A Dynamic Model of Interactions of Ca^(2+), Calmodulin, and Catalytic Subunits of Ca^(2+)/Calmodulin-Dependent Protein Kinase II

During the acquisition of memories, influx of Ca^(2+) into the postsynaptic spine through the pores of activated N-methyl-D-aspartate-type glutamate receptors triggers processes that change the strength of excitatory synapses. The pattern of Ca^(2+) influx during the first few seconds of activity is interpreted within the Ca^(2+)-dependent signaling network such that synaptic strength is eventually either potentiated or depressed. Many of the critical signaling enzymes that control synaptic plasticity, including Ca^(2+)/calmodulin-dependent protein kinase II (CaMKII), are regulated by calmodulin, a small protein that can bind up to 4 Ca^(2+) ions. As a first step toward clarifying how the Ca^(2+)-signaling network decides between potentiation or depression, we have created a kinetic model of the interactions of Ca^(2+), calmodulin, and CaMKII that represents our best understanding of the dynamics of these interactions under conditions that resemble those in a postsynaptic spine. We constrained parameters of the model from data in the literature, or from our own measurements, and then predicted time courses of activation and autophosphorylation of CaMKII under a variety of conditions. Simulations showed that species of calmodulin with fewer than four bound Ca^(2+) play a significant role in activation of CaMKII in the physiological regime, supporting the notion that processing ofCa^(2+) signals in a spine involves competition among target enzymes for binding to unsaturated species of CaM in an environment in which the concentration of Ca^(2+) is fluctuating rapidly. Indeed, we showed that dependence of activation on the frequency of Ca^(2+) transients arises from the kinetics of interaction of fluctuating Ca^(2+) with calmodulin/CaMKII complexes. We used parameter sensitivity analysis to identify which parameters will be most beneficial to measure more carefully to improve the accuracy of predictions. This model provides a quantitative base from which to build more complex dynamic models of postsynaptic signal transduction during learning

The Nondeterministic Waiting Time Algorithm: A Review

We present briefly the Nondeterministic Waiting Time algorithm. Our technique for the simulation of biochemical reaction networks has the ability to mimic the Gillespie Algorithm for some networks and solutions to ordinary differential equations for other networks, depending on the rules of the system, the kinetic rates and numbers of molecules. We provide a full description of the algorithm as well as specifics on its implementation. Some results for two well-known models are reported. We have used the algorithm to explore Fas-mediated apoptosis models in cancerous and HIV-1 infected T cells

Generic Schemes for Single Molecule Kinetics 2: Information Content of the Poisson Indicator

Recently, we described a pathway analysis technique (paper 1) for analyzing generic schemes for single-molecule kinetics based upon the first-passage time distribution. Here, we employ this method to derive expressions for the Poisson indicator, a measure of stochastic variation (essentially equivalent to the Fano factor and Mandel's Q parameter), for various renewal (memoryless) enzymatic reactions. We examine its dependence on substrate concentration, without assuming all steps follow Poissonian kinetics. Based upon fitting to the functional forms of the first two waiting time moments, we show that, to second order, the non-Poissonian kinetics are generally underdetermined but can be specified in certain scenarios. For an enzymatic reaction with an arbitrary intermediate topology, we identify a generic minimum of the Poisson indicator as a function of substrate concentration, which can be used to tune substrate concentration to the stochastic fluctuations and estimate the largest number of underlying consecutive links in a turnover cycle. We identify a local maximum of the Poisson indicator (with respect to substrate concentration) for a renewal process as a signature of competitive binding, either between a substrate and an inhibitor or between multiple substrates. Our analysis explores the rich connections between Poisson indicator measurements and microscopic kinetic mechanisms

Frustration in Biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with a finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of "frustration" in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and how structure connects to function. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding, how a large part of the biological functions of proteins are related to subtle local frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. We hope to illustrate how Frustration is a fundamental concept in relating function to structural biology.Comment: 97 pages, 30 figure

A robust and efficient method for estimating enzyme complex abundance and metabolic flux from expression data

