Thermodynamic Analysis of Interacting Nucleic Acid Strands

Motivated by the analysis of natural and engineered DNA and RNA systems, we present the first algorithm for calculating the partition function of an unpseudoknotted complex of multiple interacting nucleic acid strands. This dynamic program is based on a rigorous extension of secondary structure models to the multistranded case, addressing representation and distinguishability issues that do not arise for single-stranded structures. We then derive the form of the partition function for a fixed volume containing a dilute solution of nucleic acid complexes. This expression can be evaluated explicitly for small numbers of strands, allowing the calculation of the equilibrium population distribution for each species of complex. Alternatively, for large systems (e.g., a test tube), we show that the unique complex concentrations corresponding to thermodynamic equilibrium can be obtained by solving a convex programming problem. Partition function and concentration information can then be used to calculate equilibrium base-pairing observables. The underlying physics and mathematical formulation of these problems lead to an interesting blend of approaches, including ideas from graph theory, group theory, dynamic programming, combinatorics, convex optimization, and Lagrange duality

On the Growth Rate of Non-Enzymatic Molecular Replicators

It is well known that non-enzymatic template directed molecular replicators X + nO ---> 2X exhibit parabolic growth d[X]/dt = k [X]^{1/2}. Here, we analyze the dependence of the effective replication rate constant k on hybridization energies, temperature, strand length, and sequence composition. First we derive analytical criteria for the replication rate k based on simple thermodynamic arguments. Second we present a Brownian dynamics model for oligonucleotides that allows us to simulate their diffusion and hybridization behavior. The simulation is used to generate and analyze the effect of strand length, temperature, and to some extent sequence composition, on the hybridization rates and the resulting optimal overall rate constant k. Combining the two approaches allows us to semi-analytically depict a fitness landscape for template directed replicators. The results indicate a clear replication advantage for longer strands at low temperatures.Comment: Submitted to: Entrop

Theoretical Perspectives on Protein Folding

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid residues (N) and polymer concepts. The sizes of proteins in the denatured and folded states, cooperativity of the folding transition, dispersions in the melting temperatures at the residue level, and time scales of folding are to a large extent determined by N. The consequences of finite N especially on how individual residues order upon folding depends on the topology of the folded states. Such intricate details can be predicted using the Molecular Transfer Model that combines simulations with measured transfer free energies of protein building blocks from water to the desired concentration of the denaturant. By watching one molecule fold at a time, using single molecule methods, the validity of the theoretically anticipated heterogeneity in the folding routes, and the N-dependent time scales for the three stages in the approach to the native state have been established. Despite the successes of theory, of which only a few examples are documented here, we conclude that much remains to be done to solve the "protein folding problem" in the broadest sense.Comment: 48 pages, 9 figure

Self-reinoculation with fecal flora changes microbiota density and composition leading to an altered bile-acid profile in the mouse small intestine

Background: The upper gastrointestinal tract plays a prominent role in human physiology as the primary site for enzymatic digestion and nutrient absorption, immune sampling, and drug uptake. Alterations to the small intestine microbiome have been implicated in various human diseases, such as non-alcoholic steatohepatitis and inflammatory bowel conditions. Yet, the physiological and functional roles of the small intestine microbiota in humans remain poorly characterized because of the complexities associated with its sampling. Rodent models are used extensively in microbiome research and enable the spatial, temporal, compositional, and functional interrogation of the gastrointestinal microbiota and its effects on the host physiology and disease phenotype. Classical, culture-based studies have documented that fecal microbial self-reinoculation (via coprophagy) affects the composition and abundance of microbes in the murine proximal gastrointestinal tract. This pervasive self-reinoculation behavior could be a particularly relevant study factor when investigating small intestine microbiota. Modern microbiome studies either do not take self-reinoculation into account, or assume that approaches such as single housing mice or housing on wire mesh floors eliminate it. These assumptions have not been rigorously tested with modern tools. Here, we used quantitative 16S rRNA gene amplicon sequencing, quantitative microbial functional gene content inference, and metabolomic analyses of bile acids to evaluate the effects of self-reinoculation on microbial loads, composition, and function in the murine upper gastrointestinal tract. Results: In coprophagic mice, continuous self-exposure to the fecal flora had substantial quantitative and qualitative effects on the upper gastrointestinal microbiome. These differences in microbial abundance and community composition were associated with an altered profile of the small intestine bile acid pool, and, importantly, could not be inferred from analyzing large intestine or stool samples. Overall, the patterns observed in the small intestine of non-coprophagic mice (reduced total microbial load, low abundance of anaerobic microbiota, and bile acids predominantly in the conjugated form) resemble those typically seen in the human small intestine. Conclusions: Future studies need to take self-reinoculation into account when using mouse models to evaluate gastrointestinal microbial colonization and function in relation to xenobiotic transformation and pharmacokinetics or in the context of physiological states and diseases linked to small intestine microbiome and to small intestine dysbiosis