Potential immunosuppressive clonal hematopoietic mutations in tumor infiltrating immune cells in breast invasive carcinoma.

A hallmark of cancer is a tumor cell's ability to evade immune destruction. Somatic mutations in tumor cells that prevent immune destruction have been extensively studied. However, somatic mutations in tumor infiltrating immune (TII) cells, to our knowledge, have not been previously studied. Understandably so since normal hematopoiesis prevents the accumulation of somatic mutations in immune cells. However, clonal hematopoiesis does result in the accumulation of somatic mutations in immune cells. These mutations cannot "drive" tumor growth, however, they may "facilitate" it by inhibiting an effective anti-tumor immune response. To identify potential immunosuppressive clonal hematopoietic (CH) mutations in TII cells, we analyzed exome and RNA sequencing data from matched tumor and normal blood samples, and single-cell RNA sequencing data, from breast cancer patients. We selected mutations that were somatic, present in TII cells, clonally expanded, potentially pathogenic, expressed in TII cells, unlikely to be a passenger mutation, and in immune response associated genes. We identified eight potential immunosuppressive CH mutations in TII cells. This work is a first step towards determining if immunosuppressive CH mutations in TII cells can affect the progression of solid tumors. Subsequent experimental confirmation could represent a new paradigm in the etiology of cancer.

Biophysical insights into OR2T7: Investigation of a potential prognostic marker for glioblastoma.

Glioblastoma multiforme (GBM) is the most aggressive and prevalent form of brain cancer, with an expected survival of 12-15 months following diagnosis. GBM affects the glial cells of the central nervous system, which impairs regular brain function including memory, hearing, and vision. GBM has virtually no long-term survival even with treatment, requiring novel strategies to understand disease progression. Here, we identified a somatic mutation in OR2T7, a G-protein-coupled receptor (GPCR), that correlates with reduced progression-free survival for glioblastoma (log rank p-value = 0.05), suggesting a possible role in tumor progression. The mutation, D125V, occurred in 10% of 396 glioblastoma samples in The Cancer Genome Atlas, but not in any of the 2504 DNA sequences in the 1000 Genomes Project, suggesting that the mutation may have a deleterious functional effect. In addition, transcriptome analysis showed that the p38α mitogen-activated protein kinase (MAPK), c-Fos, c-Jun, and JunB proto-oncogenes, and putative tumor suppressors RhoB and caspase-14 were underexpressed in glioblastoma samples with the D125V mutation (false discovery rate < 0.05). Molecular modeling and molecular dynamics simulations have provided preliminary structural insight and indicate a dynamic helical movement network that is influenced by the membrane-embedded, cytofacial-facing residue 125, demonstrating a possible obstruction of G-protein binding on the cytofacial exposed region. We show that the mutation impacts the "open" GPCR conformation, potentially affecting Gα-subunit binding and associated downstream activity. Overall, our findings suggest that the Val125 mutation in OR2T7 could affect glioblastoma progression by downregulating GPCR-p38 MAPK tumor-suppression pathways and impacting the biophysical characteristics of the structure that facilitates Gα-subunit binding. This study provides the theoretical basis for further experimental investigation required to confirm that the D125V mutation in OR2T7 is not a passenger mutation. With validation, the aforementioned mutation could represent an important prognostic marker and a potential therapeutic target for glioblastoma.

Cranial manipulation affects cholinergic pathway gene expression in aged rats.

