Equilibrium Ensemble Approach to Disordered Systems I: General Theory, Exact Results

An outline of Morita's equilibrium ensemble approach to disordered systems is given, and hitherto unnoticed relations to other, more conventional approaches in the theory of disordered systems are pointed out. It is demonstrated to constitute a generalization of the idea of grand ensembles and to be intimately related also to conventional low--concentration expansions as well as to perturbation expansions about ordered reference systems. Moreover, we draw attention to the variational content of the equilibrium ensemble formulation. A number of exact results are presented, among them general solutions for site-- and bond-- diluted systems in one dimension, both for uncorrelated, and for correlated disorder.Comment: 24 pages, Late

Evolution of sparsity and modularity in a model of protein allostery

The sequence of a protein is not only constrained by its physical and biochemical properties under current selection, but also by features of its past evolutionary history. Understanding the extent and the form that these evolutionary constraints may take is important to interpret the information in protein sequences. To study this problem, we introduce a simple but physical model of protein evolution where selection targets allostery, the functional coupling of distal sites on protein surfaces. This model shows how the geometrical organization of couplings between amino acids within a protein structure can depend crucially on its evolutionary history. In particular, two scenarios are found to generate a spatial concentration of functional constraints: high mutation rates and fluctuating selective pressures. This second scenario offers a plausible explanation for the high tolerance of natural proteins to mutations and for the spatial organization of their least tolerant amino acids, as revealed by sequence analyses and mutagenesis experiments. It also implies a faculty to adapt to new selective pressures that is consistent with observations. Besides, the model illustrates how several independent functional modules may emerge within a same protein structure, depending on the nature of past environmental fluctuations. Our model thus relates the evolutionary history and evolutionary potential of proteins to the geometry of their functional constraints, with implications for decoding and engineering protein sequences

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

Cyclic-AMP regulates postnatal development of neural and behavioral responses to NaCl in rats

During postnatal development rats demonstrate an age-dependent increase in NaCl chorda tympani (CT) responses and the number of functional apical amiloride-sensitive epithelial Na+channels (ENaCs) in salt sensing fungiform (FF) taste receptor cells (TRCs). Currently, the intracellular signals that regulate the postnatal development of salt taste have not been identified. We investigated the effect of cAMP, a downstream signal for arginine vasopressin (AVP) action, on the postnatal development of NaCl responses in 19–23 day old rats. ENaC-dependent NaCl CT responses were monitored after lingual application of 8-chlorophenylthio-cAMP (8-CPT-cAMP) under open-circuit conditions and under ±60 mV lingual voltage clamp. Behavioral responses were tested using 2 bottle/24h NaCl preference tests. The effect of [deamino-Cys1, D-Arg8]-vasopressin (dDAVP, a specific V2R agonist) was investigated on ENaC subunit trafficking in rat FF TRCs and on cAMP generation in cultured adult human FF taste cells (HBO cells). Our results show that in 19–23 day old rats, the ENaC-dependent maximum NaCl CT response was a saturating sigmoidal function of 8-CPT-cAMP concentration. 8-CPT-cAMP increased the voltage-sensitivity of the NaCl CT response and the apical Na+ response conductance. Intravenous injections of dDAVP increased ENaC expression and γ-ENaC trafficking from cytosolic compartment to the apical compartment in rat FF TRCs. In HBO cells dDAVP increased intracellular cAMP and cAMP increased trafficking of γ- and δ-ENaC from cytosolic compartment to the apical compartment 10 min post-cAMP treatment. Control 19–23 day old rats were indifferent to NaCl, but showed clear preference for appetitive NaCl concentrations after 8-CPT-cAMP treatment. Relative to adult rats, 14 day old rats demonstrated significantly less V2R antibody binding in circumvallate TRCs. We conclude that an age-dependent increase in V2R expression produces an AVP-induced incremental increase in cAMP that modulates the postnatal increase in TRC ENaC and the neural and behavioral responses to NaCl

First Passage Properties of the Erdos-Renyi Random Graph

We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first-passage time, are insensitive to the fraction p of occupied links. This prediction qualitatively agrees with numerical simulations away from the percolation threshold. Near the percolation threshold, the statistically meaningful quantity is the mean transit rate, namely, the inverse of the first-passage time. This rate varies non-monotonically with p near the percolation transition. Much of this behavior can be understood by simple heuristic arguments.Comment: 10 pages, 9 figures, 2-column revtex4 forma

Association of Exposure to Phthalates with Endometriosis and Uterine Leiomyomata: Findings from NHANES, 1999-2004

BACKGROUND. Phthalates are ubiquitous chemicals used in consumer products. Some phthalates are reproductive toxicants in experimental animals, but human data are limited. OBJECTIVE. We conducted a cross-sectional study of urinary phthalate metabolite concentrations in relation to self-reported history of endometriosis and uterine leiomyomata among 1,227 women 20-54 years of age from three cycles of the National Health and Nutrition Examination Survey (NHANES), 1999-2004. METHODS. We examined four phthalate metabolites: mono(2-ethylhexyl) phthalate (MEHP), monobutyl phthalate (MBP), monoethyl phthalate (MEP), and monobenzyl phthalate (MBzP). From the last two NHANES cycles, we also examined mono(2-ethyl-5-hydroxyhexyl) phthalate (MEHHP) and mono(2-ethyl-5-oxohexyl) phthalate (MEOHP). We used logistic regression to estimate odds ratios (ORs) and 95% confidence intervals (CIs), adjusting for potential confounders. RESULTS. Eighty-seven (7%) and 151 (12%) women reported diagnoses of endometriosis and leiomyomata, respectively. The ORs comparing the highest versus lowest three quartiles of urinary MBP were 1.36 (95% CI, 0.77-2.41) for endometriosis, 1.56 (95% CI, 0.93-2.61) for leiomyomata, and 1.71 (95% CI, 1.07-2.75) for both conditions combined. The corresponding ORs for MEHP were 0.44 (95% CI, 0.19-1.02) for endometriosis, 0.63 (95% CI, 0.35-1.12) for leiomyomata, and 0.59 (95% CI, 0.37-0.95) for both conditions combined. Findings for MEHHP and MEOHP agreed with findings for MEHP with respect to endometriosis only. We observed null associations for MEP and MBzP. Associations were similar when we excluded women diagnosed > 7 years before their NHANES evaluation. CONCLUSION. The positive associations for MBP and inverse associations for MEHP in relation to endometriosis and leiomyomata warrant investigation in prospective studies