Binomial leap methods for simulating stochastic chemical kinetics

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the tau-leap and midpoint tau-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches. (C) 2004 American Institute of Physics.

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

Thermal, chemical, and enzymatic stability of the cyclotide kalata B1: The importance of the cyclic cystine knot

The cyclotides constitute a recently discovered family of plant-derived peptides that have the unusual features of a head-to-tail cyclized backbone and a cystine knot core. These features are thought to contribute to their exceptional stability, as qualitatively observed during experiments aimed at sequencing and characterizing early members of the family. However, to date there has been no quantitative study of the thermal, chemical, or enzymatic stability of the cyclotides. In this study, we demonstrate the stability of the prototypic cyclotide kalata B1 to the chaotropic agents 6 M guanidine hydrochloride (GdHCl) and 8 M urea, to temperatures approaching boiling, to acid, and following incubation with a range of proteases, conditions under which most proteins readily unfold. NMR spectroscopy was used to demonstrate the thermal stability, while fluorescence and circular dichroism were used to monitor the chemical stability. Several variants of kalata B1 were also examined, including kalata 132, which has five amino acid substitutions from B1, two acyclic permutants in which the backbone was broken but the cystine knot was retained, and a two-disulfide bond mutant. Together, these allowed determinations of the relative roles of the cystine knot and the circular backbone on the stability of the cyclotides. Addition of a denaturant to kalata B1 or an acyclic permutant did not cause unfolding, but the two-disulfide derivative was less stable, despite having a similar three-dimensional structure. It appears that the cystine knot is more important than the circular backbone in the chemical stability of the cyclotides. Furthermore, the cystine knot of the cyclotides is more stable than those in similar-sized molecules, judging by a comparison with the conotoxin PVIIA. There was no evidence for enzymatic digestion of native kalata B1 as monitored by LC-MS, but the reduced form was susceptible to proteolysis by trypsin, endoproteinase Glu-C, and thermolysin. Fluorescence spectra of kalata B1 in the presence of dithiothreitol, a reducing agent, showed a marked increase in intensity thought to be due to removal of the quenching effect on the Trp residue by the neighboring Cys5-Cys17 disulfide bond. In general, the reduced peptides were significantly more susceptible to chemical or enzymatic breakdown than the oxidized species.

Small molecules that mimic components of bioactive protein surfaces

Small molecules designed to mimic specific structural components of a protein (peptide strands, sheets, turns, helices, or amino acids) can be expected to display agonist or antagonist biological responses by virtue of interacting with the same receptors that recognize the protein. Here we describe some minimalist approaches to structural mimetics of amino acids and of strand, turn, or helix segments of proteins. The designed molecules show potent and selective inhibition of protease, transferase, and phospholipase enzymes, or antagonism of G-protein coupled or transcriptional receptors, and have potent anti-tumour, anti-inflammatory, or antiviral activity.

Research on the BET surface area and packing of molecules on the activated carbon

Adsorption of different aromatic compounds (two of them are electrolytes) onto an untreated activated carbon (F100) is investigated. The experimental isotherms are fitted into Langmuir homogenous and heterogeneous Model. Theoretical maximum adsorption capacities that are based on the BET surface area of the adsorbent cannot be close to the real value. The affinity and the heterogeneity of the adsorption system observed to be related to the pK(a) of the solutes. The maximum adsorption capacity (Q(max)) of activated carbon for each solute dependent on the molecular area as well as the type of functional group attached on the aromatic compound and also pH of solution. The arrangement of the molecules on the carbon surface is not face down. Furthermore, it is illustrated that the packing arrangement is most likely edge to face (sorbate-sorbent) with various tilt angles. For characterization of the carbon, the N-2 and CO2 adsorption were used. X-ray Photoelectron Spectroscopy (XPS) measurement was used to surface elemental analysis of activated carbon.

Impact of potential models on adsorption of linear molecules on carbon black

In this paper, we investigate the effects of potential models on the description of equilibria of linear molecules (ethylene and ethane) adsorption on graphitized thermal carbon black. GCMC simulation is used as a tool to give adsorption isotherms, isosteric heat of adsorption and the microscopic configurations of these molecules. At the heart of the GCMC are the potential models, describing fluid-fluid interaction and solid-fluid interaction. Here we studied the two potential models recently proposed in the literature, the UA-TraPPE and AUA4. Their impact in the description of adsorption behavior of pure components will be discussed. Mixtures of these components with nitrogen and argon are also studied. Nitrogen is modeled a two-site plus discrete charges while argon as a spherical particle. GCMC simulation is also used for generating simulation mixture isotherms. It is found that co-operation between species occurs when the surface is fractionally covered while competition is important when surface is fully loaded.

Novel natriuretic peptides from the venom of the inland taipan (Oxyuranus microlepidotus): isolation, chemical and biological characterisation

Three natriuretic-like peptides (TNP-a, TNP-b, and TNP-c) were isolated from the venom of Oxyuranus microlepidotus (inland taipan) and were also present in the venoms of Oxyuranus scutellatus canni (New Guinea taipan) and Oxyuranus scutellatus scutellatus (coastal taipan). They were isolated by HPLC, characterised by mass spectrometry and Edman analysis, and consist of 35-39 amino acid residues. These molecules differ from ANP/BNP through replacement of invariant residues within the 17-membered ring structure and by inclusion of proline residues in the C-terminal tail. TNP-c was equipotent to ANP in specific GC-A assays or aortic ring assays whereas TNP-a and TNP-b were either inactive (GC-A over-expressing cells and endothelium-denuded aortic rings) or weakly active (endothelium-in tact aortic rings). TNP-a and TNP-b were also unable to competitively inhibit the binding of TNP-c in endothelium-denuded aortae (GC-A) or endothelium-in tact aortae (NPR-C). Thus, these naturally occurring isoforms provide a new platform for further investigation of structure-function relationships of natriuretic peptides. (C) 2004 Elsevier Inc. All rights reserved.

Electrostatically mediated specific adsorption of small molecules in metallo-organic frameworks

We investigate the interaction of ethylene and ethane with a Cu-tricarboxylate complex and show that at low loadings the lighter molecule has a higher binding energy as a result of an increased interaction with the framework Cu and stronger hydrogen bonding with the basic framework oxygens. This leads to selective adsorption of ethylene by a factor of about 2 at low pressure, which is overcome by the stronger van der Waals interaction of ethane at high loadings, explaining recent literature data. The results suggest the possibility of separation of light hydrocarbons at low pressures or in trace amounts.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.