CONTEXT: Age-dependent dementia is a devastating disorder afflicting a growing older population. Although pharmacological agents improve symptoms of dementia, age-related comorbidities combined with adverse effects often outweigh their clinical benefits. Therefore, nonpharmacological therapies are being investigated as an alternative. In a previous pilot study, aged rats demonstrated improved spatial memory after osteopathic cranial manipulative medicine (OCMM) treatment. OBJECTIVES: In this continuation of the pilot study, we examine the effect of OCMM on gene expression to elicit possible explanations for the improvement in spatial memory. METHODS: OCMM was performed on six of 12 elderly rats every day for 7 days. Rats were then euthanized to obtain the brain tissue, from which RNA samples were extracted. RNA from three treated and three controls were of sufficient quality for sequencing. These samples were sequenced utilizing next-generation sequencing from Illumina NextSeq. The Cufflinks software suite was utilized to assemble transcriptomes and quantify the RNA expression level for each sample. RESULTS: Transcriptome analysis revealed that OCMM significantly affected the expression of 36 genes in the neuronal pathway (false discovery rate [FDR] <0.004). The top five neuronal genes with the largest-fold change were part of the cholinergic neurotransmission mechanism, which is known to affect cognitive function. In addition, 39.9% of 426 significant differentially expressed (SDE) genes (FDR<0.004) have been previously implicated in neurological disorders. Overall, changes in SDE genes combined with their role in central nervous system signaling pathways suggest a connection to previously reported OCMM-induced behavioral and biochemical changes in aged rats. CONCLUSIONS: Results from this pilot study provide sufficient evidence to support a more extensive study with a larger sample size. Further investigation in this direction will provide a better understanding of the molecular mechanisms of OCMM and its potential in clinical applications. With clinical validation, OCMM could represent a much-needed low-risk adjunct treatment for age-related dementia including Alzheimer's disease.

Ethnically biased microsatellites contribute to differential gene expression and glutathione metabolism in Africans and Europeans.

Approximately three percent of the human genome is occupied by microsatellites: a type of short tandem repeat (STR). Microsatellites have well established effects on (a) the genetic structure of diverse human populations and (b) expression of nearby genes. These lines of inquiry have uncovered 3,984 ethnically biased microsatellite loci (EBML) and 28,375 expression STRs (eSTRs), respectively. We hypothesize that a combination of EBML, eSTRs, and gene expression data (RNA-seq) can be used to show that microsatellites contribute to differential gene expression and phenotype in human populations. In fact, our previous study demonstrated a degree of mutual overlap between EBML and eSTRs but fell short of quantifying effects on gene expression. The present work aims to narrow the gap. First, we identify 313 overlapping EBML/eSTRs and recapitulate their mutual overlap. The 313 EBML/eSTRs are then characterized across ethnicity and tissue type. We use RNA-seq data to pursue validation of 49 regions that affect whole blood gene expression; 32 out of 54 affected genes are differentially expressed in Africans and Europeans. We quantify the relative contribution of these 32 genes to differential expression; fold change tends to be less than other differentially expressed genes. Repeat length correlates with expression for 15 of the 32 genes; two are conspicuously involved in glutathione metabolism. Finally, we repurpose a mathematical model of glutathione metabolism to investigate how a single polymorphic microsatellite affects phenotype. We conclude with a testable prediction that microsatellite polymorphisms affect GPX7 expression and oxidative stress in Africans and Europeans.

DNA sequencing of anatomy lab cadavers to provide hands-on precision medicine introduction to medical students.

BACKGROUND: Medical treatment informed by Precision Medicine is becoming a standard practice for many diseases, and patients are curious about the consequences of genomic variants in their genome. However, most medical students' understanding of Precision Medicine derives from classroom lectures. This format does little to foster an understanding for the potential and limitations of Precision Medicine. To close this gap, we implemented a hands-on Precision Medicine training program utilizing exome sequencing to prepare a clinical genetic report of cadavers studied in the anatomy lab. The program reinforces Precision Medicine related learning objectives for the Genetics curriculum. METHODS: Pre-embalmed blood samples and embalmed tissue were obtained from cadavers (donors) used in the anatomy lab. DNA was isolated and sequenced and illustrative genetic reports provided to the students. The reports were used to facilitate discussion with students on the implications of pathogenic genomic variants and the potential correlation of these variants in each "donor" with any anatomical anomalies identified during cadaver dissection. RESULTS: In 75% of cases, analysis of whole exome sequencing data identified a variant associated with increased risk for a disease/abnormal condition noted in the donor's cause of death or in the students' anatomical findings. This provided students with real-world examples of the potential relationship between genomic variants and disease risk. Our students also noted that diseases associated with 92% of the pathogenic variants identified were not related to the anatomical findings, demonstrating the limitations of Precision Medicine. CONCLUSION: With this study, we have established protocols and classroom procedures incorporating hands-on Precision Medicine training in the medical student curriculum and a template for other medical educators interested in enhancing their Precision Medicine training program. The program engaged students in discovering variants that were associated with the pathophysiology of the cadaver they were studying, which led to more exposure and understanding of the potential risks and benefits of genomic medicine.

