Using cellzilla for plant growth simulations at the cellular level

Cellzilla is a two-dimensional tissue simulation platform for plant modeling utilizing Cellerator arrows. Cellerator describes biochemical interactions with a simplified arrow-based notation; all interactions are input as reactions and are automatically translated to the appropriate differential equations using a computer algebra system. Cells are represented by a polygonal mesh of well-mixed compartments. Cell constituents can interact intercellularly via Cellerator reactions utilizing diffusion, transport, and action at a distance, as well as amongst themselves within a cell. The mesh data structure consists of vertices, edges (vertex pairs), and cells (and optional intercellular wall compartments) as ordered collections of edges. Simulations may be either static, in which cell constituents change with time but cell size and shape remain fixed; or dynamic, where cells can also grow. Growth is controlled by Hookean springs associated with each mesh edge and an outward pointing pressure force. Spring rest length grows at a rate proportional to the extension beyond equilibrium. Cell division occurs when a specified constituent (or cell mass) passes a (random, normally distributed) threshold. The orientation of new cell walls is determined either by Errera's rule, or by a potential model that weighs contributions due to equalizing daughter areas, minimizing wall length, alignment perpendicular to cell extension, and alignment perpendicular to actual growth direction

Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies

<p>Abstract</p> <p>Background</p> <p>To understand the dynamic behavior of cellular systems, mathematical modeling is often necessary and comprises three steps: (1) experimental measurement of participating molecules, (2) assignment of rate laws to each reaction, and (3) parameter calibration with respect to the measurements. In each of these steps the modeler is confronted with a plethora of alternative approaches, e. g., the selection of approximative rate laws in step two as specific equations are often unknown, or the choice of an estimation procedure with its specific settings in step three. This overall process with its numerous choices and the mutual influence between them makes it hard to single out the best modeling approach for a given problem.</p> <p>Results</p> <p>We investigate the modeling process using multiple kinetic equations together with various parameter optimization methods for a well-characterized example network, the biosynthesis of valine and leucine in <it>C. glutamicum</it>. For this purpose, we derive seven dynamic models based on generalized mass action, Michaelis-Menten and convenience kinetics as well as the stochastic Langevin equation. In addition, we introduce two modeling approaches for feedback inhibition to the mass action kinetics. The parameters of each model are estimated using eight optimization strategies. To determine the most promising modeling approaches together with the best optimization algorithms, we carry out a two-step benchmark: (1) coarse-grained comparison of the algorithms on all models and (2) fine-grained tuning of the best optimization algorithms and models. To analyze the space of the best parameters found for each model, we apply clustering, variance, and correlation analysis.</p> <p>Conclusion</p> <p>A mixed model based on the convenience rate law and the Michaelis-Menten equation, in which all reactions are assumed to be reversible, is the most suitable deterministic modeling approach followed by a reversible generalized mass action kinetics model. A Langevin model is advisable to take stochastic effects into account. To estimate the model parameters, three algorithms are particularly useful: For first attempts the settings-free Tribes algorithm yields valuable results. Particle swarm optimization and differential evolution provide significantly better results with appropriate settings.</p

Prospects for Declarative Mathematical Modeling of Complex Biological Systems

Declarative modeling uses symbolic expressions to represent models. With such expressions one can formalize high-level mathematical computations on models that would be difficult or impossible to perform directly on a lower-level simulation program, in a general-purpose programming language. Examples of such computations on models include model analysis, relatively general-purpose model-reduction maps, and the initial phases of model implementation, all of which should preserve or approximate the mathematical semantics of a complex biological model. The potential advantages are particularly relevant in the case of developmental modeling, wherein complex spatial structures exhibit dynamics at molecular, cellular, and organogenic levels to relate genotype to multicellular phenotype. Multiscale modeling can benefit from both the expressive power of declarative modeling languages and the application of model reduction methods to link models across scale. Based on previous work, here we define declarative modeling of complex biological systems by defining the operator algebra semantics of an increasingly powerful series of declarative modeling languages including reaction-like dynamics of parameterized and extended objects; we define semantics-preserving implementation and semantics-approximating model reduction transformations; and we outline a "meta-hierarchy" for organizing declarative models and the mathematical methods that can fruitfully manipulate them

The Effect of Hydration on Enzyme Activity and Dynamics

Water has long been assumed to be essential for biological function. To understand the molecular basis of the role of water in protein function, several studies have established a correlation between enzyme activity and hydration level. While a threshold of hydration of 0.2 h (grams of water per gram of dried protein) is usually accepted for the onset of enzyme activity, recent works show that enzyme activity is possible at water contents as low as 0.03 h (Lind et al., 2004). Diffusion limitation in these experiments was avoided by monitoring enzyme-catalyzed hydrolysis of gas-phase esters. However, since water is also a substrate for the enzyme used in these experiments, they cannot be used to probe the possibility of activity at zero hydration. However, the pig liver esterase and C. rugosa lipase B are able to catalyse alcoholysis reactions in which an acyl group is transferred between an ester and an alcohol. Therefore, by following this reaction and using a gas phase catalytic system, we have been able to show that activity can occur at 0 g/g. These results led to the question of the accuracy of determinations of very low water concentrations; i.e., how dry is 0 g/g? Although gravimetric measurements of the hydration level do not allow us to define the anhydrous state of the protein with sufficient sensitivity, using 18O-labeled water, we have been able to quantify the small number of water molecules bound to the protein after drying, using a modification of the method of Dolman et al. (1997). Testing different drying methods, we have been able to determine a level of hydration as low as 2 moles of water per mole of protein (equivalent to 0.0006 h in the case of pig liver esterase) and have shown that in the case of the pig liver esterase, activity can occur at this hydration level. At the molecular level, if the hydration level affects activity, we can expect an effect on the protein dynamics. Neutron scattering spectra of hydrated powders, for instance, show that diffusive motions of the protein increase with the hydration (Kurkal et al., 2005) To address the question of the protein motions involved in the onset of enzyme activity at low hydration, we performed neutron scattering experiments on a pico-second time scale on dried powders. Preliminary results show a dynamical transition at hydration levels as low as 3 h. Molecular dynamic simulations have also been used in this study to access the dynamics of the active site. Overall, the results here show that pig liver esterase can function at zero hydration, or as close to zero hydration as current methods allow us to determine. Since the experimental methodology restricts this work to a small number of enzymes, it is unlikely that it will ever be possible to determine if all enzymes can function in the anhydrous state: however, the results here indicate that water is not an obligatory requirement for enzyme function