A major theme in constraint-based modeling is unifying experimental data, such as biochemical information about the reactions that can occur in a system or the composition and localization of enzyme complexes, with highthroughput data including expression data, metabolomics, or DNA sequencing. The desired result is to increase predictive capability resulting in improved understanding of metabolism. The approach typically employed when only gene (or protein) intensities are available is the creation of tissue-specific models, which reduces the available reactions in an organism model, and does not provide an objective function for the estimation of fluxes, which is an important limitation in many modeling applications. We develop a method, flux assignment with LAD (least absolute deviation) convex objectives and normalization (FALCON), that employs metabolic network reconstructions along with expression data to estimate fluxes. In order to use such a method, accurate measures of enzyme complex abundance are needed, so we first present a new algorithm that addresses quantification of complex abundance. Our extensions to prior techniques include the capability to work with large models and significantly improved run-time performance even for smaller models, an improved analysis of enzyme complex formation logic, the ability to handle very large enzyme complex rules that may incorporate multiple isoforms, and depending on the model constraints, either maintained or significantly improved correlation with experimentally measured fluxes. FALCON has been implemented in MATLAB and ATS, and can be downloaded from: https://github.com/bbarker/FALCON. ATS is not required to compile the software, as intermediate C source code is available, and binaries are provided for Linux x86-64 systems. FALCON requires use of the COBRA Toolbox, also implemented in MATLAB.Comment: 30 pages, 12 figures, 4 table

Kinetic studies on the fidelity of DNA replication involving DNA templates containing O6-methylguanine

Production by N-nitroso compounds of O6-alkylguanine (O6-alkylG) in DNA directs the misincorporation of thymine during DNA replication, leading to G:C to A:T transition mutations, despite the fact that DNA containing O6>alkylG:T base-pairs is less stable than that containing O6-alkylG:C pairs. In the work presented in this thesis, the kinetics of incorporation by Klenow fragment of Escherichia coli DNA polymerase I of thymine (T), and of cytosine (C), opposite O6-meG in the template DNA strand were examined. Both T and C were incorporated opposite O6-meG much slower than nucleotides forming regular A:T or G:C base pairs. Using an excess of Klenow over DNA and various concentrations of dXTF and dCTP, the progress of incorporation of a single nucleotide in a single catalytic cycle of a preformed Klenow-DNA complex was measured (pre-steady state kinetics). The results were consistent with the kinetic scheme: 1. polymerase-DNA binds dNTP; 2. conformational change in polymerase; 3. formation of phosphodiester between the dNTP and the 3'-OH of primer; 4. conformational change of polymerase; 5. release of pyrophsphate. The results were analysed mathematically to identify the steps at which the rate constants differ significantly between the incorporation of T and C. The only significant difference was the 5-fold difference in the rates of formation of the phosphodiester bond (for dTTP, kforward = 3.9 s-1 and kback = 1.9 s-1 for dCTP, kforward = 0.7 s-1 and kback = 0.9 s-l). The equilibrium constants for each step suggest that the greatest change in the Gibbs' free energy occurs at the conformational change after polymerisation, and that while the formation of the phosphodiester bond to T is slightly exothermic, that to C is slightly endothermic. The Kms calculated from the rate constants (Km = 33.5 μM (24.0-46.7)* for both dTTP and dCTP [* 5% and 95% confidence limits]) were close to the approximate Kms obtained from Michaelis-Menten analysis of the initial rates of pre-steady state polymerisation (Km, = 30-35 μM for T and C). The measured progress of independently determined steady state experiments (i.e. polymerisation under conditions of excess DNA over Klenow) was close to that predicted from these calculated rate constants. The incorporation of the nucleotide following C in an O6-meG:C pair was much slower than that following T in an O^-meGiT pair. Taken with the available structural data (Kalnik et al., 1988a, b), this suggests that the discrimination in favour of the incorporation of T opposite O6-meG arises mainly because the T:O6-meG base-pair retains the Watson-Crick configuration (with the N1 of the purine juxtaposed to N3 of the pyrimidine), whereas the C:O6-meG base-pair is a wobble base pair with a distorted phosphodiester link 3' to the C. The slow incorporation of C opposite O6-meG, and of the next correct nucleotide following the incorporation of C, can be ascribed to the stereochemical problems encountered when forming the distorted phosphodiester links. The recent X-ray crystallography data (Beese et al., 1993) of a Klenow complexed with duplex DNA provided evidence that Klenow fragment interacts with the primer-template through the phosphodiester backbone, thus an incorporation event that produces a distortion in the phosphodiester backbone, such as the incorporation of C opposite O6-meG, could very well reduce the rate of its incorporation