Crossing complexity of space-filling curves reveals entanglement of S-phase DNA.

Space-filling curves have been used for decades to study the folding principles of globular proteins, compact polymers, and chromatin. Formally, space-filling curves trace a single circuit through a set of points (x,y,z); informally, they correspond to a polymer melt. Although not quite a melt, the folding principles of Human chromatin are likened to the Hilbert curve: a type of space-filling curve. Hilbert-like curves in general make biologically compelling models of chromatin; in particular, they lack knots which facilitates chromatin folding, unfolding, and easy access to genes. Knot complexity has been intensely studied with the aid of Alexander polynomials; however, the approach does not generalize well to cases of more than one chromosome. Crossing complexity is an understudied alternative better suited for quantifying entanglement between chromosomes. Do Hilbert-like configurations limit crossing complexity between chromosomes? How does crossing complexity for Hilbert-like configurations compare to equilibrium configurations? To address these questions, we extend the Mansfield algorithm to enable sampling of Hilbert-like space filling curves on a simple cubic lattice. We use the extended algorithm to generate equilibrium, intermediate, and Hilbert-like configurational ensembles and compute crossing complexity between curves (chromosomes) in each configurational snapshot. Our main results are twofold: (a) Hilbert-like configurations limit entanglement between chromosomes and (b) Hilbert-like configurations do not limit entanglement in a model of S-phase DNA. Our second result is particularly surprising yet easily rationalized with a geometric argument. We explore ergodicity of the extended algorithm and discuss our results in the context of more sophisticated models of chromatin.

Identifying multi-hit carcinogenic gene combinations: Scaling up a weighted set cover algorithm using compressed binary matrix representation on a GPU.

Despite decades of research, effective treatments for most cancers remain elusive. One reason is that different instances of cancer result from different combinations of multiple genetic mutations (hits). Therefore, treatments that may be effective in some cases are not effective in others. We previously developed an algorithm for identifying combinations of carcinogenic genes with mutations (multi-hit combinations), which could suggest a likely cause for individual instances of cancer. Most cancers are estimated to require three or more hits. However, the computational complexity of the algorithm scales exponentially with the number of hits, making it impractical for identifying combinations of more than two hits. To identify combinations of greater than two hits, we used a compressed binary matrix representation, and optimized the algorithm for parallel execution on an NVIDIA V100 graphics processing unit (GPU). With these enhancements, the optimized GPU implementation was on average an estimated 12,144 times faster than the original integer matrix based CPU implementation, for the 3-hit algorithm, allowing us to identify 3-hit combinations. The 3-hit combinations identified using a training set were able to differentiate between tumor and normal samples in a separate test set with 90% overall sensitivity and 93% overall specificity. We illustrate how the distribution of mutations in tumor and normal samples in the multi-hit gene combinations can suggest potential driver mutations for further investigation. With experimental validation, these combinations may provide insight into the etiology of cancer and a rational basis for targeted combination therapy.

Abundance of ethnically biased microsatellites in human gene regions.

Microsatellites-a type of short tandem repeat (STR)-have been used for decades as putatively neutral markers to study the genetic structure of diverse human populations. However, recent studies have demonstrated that some microsatellites contribute to gene expression, cis heritability, and phenotype. As a corollary, some microsatellites may contribute to differential gene expression and RNA/protein structure stability in distinct human populations. To test this hypothesis, we investigate genotype frequencies, functional relevance, and adaptive potential of microsatellites in five super-populations (ethnicities) drawn from the 1000 Genomes Project. We discover 3,984 ethnically-biased microsatellite loci (EBML); for each EBML at least one ethnicity has genotype frequencies statistically different from the remaining four. South Asian, East Asian, European, and American EBML show significant overlap; on the contrary, the set of African EBML is mostly unique. We cross-reference the 3,984 EBML with 2,060 previously identified expression STRs (eSTRs); repeats known to affect gene expression (64 total) are over-represented. The most significant pathway enrichments are those associated with the matrisome: a broad collection of genes encoding the extracellular matrix and its associated proteins. At least 14 of the EBML have established links to human disease. Analysis of the 3,984 EBML with respect to known selective sweep regions in the genome shows that allelic variation in some of them is likely associated with adaptive evolution.