Myristoyl CoA:Protein N-Myristoyl Transferase: A Target for a Novel Antimalarial Drug

Malaria, an illness caused by protozoan parasites of the genus Plasmodium, continues to be a key global health issue; around 40% of the world’s population are at risk and more than one million people are killed each year according to the World Health Organisation (WHO). It is transmitted via bites of infected female mosquitoes (Anopheles) and its severest form, falciparum malaria, can lead to death if left untreated. Effective malarial treatment is complex due to drug resistance and socioeconomic issues in many of the most affected areas. An enzyme from the parasite, myristoyl CoA:protein N-myristoyl transferase (NMT), has been identified as a potential target for antimalarial drugs. N-Myristoyl transferase, which catalyses the co-translational transfer of myristic acid to an N-terminal glycine of certain substrate proteins, has been shown to be essential for various pathogens. This thesis demonstrates the design, synthesis and analysis of potential inhibitors of Plasmodium falciparum NMT. Approximately 50 inhibitors with systematic variations based on a benzothiazole scaffold have been synthesised. It is known that these benzothiazoles compete with binding of peptide substrate within the NMT enzyme binding cleft. Differences between the peptide binding pockets of P. falciparum and human NMTs were exploited to design effective and selective new antimalarial treatments. The level of inhibition was measured using SPA that monitors the transfer of 3H-labelled myristoyl CoA to the N-terminus of a polypeptide substrate. A plot of enzyme activity as a function of inhibitor concentration gave inhibition curves from which IC50-values were derived. In vitro tests resulted in four hits with improved activity in the low micromolar region against P. falciparum NMT compared to the lead compound. Nevertheless, the inhibitors were not exceptionally selective over Homo sapiens NMT with an IC50 in the low micromolar region also. Selections of the most promising inhibitors have been tested in vivo and considerable reductions in parasitemia were noted

Investigating azoreductases and NAD(P)H dependent quinone oxidoreductases in 'Pseudomonas aeruginosa'

'Psedomonas aeruginosa' is a prevalent nosocmial pathogen predominantly associated with infections in immune compromised individuals and long term colonisation and pathogenesis in the lungs of Cystic Fibrosis patients. With multi-drug resistant strains increasingly common, the discovery of novel targets for antimicrobial chemotherapy is of utmost importance and expansion of data on 'P. aeruginosa's' complex genome could facilitate this. Azoreductases are a group of enzymes mainly noted for their reductive capacity against azo and quinone compounds. Ubiquitous amongst many classes of organism including prokaryotes and eukaryotes, the primary physiological role of azoreductases remians unclear. This study characterises azoreductase-like enzymes from 'P. aeruginosa' in terms of biochemical properties, substrate specificity and structural analysis. The effect of these enzymes on bacterial physiology in 'P. aeruginosa' is also explored in relation to antibiotic susceptibility. Three azoreductase-like genes from 'P. aeruginosa' (pa1224, pa1225 and pa4975) were overexpressed in 'E. coli' strains following molecular cloning. Recombinant proteins were biochemically characterised by means of Thin Layer Chromatography, Differential Scanning Fluorimetry and ezymatic assays. All enzymes were noted to be selective for FAD as the flavin cofactor and NADPH as the preferred reductant. All three enzymes were confirmed as NAD(P)H dependent quinone oxidoreductases (NQOs) with PA1224 also catalysing reduction of the azo substrate methyl red, albeit at a rate an order of magnitude lower than that observed for the quinone compounds. The preferred flavin cofactor for four previously characterised azoreductase and NQO enzymes (PA2280, PA2580, PA1204 and PA0949) was also explored and PA2280 and PA0949 were observed to select for FMN while PA2580 and PA1204 were selective for FAD. The crystal structure of PA2580 was solved with the nicotinamide group of NADPH bound and was noted to form a homodimer with the same short flavodoxin-like fold as previously described for other members of this enzyme family. Complemented strains of azoreductase-like gene deletion mutants of 'P. aeruginosa' PAO1 were generated via molecular cloning and used to monitor the effects of these enzymes on antibiotic susceptibility. Antimicrobial sensitivity assays were carried out and although the knockout strains displayed increased sensitivity to fluroquinolones, they did not revert to the wild type phenotype upon reinsertion of the genes of interest. This study has for the first time characterised three new NQO's from 'P. aeruginosa' PAO1 and solved the crystal structure of an azoreductase/NQO with nicotinamide bound. With these findings and a library of complemented strains generated, this original study offers a platform for the continued research into the physiological role of these enzymes