Modelling the evolution of the archaeal tryptophan synthase

Background  

Microorganisms and plants are able to produce tryptophan. Enzymes catalysing the last seven steps of tryptophan biosynthesis are encoded in the canonical trp operon. Among the trp genes are most frequently trpA and trpB, which code for the alpha and beta subunit of tryptophan synthase. In several prokaryotic genomes, two variants of trpB (named trpB1 or trpB2) occur in different combinations. The evolutionary history of these trpB genes is under debate.     

Modeling real eukaryotic control gene subnetworks based on generalized threshold models]

Mathematical and computational means are developed that take into consideration the specifics of control processes at the molecular level and allow one to obtain both qualitative and quantitative patterns of gene network dynamics. Using the method of generalized threshold models, models are constructed for the Arabidopsis thaliana flower morphogenesis control subsystem and gene subnetwork controlling the Drosophila melanogaster early ontogeny. The dynamics of these systems are investigated: kinetic curves are computed for molecular components (RNA, proteins), possible modes of functioning and steady states of the nets are revealed and biologically interpreted. The models are shown to be adequate to the real processes. The effectiveness of the generalized threshold model method is evaluated in the analysis of the actual eukaryotic gene networks.     

Isolation of the novel regulatory mutants of the tryptophan biosynthetic system in Escherichia coli

Summary A novel type of tryptophan requiring mutants of Escherichia coli was isolated. The mutation maps between str and malA.These mutants, designated as trpS, have alterations in the regulation of the tryptophan operon. Neither derepression nor complete repression of the tryptophan biosynthetic enzymes was observed with this mutant. Dominance test shows that the trpS mutation is recessive to the wild type allele. TrpS mutant, therefore, is a type of super-repressed mutants distinct from i ^s mutant in the lactose system of E. coli.It was found that the tryptophanyl-tRNA synthetase is specified by the trpS gene. This indicates that the transfer mechanism of tryptophan is related to repression of the tryptophan operon.     

Lung cancer rate predictions using generalized additive models

Predictions of lung cancer incidence and mortality are necessary for planning public health programs and clinical services. It is proposed that generalized additive models (GAMs) are practical for cancer rate prediction. Smooth equivalents for classical age-period, age-cohort, and age-period-cohort models are available using one-dimensional smoothing splines. We also propose using two-dimensional smoothing splines for age and period. Variance estimation can be based on the bootstrap. To assess predictive performance, we compared the models with a Bayesian age-period-cohort model. Model comparison used cross-validation and measures of predictive performance for recent predictions. The models were applied to data from the World Health Organization Mortality Database for females in five countries. Model choice between the age-period-cohort models and the two-dimensional models was equivocal with respect to cross-validation, while the two-dimensional GAMs had very good predictive performance. The Bayesian model performed poorly due to imprecise predictions and the assumption of linearity outside of observed data. In summary, the two-dimensional GAM performed well. The GAMs make the important prediction that female lung cancer rates in these countries will be stable or begin to decline in the future.     

Modelling biological processes using workflow and Petri Net models

MOTIVATION: Biological processes can be considered at many levels of detail, ranging from atomic mechanism to general processes such as cell division, cell adhesion or cell invasion. The experimental study of protein function and gene regulation typically provides information at many levels. The representation of hierarchical process knowledge in biology is therefore a major challenge for bioinformatics. To represent high-level processes in the context of their component functions, we have developed a graphical knowledge model for biological processes that supports methods for qualitative reasoning. RESULTS: We assessed eleven diverse models that were developed in the fields of software engineering, business, and biology, to evaluate their suitability for representing and simulating biological processes. Based on this assessment, we combined the best aspects of two models: Workflow/Petri Net and a biological concept model. The Workflow model can represent nesting and ordering of processes, the structural components that participate in the processes, and the roles that they play. It also maps to Petri Nets, which allow verification of formal properties and qualitative simulation. The biological concept model, TAMBIS, provides a framework for describing biological entities that can be mapped to the workflow model. We tested our model by representing malaria parasites invading host erythrocytes, and composed queries, in five general classes, to discover relationships among processes and structural components. We used reachability analysis to answer queries about the dynamic aspects of the model. AVAILABILITY: The model is available at http://smi.stanford.edu/projects/helix/pubs/process-model/.     

Modelling the evolution of genetic regulatory networks

An evolutionary model of genetic regulatory networks is developed, based on a model of network encoding and dynamics called the Artificial Genome (AG). This model derives a number of specific genes and their interactions from a string of (initially random) bases in an idealized manner analogous to that employed by natural DNA. The gene expression dynamics are determined by updating the gene network as if it were a simple Boolean network. The generic behaviour of the AG model is investigated in detail. In particular, we explore the characteristic network topologies generated by the model, their dynamical behaviours, and the typical variance of network connectivities and network structures. These properties are demonstrated to agree with a probabilistic analysis of the model, and the typical network structures generated by the model are shown to lie between those of random networks and scale-free networks in terms of their degree distribution. Evolutionary processes are simulated using a genetic algorithm, with selection acting on a range of properties from gene number and degree of connectivity through periodic behaviour to specific patterns of gene expression. The evolvability of increasingly complex patterns of gene expression is examined in detail. When a degree of redundancy is introduced, the average number of generations required to evolve given targets is reduced, but limits on evolution of complex gene expression patterns remain. In addition, cyclic gene expression patterns with periods that are multiples of shorter expression patterns are shown to be inherently easier to evolve than others. Constraints imposed by the template-matching nature of the AG model generate similar biases towards such expression patterns in networks in initial populations, in addition to the somewhat scale-free nature of these networks. The significance of these results on current understanding of biological evolution is discussed.     