Author Correction: Differentiating between cancer and normal tissue samples using multi-hit combinations of genetic mutations.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Estimating the number of genetic mutations (hits) required for carcinogenesis based on the distribution of somatic mutations.

Individual instances of cancer are primarily a result of a combination of a small number of genetic mutations (hits). Knowing the number of such mutations is a prerequisite for identifying specific combinations of carcinogenic mutations and understanding the etiology of cancer. We present a mathematical model for estimating the number of hits based on the distribution of somatic mutations. The model is fundamentally different from previous approaches, which are based on cancer incidence by age. Our somatic mutation based model is likely to be more robust than age-based models since it does not require knowing or accounting for the highly variable mutation rate, which can vary by over three orders of magnitude. In fact, we find that the number of somatic mutations at diagnosis is weakly correlated with age at cancer diagnosis, most likely due to the extreme variability in mutation rates between individuals. Comparing the distribution of somatic mutations predicted by our model to the actual distribution from 6904 tumor samples we estimate the number of hits required for carcinogenesis for 17 cancer types. We find that different cancer types exhibit distinct somatic mutational profiles corresponding to different numbers of hits. Why might different cancer types require different numbers of hits for carcinogenesis? The answer may provide insight into the unique etiology of different cancer types.

Differentiating between cancer and normal tissue samples using multi-hit combinations of genetic mutations.

Cancer is known to result from a combination of a small number of genetic defects. However, the specific combinations of mutations responsible for the vast majority of cancers have not been identified. Current computational approaches focus on identifying driver genes and mutations. Although individually these mutations can increase the risk of cancer they do not result in cancer without additional mutations. We present a fundamentally different approach for identifying the cause of individual instances of cancer: we search for combinations of genes with carcinogenic mutations (multi-hit combinations) instead of individual driver genes or mutations. We developed an algorithm that identified a set of multi-hit combinations that differentiate between tumor and normal tissue samples with 91% sensitivity (95% Confidence Interval (CI) = 89-92%) and 93% specificity (95% CI = 91-94%) on average for seventeen cancer types. We then present an approach based on mutational profile that can be used to distinguish between driver and passenger mutations within these genes. These combinations, with experimental validation, can aid in better diagnosis, provide insights into the etiology of cancer, and provide a rational basis for designing targeted combination therapies.

CAGm: a repository of germline microsatellite variations in the 1000 genomes project.

The human genome harbors an abundance of repetitive DNA; however, its function continues to be debated. Microsatellites-a class of short tandem repeat-are established as an important source of genetic variation. Array length variants are common among microsatellites and affect gene expression; but, efforts to understand the role and diversity of microsatellite variation has been hampered by several challenges. Without adequate depth, both long-read and short-read sequencing may not detect the variants present in a sample; additionally, large sample sizes are needed to reveal the degree of population-level polymorphism. To address these challenges we present the Comparative Analysis of Germline Microsatellites (CAGm): a database of germline microsatellites from 2529 individuals in the 1000 genomes project. A key novelty of CAGm is the ability to aggregate microsatellite variation by population, ethnicity (super population) and gender. The database provides advanced searching for microsatellites embedded in genes and functional elements. All data can be downloaded as Microsoft Excel spreadsheets. Two use-case scenarios are presented to demonstrate its utility: a mononucleotide (A) microsatellite at the BAT-26 locus and a dinucleotide (CA) microsatellite in the coding region of FGFRL1. CAGm is freely available at http://www.cagmdb.org/.

Why Computed Protein Folding Landscapes Are Sensitive to the Water Model.

