Mathematical simulation of the interactions among cyanobacteria, purple sulfur bacteria and chemotrophic sulfur bacteria in microbial mat communities

Abstract: A deterministic one-dimensional reaction diffusion model was constructed to simulate benthic stratification patterns and population dynamics of cyanobacteria, purple and colorless sulfur bacteria as found in marine microbial mats. The model involves the major biogeochemical processes of the sulfur cycle and includes growth metabolism and their kinetic parameters as described from laboratory experimentation. Hence, the metabolic production and consumption processes are coupled to population growth. The model is used to calculate benthic oxygen, sulfide and light profiles and to infer spatial relationships and interactions among the different populations. Furthermore, the model is used to explore the effect of different abiotic and biotic environmental parameters on the community structure. A strikingly clear pattern emerged of the interaction between purple and colorless sulfur bacteria: either colorless sulfur bacteria dominate or a coexistence is found of colorless and purple sulfur bacteria. The model predicts that purple sulfur bacteria only proliferate when the studied environmental parameters surpass well-defined threshold levels. However, once the appropriate conditions do occur, the purple sulfur bacteria are extremely successful as their biomass outweighs that of colorless sulfur bacteria by a factor of up to 17. The typical stratification pattern predicted closely resembles the often described bilayer communities which comprise a layer of purple sulfur bacteria below a cyanobacterial top-layer; colorless sulfur bacteria are predicted to sandwich in between both layers. The profiles of oxygen and sulfide shift on a diel basis similarly as observed in real systems.     

Evaluation of several methods for estimating phylogenetic trees when substitution rates differ over nucleotide sites

Several maximum likelihood and distance matrix methods for estimating phylogenetic trees from homologous DNA sequences were compared when substitution rates at sites were assumed to follow a gamma distribution. Computer simulations were performed to estimate the probabilities that various tree estimation methods recover the true tree topology. The case of four species was considered, and a few combinations of parameters were examined. Attention was applied to discriminating among different sources of error in tree reconstruction, i.e., the inconsistency of the tree estimation method, the sampling error in the estimated tree due to limited sequence length, and the sampling error in the estimated probability due to the number of simulations being limited. Compared to the least squares method based on pairwise distance estimates, the joint likelihood analysis is found to be more robust when rate variation over sites is present but ignored and an assumption is thus violated. With limited data, the likelihood method has a much higher probability of recovering the true tree and is therefore more efficient than the least squares method. The concept of statistical consistency of a tree estimation method and its implications were explored, and it is suggested that, while the efficiency (or sampling error) of a tree estimation method is a very important property, statistical consistency of the method over a wide range of, if not all, parameter values is prerequisite.     

Monte Carlo Study of Structural and Thermodynamic Properties of Liquid Chloroform Using a Five Site Model

A five site potential model combining Lennard–Jones plus Coulomb potential functions has been developed for chloroform molecule. The partial charges needed for Coulombic interactions were derived using the chelpg procedure implemented in the gaussian 92 program. These calculations were performed at the MP2 level with MC-311G* basis set for Cl and 6-311G** for C and H atoms. The parameters for the Lennard–Jones potentials were optimized to reproduce experimental values for the density and enthalpy of vaporization of the pure liquid at 298 K and 1 atm. The statistical mechanics calculations were performed with the Monte Carlo method in the isothermic and isobaric (NpT) ensemble. Besides the values obtained for density, ρ, and molar enthalpy of vaporization at constant pressure, Δ H_V, for liquid chloroform, results for molar volume, V_m, molar heat capacity, C_p, isobaric thermal expansivity, α_p, and isothermal compressibility, κ_T, for this pure liquid are also in very good agreement with experimental observations. Size effects on the values of thermodynamic properties were investigated. The potential model was also tested by computing the free energy for solvating one chloroform molecule into its own liquid at 298 K using a statistical perturbation approach. The result obtained compares well with the experimental value. Site–site pair correlation functions were calculated and are in good accordance with theoretical results available in the literature. Dipole–dipole correlation functions for the present five site model were also calculated at different carbon–carbon distances. These correlations were compared to those obtained using the four site model reported in the literature. An investigation of the solvent dependence of the relative free energy for cis/trans conversion of a hypothetical solute in TIP4P water and chloroform was accomplished. The results show strong interaction of water and chloroform molecules with the gauche conformer. The value obtained for the free energy barrier for cis/trans rotation in TIP4P water is higher than that for chloroform. This result is in agreement with the continuous theory for solvation as the conformer with higher dipole moment is more favoured by the solvent with higher dieletric constant. The results also show an increase in entropy as the solute goes from the cis to the trans geometry and this result is more appreciable in the aqueous solution. This revised version was published online in June 2006 with corrections to the Cover Date.     