Kinetic determination of tryptophan by using the B-Z oscillating chemical system

A simple and rapid method was devised for determination of tryptophan, based on the Belousov-Zhabotinskii (B-Z) oscillating chemical system. Changes in oscillating period and amplitude were linearly proportional to the negative logarithm of l-tryptophan concentration over the range of 6.44 × 10⁻⁷–2.55 × 10⁻⁴ M, with the regression coefficients of near unity and a lower detection limit of 6.5 × 10⁻⁸ M. d-tryptophan was also examined although it is rarely found in most biological fluids, and perhaps not at all in natural proteins. The change of period against to negative logarithm of d-tryptophan concentration over the range of 4.9 × 10⁻⁵–8.24 × 10⁻⁴ M is linear. Because the optimum conditions for determination of l- and d-tryptophan are not the same, a little amount of d-tryptophan does not affect the determination of l-tryptophan. Various influences were studied and a possible mechanism of perturbation to the B-Z oscillator by tryptophan was also discussed. Spectrophotometry and fluorescence spectrophotofluorimetry were used for comparision and confirmation of the results.     

Modelling spatial vision at the threshold level.

Some available single- and multiple-channel models are reviewed. Multichannel models are generalized and tested against threshold data on various stimulus sets. Without using the explicit assumption of spatial probability summation, simple multichannel models are shown to provide good simultaneous predictions of threshold curves of sinewave gratings and other gratings. They fail in predicting threshold curves of disk-shaped stimuli. If global or local spatial probability summation within channels is incorporated into the models, correctly shaped threshold curves of disks can be predicted. However, the predicted curves appear still too low if compared to measured curves. The same holds for noise gratings. Possible extensions of the models, based on local summation between channel responses and/or models consisting of initial isotropic channels (retina) followed by anisotropic channels (cortex), are discussed.     

Naturally occurring sites within the Shigella dysenteriae tryptophan operon severely limit tryptophan biosynthesis.

We investigated the structural, functional, and regulatory properties of the Shigella dysenteriae tryptophan (trp.) operon in transduction hybrids in which the cysB-trp-region of Escherichia coli is replaced by the corresponding region from S. dysenteriae. Tryptophan biosynthesis was largely blocked in the hybrids, although the order of the structural genes was identical with that of E. coli. Nutritional tests and enzyme assays revealed that the hybrids produced a defective anthranilate synthetase (ASase). Deletion mapping identified two distinct sites in trpE, each of which was partially responsible for the instability and low activity of ASase. We also discovered a pleiotropic site trpP (S) that maps outside the structural gene region and is closely linked to the S. dysenteriae trp operator. trpP (S) reduced the rate of trp messenger ribonucleic acid synthesis, and consequently trp enzyme levels, 10-fold relative to wild-type E. coli. In recombinants in which the structural genes of E coli were under the control of the S. dysenteriae promoter, enzyme levels were also reduced 10-fold. In some fast-growing revertants of the original hybrids, the rates of trp messenger ribonucleic acid synthesis and levels of tryptophan synthetase were restored to values characteristic of wild-type E.coli. Thus, the Trp auxotrophy associated with the S dysenteriae trp operon derives from the combination of a defective ASase and decreased expression of the entire operon imposed by trpP (S).     

Modelling the growth curve of Maine-Anjou beef cattle using heteroskedastic random coefficients models

A heteroskedastic random coefficients model was described for analyzing weight performances between the 100th and the 650th days of age of Maine-Anjou beef cattle. This model contained both fixed effects, random linear regression and heterogeneous variance components. The objective of this study was to analyze the difference of growth curves between animals born as twin and single bull calves. The method was based on log-linear models for residual and individual variances expressed as functions of explanatory variables. An expectation-maximization (EM) algorithm was proposed for calculating restricted maximum likelihood (REML) estimates of the residual and individual components of variances and covariances. Likelihood ratio tests were used to assess hypotheses about parameters of this model. Growth of Maine-Anjou cattle was described by a third order regression on age for a mean growth curve, two correlated random effects for the individual variability and independent errors. Three sources of heterogeneity of residual variances were detected. The difference of weight performance between bulls born as single and twin bull calves was estimated to be equal to about 15 kg for the growth period considered.     

Estimating parameters for generalized mass action models using constraint propagation

As modern molecular biology moves towards the analysis of biological systems as opposed to their individual components, the need for appropriate mathematical and computational techniques for understanding the dynamics and structure of such systems is becoming more pressing. For example, the modeling of biochemical systems using ordinary differential equations (ODEs) based on high-throughput, time-dense profiles is becoming more common-place, which is necessitating the development of improved techniques to estimate model parameters from such data. Due to the high dimensionality of this estimation problem, straight-forward optimization strategies rarely produce correct parameter values, and hence current methods tend to utilize genetic/evolutionary algorithms to perform non-linear parameter fitting. Here, we describe a completely deterministic approach, which is based on interval analysis. This allows us to examine entire sets of parameters, and thus to exhaust the global search within a finite number of steps. In particular, we show how our method may be applied to a generic class of ODEs used for modeling biochemical systems called Generalized Mass Action Models (GMAs). In addition, we show that for GMAs our method is amenable to the technique in interval arithmetic called constraint propagation, which allows great improvement of its efficiency. To illustrate the applicability of our method we apply it to some networks of biochemical reactions appearing in the literature, showing in particular that, in addition to estimating system parameters in the absence of noise, our method may also be used to recover the topology of these networks.