We investigate the effect of solvent models on the computed thermodynamics of protein folding. Atomistic folding simulations of a fast-folding mini-protein, CLN025, were employed to compare two commonly used explicit solvent water models, TIP3P and TIP4P/Ew, and one implicit solvent (AMBER generalized Born) model. Although all three solvent models correctly identify the same native folded state (RMSD = 1.5 ± 0.1 Å relative to the experimental structure), the corresponding free energy landscapes vary drastically between water models: almost an order-of-magnitude difference is seen in the predicted fraction of the unfolded state between the two explicit solvent models, with even larger differences between the implicit and the explicit models. Quantitative arguments are presented for why the sensitivity is expected to hold for other proteins, as well as for other conformational transitions involving large changes in solvent exposed areas such as protein-ligand binding. Comparing protein-solvent and solvent-solvent contributions to the folding energy between different water models, water-water electrostatic interactions are identified as the largest contributor to the differences in the predicted folding energy, which helps explain the strong sensitivity of the folding landscape to subtle details of the water model. For the two explicit solvent models, differences in water model parameters also result in the average number of water molecules surrounding the protein being noticeably different. Water models that poorly reproduce certain bulk properties of liquid water such as self-diffusion are likely to misrepresent water-water interactions; we argue that within a pairwise additive energy function this error cannot, in general, be compensated by an adjustment to the solute-solute and solute-solvent parts of the energy.

Modulation of nucleosomal DNA accessibility via charge-altering post-translational modifications in histone core.

BACKGROUND: Controlled modulation of nucleosomal DNA accessibility via post-translational modifications (PTM) is a critical component to many cellular functions. Charge-altering PTMs in the globular histone core-including acetylation, phosphorylation, crotonylation, propionylation, butyrylation, formylation, and citrullination-can alter the strong electrostatic interactions between the oppositely charged nucleosomal DNA and the histone proteins and thus modulate accessibility of the nucleosomal DNA, affecting processes that depend on access to the genetic information, such as transcription. However, direct experimental investigation of the effects of these PTMs is very difficult. Theoretical models can rationalize existing observations, suggest working hypotheses for future experiments, and provide a unifying framework for connecting PTMs with the observed effects. RESULTS: A physics-based framework is proposed that predicts the effect of charge-altering PTMs in the histone core, quantitatively for several types of lysine charge-neutralizing PTMs including acetylation, and qualitatively for all phosphorylations, on the nucleosome stability and subsequent changes in DNA accessibility, making a connection to resulting biological phenotypes. The framework takes into account multiple partially assembled states of the nucleosome at the atomic resolution. The framework is validated against experimentally known nucleosome stability changes due to the acetylation of specific lysines, and their effect on transcription. The predicted effect of charge-altering PTMs on DNA accessibility can vary dramatically, from virtually none to a strong, region-dependent increase in accessibility of the nucleosomal DNA; in some cases, e.g., H4K44, H2AK75, and H2BK57, the effect is significantly stronger than that of the extensively studied acetylation sites such H3K56, H3K115 or H3K122. Proximity to the DNA is suggestive of the strength of the PTM effect, but there are many exceptions. For the vast majority of charge-altering PTMs, the predicted increase in the DNA accessibility should be large enough to result in a measurable modulation of transcription. However, a few possible PTMs, such as acetylation of H4K77, counterintuitively decrease the DNA accessibility, suggestive of the repressed chromatin. A structural explanation for the phenomenon is provided. For the majority of charge-altering PTMs, the effect on DNA accessibility is simply additive (noncooperative), but there are exceptions, e.g., simultaneous acetylation of H4K79 and H3K122, where the combined effect is amplified. The amplification is a direct consequence of the nucleosome-DNA complex having more than two structural states. The effect of individual PTMs is classified based on changes in the accessibility of various regions throughout the nucleosomal DNA. The PTM's resulting imprint on the DNA accessibility, "PTMprint," is used to predict effects of many yet unexplored PTMs. For example, acetylation of H4K44 yields a PTMprint similar to the PTMprint of H3K56, and thus acetylation of H4K44 is predicted to lead to a wide range of strong biological effects. CONCLUSION: Charge-altering post-translational modifications in the relatively unexplored globular histone core may provide a precision mechanism for controlling accessibility to the nucleosomal DNA.

ZDHHC3 as a Risk and Mortality Marker for Breast Cancer in African American Women.