Molecular dynamics simulations of phenylimidazole inhibitor complexes of cytochrome P450 cam

Molecular dynamics simulations have been performed on three phenylimidazole inhibitor complexes ofP450 _cam, utilizing the X-ray structures and the AMBER suite of programs. Compared to their corresponding optimized X-ray structures, very similar features were observed for the 1-phenylimidazole (1-PI) and 2-phenylimidazole (2-PI) complexes during a 100 ps MD simulation. The 1-PI inhibitor binds as a Type II complex with the imidazole nitrogen as a ligand of the heme iron. Analysis of the inhibitor-enzyme interctions during the MD simulations reveals that electrostatic interactions of the imidazole with the heme and van der Waals interactions of the phenyl ring with nearby hydrophobic residues are dominant. By contrast, 2-PI binds as a Type I inhibitor in the substrate binding pocket, but not as a ligand of the iron. The interactions of this inhibitor are qualitatively different from that of the Type II 1-PI, being mainly electrostatic/H-bonding interactions with a bound water and polar residues. Although the third compound, 4-PI, in common with 1-PI, also binds as a Type II inhibitor, with one nitrogen of the imidazole as a ligand to the iron, the MD average binding orientation deviates significantly from the X-ray structure. The most important changes observed include: (1) the rotation of the imidazole ring of this inhibitor by about 90° to enhance electrostatic interactions of the imidazole NH group with the carbonyl group of LEU244, and (2) the rotation of the carbonyl group of ASP251 to form a H-bond with VAL254. An analysis of the H-bonding network surrounding this substrate in the optimized crystal structure revealed that there is no H-bonding partner either for the free polar NH group in the imidazole ring of 4-phenylimidazole or for the polar carbonyl group of the nearby ASP251 residue. The deviation of the dynamically averaged inhibitor-enzyme structure of the 4-PI complex from the optimized crystal structure can therefore be rationalized as a consequence of the optimization of the electrostatic interactions among the polar groups.     

Computer simulation and interpretation of45Ca efflux profile patterns

Summary Stimulations or inhibitions by various agents of⁴⁵Ca efflux from prelabeled cells or tissues display distinct and reproducible profile patterns when the results are plotted against time as fractional efflux ratios (FER). FER is the fractional efflux of⁴⁵Ca from stimulated cells divided by the fractional efflux from a control unstimulated group. These profile patterns fall into three categories: peak patterns, exponential patterns, and mixed patterns. Each category can be positive (stimulation) or negative (inhibition). The interpretation of these profiles is difficult because⁴⁵Ca efflux depends on three variables: the rate of calcium transport out of the cell, the specific activity of the cell compartment from which the calcium originates, and the concentration of free calcium in this compartment. A computer model based on data obtained by kinetic analyses of⁴⁵Ca desaturation curves and consisting of two distinct intracellular pools was designed to follow the concentration of the traced substance (⁴⁰Ca), the tracer (⁴⁵Ca), and the specific activity of each compartment before, during, and after the stimulation or the inhibition of calcium fluxes at various pool boundaries. The computer model can reproduce all the FER profiles obtained experimentally and bring information which may be helpful to the interpretation of this type of data. Some predictions of the model were tested experimentally, and the results support the views that a peak pattern may reflect a sustained change in calcium transport across the plasma membrane, that an exponential pattern arises from calcium mobilization from an internal subcellular pool, and that a mixed pattern may be caused by a simultaneous change in calcium fluxes at both compartment boundaries.     

Infanticide and fertility among Eskimos: A computer simulation

Until recently, certain Eskimo groups were reported to practice female infanticide in the belief that the time spent suckling a girl would delay the mother's next opportunity to bear a son, males being preferred to females because of their future role as providers in a hunting economy. From sex ratios in census data, rates of female infanticide of up to 66% for some groups have been inferred, leading some ethnographers to conclude that these groups were headed for extinction. Eskimo beliefs regarding the effects of infanticide on fertility, however, are in accord with the results of research on the relation of fertility and lactation: The cessation of lactation following infanticide would significantly shortern the expected interval until the next birth. Given this fact and available field data regarding the parameters of Eskimo population growth, the present computer simulation indicates that Eskimo populations could sustain a rate of 30% female infanticide and still survive. Higher reported rates are explained as the combined result of female infanticide plus the tendency of ethnographers to overestimate to overestimate the ages of juvenile females relative to juvenile males.     

Rate-controlling steps of oxidative phosphorylation in rat liver mitochondria. A synoptic approach of model and experiment

The contribution of different steps to the control of oxidative phosphorylation in isolated rat liver mitochondria was investigated by a combination of experiments and computer simulations. The parameters of the mathematical model of phosphorylating mitochondria were derived from experimental data. The model correctly describes the competition between ATP utilization inside and outside mitochondria for the ATP generated in mitochondria. On the basis of the good agreement between experiments and simulations, the contribution of different steps to the control of respiration was estimated by computing their control strengths, i.e., the influence of their activities on the rate of respiration. The rate-controlling influences vary depending on the load of oxidative phosphorylation. The predominant steps are: in the fully active state (State 3) — the hydrogen supply to the respiratory chain; in the resting state (State 4) — the proton leak of the mitochondrial inner membrane; in states of non-maximum ATP export — the adenine nucleotide translocator. Titrations of respiration with phenylsuccinate, antimycin, oligomycin and carboxyatractyloside completely support these conclusions.     

Simulation of fermentation conditions for vitamin B12 biosynthesis from whey

Vitamin B₁₂ production in fermentation of Propionibacterium shermanii and Propionibacterium arl AKU 1251 in whey permeate medium has been studied. The observed results and simulated expected values obtained by fitting statistical equations to the recorded data showed that 24 h old inoculum, 5 mg iron l^?1 and 4% whey lactose were optimal for vitamin B₁₂ biosynthesis in both strains when fermentation was carried out under anerobic (84 h) and aerobic (84 h) conditions at 30°C. The supplementation of whey medium with 0.5% (NH₄)₂HPO₄ enhanced further the metabolite yield; however, the preference for a mixed carbon source (lactose + d-glucose or lactose + d-fructose) at different levels varied in the strains under study. P. shermanii, under optimal cultural conditions, was found to be a better strain than Propionibacterium arl AKU, 1251 in fermenting whey lactose for product (vitamin B₁₂) formation.