings of 23 families with a child with variable hearing status; accuracy of LENA was then determined for each recording by comparing LENA and human-derived labels for 100-ms frames of sampled audio. Preliminary analysis suggests that LENA accurately identified communicative vocalizations of the target child wearing the device as being produced by that target child 65% of the time (35% error); accuracy ranged from 49%—79% across recordings. When any child vocalization was correctly identified, LENA accurately distinguished whether this belonged to the target child or another child 75% of the time (25% error); accuracy, however, ranged from 7%—96%. These accuracy levels suggest caution is needed in applying popular speech processing systems like LENA to clinical and scientific questions in absence of additional validation measures.

Considerable mechanistic insight has been gained into amyloid aggregation; however, a large class of non-amyloid protein aggregates are considered 'amorphous,' and in most cases little is known about their mechanisms. Amorphous aggregation of ��-crystallins in the eye lens causes a widespread disease of aging, cataract. We combined simulations and experiments to study the mechanism of aggregation of two ��D-crystallin mutants, W42R and W42Q - the former a congenital cataract mutation, and the latter a mimic of age-related oxidative damage. We found that formation of an internal disulfide was necessary and sufficient for aggregation under physiological conditions. Two-chain all-atom simulations predicted that one non-native disulfide in particular, between Cys32 and Cys41, was likely to stabilize an unfolding intermediate prone to intermolecular interactions. Mass spectrometry and mutagenesis experiments confirmed the presence of this bond in the aggregates and its necessity for oxidative aggregation under physiological conditions in vitro. Mining the simulation data linked formation of this disulfide to extrusion of the N-terminal \b{eta}-hairpin and rearrangement of the native \b{eta}-sheet topology. Specific binding between the extruded hairpin and a distal \b{eta}-sheet, in an intermolecular chain reaction similar to domain swapping, is the most probable mechanism of aggregate propagation., *equal contribution; {\dag}corresponding authors

Domain swapping in proteins is an important mechanism of functional and structural innovation. However, despite its ubiquity and importance, the physical mechanisms that lead to domain swapping are poorly understood. Here, we present a simple two-dimensional coarse-grained model of protein domain swapping in the cytoplasm. In our model, two-domain proteins partially unfold and diffuse in continuous space. Monte Carlo multiprotein simulations of the model reveal that domain swapping occurs at intermediate temperatures, whereas folded dimers and folded monomers prevail at low temperatures, and partially unfolded monomers predominate at high temperatures. We use a simplified amino acid alphabet consisting of four residue types, and find that the oligomeric state at a given temperature depends on the sequence of the protein. We also show that hinge strain between domains can promote domain swapping, consistent with experimental observations for real proteins. Domain swapping depends nonmonotonically on the protein concentration, with domain-swapped dimers occurring at intermediate concentrations and nonspecific interactions between partially unfolded proteins occurring at high concentrations. For folded proteins, we recover the result obtained in three-dimensional lattice simulations, i.e., that functional dimerization is most prevalent at intermediate temperatures and nonspecific interactions increase at low temperatures.

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 r = 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 positive 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 E. coli 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., Author Summary All-atom molecular simulations have provided valuable insight into the workings of molecular machines and the folding and unfolding of proteins. However, commonly employed molecular dynamics simulations suffer from a limitation in accessible time scale, making it difficult to model large-scale unfolding events in a realistic amount of simulation time without employing unrealistically high temperatures. Here, we describe a rapid all-atom Monte Carlo simulation approach to simulate unfolding of the essential bacterial enzyme Dihydrofolate Reductase (DHFR) and all possible single point-mutants. We use these simulations to predict which mutants will be more thermodynamically stable (i.e., reside more often in the native folded state vs. the unfolded state) than the wild-type protein, and we confirm our predictions experimentally, creating several highly stable and catalytically active mutants. Thermally stable active engineered proteins can be used as a starting point in directed evolution experiments to evolve new functions on the background of this additional “reservoir of stability.” The stabilized enzyme may be able to accumulate a greater number of destabilizing yet functionally important mutations before unfolding, protease digestion, and aggregation abolish its activity.

Considerable mechanistic insight has been gained into amyloid aggregation; however, a large class of non-amyloid protein aggregates are considered 'amorphous,' and in most cases little is known about their mechanisms. Amorphous aggregation of {\gamma}-crystallins in the eye lens causes a widespread disease of aging, cataract. We combined simulations and experiments to study the mechanism of aggregation of two {\gamma}D-crystallin mutants, W42R and W42Q - the former a congenital cataract mutation, and the latter a mimic of age-related oxidative damage. We found that formation of an internal disulfide was necessary and sufficient for aggregation under physiological conditions. Two-chain all-atom simulations predicted that one non-native disulfide in particular, between Cys32 and Cys41, was likely to stabilize an unfolding intermediate prone to intermolecular interactions. Mass spectrometry and mutagenesis experiments confirmed the presence of this bond in the aggregates and its necessity for oxidative aggregation under physiological conditions in vitro. Mining the simulation data linked formation of this disulfide to extrusion of the N-terminal \b{eta}-hairpin and rearrangement of the native \b{eta}-sheet topology. Specific binding between the extruded hairpin and a distal \b{eta}-sheet, in an intermolecular chain reaction similar to domain swapping, is the most probable mechanism of aggregate propagation., Comment: *equal contribution; {\dag}corresponding authors

Surface immobilized biomolecular probes are used in many areas of biomedical research, such as genomics, proteomics, immunology, and pathology. Although the structural conformations of small DNA and peptide molecules in free solution are well studied both theoretically and experimentally, the conformation of small biomolecules bound on surfaces, especially under the influence of external electric fields, is poorly understood. Using a combination of molecular dynamics simulation and surface-enhanced Raman spectroscopy, we study the external electric field-induced conformational change of dodecapeptide probes tethered to a nanostructured metallic surface. Surface-tethered peptides with and without phosphorylated tyrosine residues are compared to show that peptide conformational change under electric field is sensitive to biochemical modification. Our study proposes a highly sensitive in vitro nanoscale electro-optical detection and manipulation method for biomolecule conformation and charge at bio-nano interfaces.

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 (13)C and (15)N 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 (13)C and (15)N 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.