African American woman are 43% more likely to die from breast cancer than white women and have increased the risk of tumor recurrence despite lower incidence. We investigate variations in microsatellite genomic regions-a type of repetitive DNA-and possible links to the breast cancer mortality gap. We screen 33 854 microsatellites in germline DNA of African American women with and without breast cancer: 4 are statistically significant. These are located in the 3' UTR (untranslated region) of gene ZDHHC3, an intron of transcribed pseudogene INTS4L1, an intron of ribosomal gene RNA5-8S5, and an intergenic region of chromosome 16. The marker in ZDHHC3 is interesting for 3 reasons: (a) the ZDHHC3 gene is located in region 3p21 which has already been linked to early invasive breast cancer, (b) the Kaplan-Meier estimator demonstrates that ZDHHC3 alterations are associated with poor breast cancer survival in all racial/ethnic groups combined, and (c) data from cBioPortal suggest that ZDHHC3 messenger RNA expression is significantly lower in African Americans compared with whites. These independent lines of evidence make ZDHHC3 a candidate for further investigation.

Biophysical comparison of ATP-driven proton pumping mechanisms suggests a kinetic advantage for the rotary process depending on coupling ratio.

ATP-driven proton pumps, which are critical to the operation of a cell, maintain cytosolic and organellar pH levels within a narrow functional range. These pumps employ two very different mechanisms: an elaborate rotary mechanism used by V-ATPase H+ pumps, and a simpler alternating access mechanism used by P-ATPase H+ pumps. Why are two different mechanisms used to perform the same function? Systematic analysis, without parameter fitting, of kinetic models of the rotary, alternating access and other possible mechanisms suggest that, when the ratio of protons transported per ATP hydrolyzed exceeds one, the one-at-a-time proton transport by the rotary mechanism is faster than other possible mechanisms across a wide range of driving conditions. When the ratio is one, there is no intrinsic difference in the free energy landscape between mechanisms, and therefore all mechanisms can exhibit the same kinetic performance. To our knowledge all known rotary pumps have an H+:ATP ratio greater than one, and all known alternating access ATP-driven proton pumps have a ratio of one. Our analysis suggests a possible explanation for this apparent relationship between coupling ratio and mechanism. When the conditions under which the pump must operate permit a coupling ratio greater than one, the rotary mechanism may have been selected for its kinetic advantage. On the other hand, when conditions require a coupling ratio of one or less, the alternating access mechanism may have been selected for other possible advantages resulting from its structural and functional simplicity.

Implicit Solvent Model for Million-Atom Atomistic Simulations: Insights into the Organization of 30-nm Chromatin Fiber.

Molecular dynamics (MD) simulations based on the implicit solvent generalized Born (GB) models can provide significant computational advantages over the traditional explicit solvent simulations. However, the standard GB becomes prohibitively expensive for all-atom simulations of large structures; the model scales poorly, ∼n2, with the number of solute atoms. Here we combine our recently developed optimal point charge approximation (OPCA) with the hierarchical charge partitioning (HCP) approximation to present an ∼n log n multiscale, yet fully atomistic, GB model (GB-HCPO). The HCP approximation exploits the natural organization of biomolecules (atoms, groups, chains, and complexes) to partition the structure into multiple hierarchical levels of components. OPCA approximates the charge distribution for each of these components by a small number of point charges so that the low order multipole moments of these components are optimally reproduced. The approximate charges are then used for computing electrostatic interactions with distant components, while the full set of atomic charges are used for nearby components. We show that GB-HCPO can deliver up to 2 orders of magnitude speedup compared to the standard GB, with minimal impact on its accuracy. For large structures, GB-HCPO can approach the same nominal speed, as in nanoseconds per day, as the highly optimized explicit-solvent simulation based on particle mesh Ewald (PME). The increase in the nominal simulation speed, relative to the standard GB, coupled with substantially faster sampling of conformational space, relative to the explicit solvent, makes GB-HCPO a suitable candidate for MD simulation of large atomistic systems in implicit solvent. As a practical demonstration, we use GB-HCPO simulation to refine a ∼1.16 million atom structure of 30 nm chromatin fiber (40 nucleosomes). The refined structure suggests important details about spatial organization of the linker DNA and the histone tails in the fiber: (1) the linker DNA fills the core region, allowing the H3 histone tails to interact with the linker DNA, which is consistent with experiment; (2) H3 and H4 tails are found mostly in the core of the structure, closer to the helical axis of the fiber, while H2A and H2B are mostly solvent exposed. Potential functional consequences of these findings are discussed. GB-HCPO is implemented in the open source MD software NAB in Amber 2016.

Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process.

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated "kinetic equivalence" of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations.

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.