Recent interest in modeling biochemical networks raises questions about the relationship between often complex mathematical models and familiar arithmetic concepts from classical enzymology, and also about connections between modeling and experimental data. This review addresses both topics by familiarizing readers with key concepts (and terminology) in the construction, validation, and application of deterministic biochemical models, with particular emphasis on a simple enzyme-catalyzed reaction. Networks of coupled ordinary differential equations (ODEs) are the natural language for describing enzyme kinetics in a mass action approximation. We illustrate this point by showing how the familiar Briggs-Haldane formulation of Michaelis-Menten kinetics derives from the outer (or quasi-steady-state) solution of a dynamical system of ODEs describing a simple reaction under special conditions. We discuss how parameters in the Michaelis-Menten approximation and in the underlying ODE network

Sequence-specific protein -nucleic acid recognition is determined, in part, by hydrogen bonding interactions between amino acid side-chains and nucleotide bases. To examine the repertoire of possible interactions, we have calculated geometrically plausible arrangements in which amino acids hydrogen bond to unpaired bases, such as those found in RNA bulges and loops, or to the 53 possible RNA base-pairs. We find 32 possible interactions that involve two or more hydrogen bonds to the six unpaired bases (including protonated A and C), 17 of which have been observed. We find 186 "spanning" interactions to base-pairs in which the amino acid hydrogen bonds to both bases, in principle allowing particular base-pairs to be selectively targeted, and nine of these have been observed. Four calculated interactions span the Watson -Crick pairs and 15 span the G:U wobble pair, including two interesting arrangements with three hydrogen bonds to the Arg guanidinum group that have not yet been observed. The inherent donor-acceptor arrangements of the bases support many possible interactions to Asn (or Gln) and Ser (or Thr or Tyr), few interactions to Asp (or Glu) even though several already have been observed, and interactions to U (or T) only if the base is in an unpaired context, as also observed in several cases. This study highlights how complementary arrangements of donors and acceptors can contribute to base-specific recognition of RNA, predicts interactions not yet observed, and provides tools to analyze proposed contacts or design novel interactions.

Natural proteins fold to a unique, thermodynamically dominant state. Modeling of the folding process and prediction of the native fold of proteins are two major unsolved problems in biophysics. Here, we show successful all-atom ab initio folding of a representative diverse set of proteins by using a minimalist transferable-energy model that consists of two-body atom-atom interactions, hydrogen bonding, and a local sequence-energy term that models sequence-specific chain stiffness. Starting from a random coil, the native-like structure was observed during replica exchange Monte Carlo (REMC) simulation for most proteins regardless of their structural classes; the lowest energy structure was close to native-in the range of 2-6 A root-mean-square deviation (rmsd). Our results demonstrate that the successful folding of a protein chain to its native state is governed by only a few crucial energetic terms.

Evolutionary traces of thermophilic adaptation are manifest, on the whole-genome level, in compositional biases toward certain types of amino acids. However, it is sometimes difficult to discern their causes without a clear understanding of underlying physical mechanisms of thermal stabilization of proteins. For example, it is well-known that hyperthermophiles feature a greater proportion of charged residues, but, surprisingly, the excess of positively charged residues is almost entirely due to lysines but not arginines in the majority of hyperthermophilic genomes. All-atom simulations show that lysines have a much greater number of accessible rotamers than arginines of similar degree of burial in folded states of proteins. This finding suggests that lysines would preferentially entropically stabilize the native state. Indeed, we show in computational experiments that arginine-to-lysine amino acid substitutions result in noticeable stabilization of proteins. We then hypothesize that if evolution uses this physical mechanism as a complement to electrostatic stabilization in its strategies of thermophilic adaptation, then hyperthermostable organisms would have much greater content of lysines in their proteomes than comparably sized and similarly charged arginines. Consistent with that, high-throughput comparative analysis of complete proteomes shows extremely strong bias toward arginine-to-lysine replacement in hyperthermophilic organisms and overall much greater content of lysines than arginines in hyperthermophiles. This finding cannot be explained by genomic GC compositional biases or by the universal trend of amino acid gain and loss in protein evolution. We discovered here a novel entropic mechanism of protein thermostability due to residual dynamics of rotamer isomerization in native state and demonstrated its immediate proteomic implications. Our study provides an example of how analysis of a fundamental physical mechanism of thermostability helps to resolve a puzzle in comparative genomics as to why amino acid compositions of hyperthermophilic proteomes are significantly biased toward lysines but not similarly charged arginines.

This investigation examines mechanisms through which optimism may influence psychological adjustment among 133 Black college students. Specifically, this study evaluates the extent to which active and avoidant coping and social support account for the association between optimism and depressive symptoms. Participants completed questionnaires that included the Life Orientation Test-Revised, the COPE, the Social Provisions Scale, and the 12-item Center for Epidemiological Studies Depression Scale. Avoidant coping and social support mediated the relation between optimism and depressive symptoms, whereas active coping did not mediate this relationship. Results partially replicate those of prior research and illustrate the need for culturally sensitive theory regarding the combined effect of personality, coping strategies, and social support on psychological adjustment to stressful situations.