Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

Software for signaling networks, electronic and cellular

Cellular signaling networks have many similarities with electronic circuits. Therefore, the tools used to test and analyze electronic circuits can be adapted to analyze cellular signaling processes. Lok describes some of these signaling network analysis tools, their underlying principles, and their limitations.

Modeling and simulation of pathways in menopause

The analytical representation and simulation of complex molecular pathways can contribute to understanding and evaluating physiological as well as pathological processes. We are interested in modeling the processes of menopause to stratify women in terms of the genotypic and environmental components and their implications for development of individualized risk of postmenopausal disorders, e.g., breast and ovarian cancer, cardiovascular disease, and osteoporosis. We have initiated this study using the UltraSAN package to analyze the pathway associated with estrogen production. This model incorporates detailed information about the hormone factors affecting estrogen production, and the simulations carried out are based on published experimental data corresponding to hormone levels during the course of the normal female reproductive cycle. The agreement between the experimental data and the simulation is typically less than 2 ng/ml or 2 pg/ml respectively for progesterone and estradiol output. This approach further permits inclusion of information about an SNP observed in the gene coding for the enzyme aromatase as a model to study the impact of reduced enzymatic activity on hormone levels.

Stochastic kinetic analysis of the Escherichia coli stress circuit using sigma(32)-targeted antisense

A stochastic Petri net model was developed for simulating the sigma(32) stress circuit in E. coli. Transcription factor sigma(32) is the principal regulator of the response of E. coli to heat shock. Stochastic Petri net (SPN) models are well suited for kinetics characterization of fluxes in biochemical pathways. Notably, there exists a one-to-one mapping of model tokens and places to molecules of particular species. Our model was validated against experiments in which ethanol (inducer of heat shock response) and sigma(32)-targeted antisense (downward regulator) were used to perturb the sigma(32) regulatory pathway. The model was also extended to simulate the effects of recombinant protein production. Results show that the stress response depends heavily on the partitioning of sigma(32) within the cell; that is, sigma(32) becomes immediately available to mediate a stress response because it exists primarily in a sequestered, inactive form, complexed with chaperones DnaK, DnaJ, and GrpE. Recombinant proteins, however, also compete for chaperone proteins, particularly when folded improperly. Our simulations indicate that when the expression of recombinant protein has a low requirement for DnaK, DnaJ, and GrpE, the overall sigma(32) levels may drop, but the level of heat shock proteins will increase. Conversely, when the overexpressed recombinant protein has a strong requirement for the chaperones, a severe response is predicted. Interestingly, both cases were observed experimentally.

The future is noisy: the role of spatial fluctuations in genetic switching

A genetic switch may be realized by a certain operator sector on the DNA strand from which either genetic code, to the left or to the right of this operator sector, can be transcribed and the corresponding information processed. This switch is controlled by messenger molecules, i.e., they determine to which side the switch is flipped. Recently, it has been realized that noise plays an elementary role in genetic switching, and the effect of number fluctuations of the messenger molecules have been explored. Here we argue that the assumption of well stirredness taken in the previous models may not be sufficient to characterize the influence of noise: spatial fluctuations play a non-negligible part in cellular genetic switching processes.

Integrating naive Bayes models and external knowledge to examine copper and iron homeostasis in S. cerevisiae

A novel suite of analytical techniques and visualization tools are applied to 78 published transcription profiling experiments monitoring 5,687 Saccharomyces cerevisiae genes in studies examining cell cycle, responses to stress, and diauxic shift. A naive Bayes model discovered and characterized 45 classes of gene profile vectors. An enrichment measure quantified the association between these classes and specific external knowledge defined by four sets of categories to which genes can be assigned: 106 protein functions, 5 stages of the cell cycle, 265 transcription factors, and 16 chromosomal locations. Many of the 38 genes in class 42 are known to play roles in copper and iron homeostasis. The 17 uncharacterized open reading frames in this class may be involved in similar homeostatic processes; human homologs of two of them could be associated with as yet undefined disease states arising from aberrant metal ion regulation. The Met4, Met31, and Met32 transcription factors may play a role in coregulating genes involved in copper and iron metabolism. Extensions of the simple graphical model used for clustering to learning more complex models of genetic networks are discussed.

Analysis of molecular profile data using generative and discriminative methods

A modular framework is proposed for modeling and understanding the relationships between molecular profile data and other domain knowledge using a combination of generative (here, graphical models) and discriminative [Support Vector Machines (SVMs)] methods. As illustration, naive Bayes models, simple graphical models, and SVMs were applied to published transcription profile data for 1,988 genes in 62 colon adenocarcinoma tissue specimens labeled as tumor or nontumor. These unsupervised and supervised learning methods identified three classes or subtypes of specimens, assigned tumor or nontumor labels to new specimens and detected six potentially mislabeled specimens. The probability parameters of the three classes were utilized to develop a novel gene relevance, ranking, and selection method. SVMs trained to discriminate nontumor from tumor specimens using only the 50-200 top-ranked genes had the same or better generalization performance than the full repertoire of 1,988 genes. Approximately 90 marker genes were pinpointed for use in understanding the basic biology of colon adenocarcinoma, defining targets for therapeutic intervention and developing diagnostic tools. These potential markers highlight the importance of tissue biology in the etiology of cancer. Comparative analysis of molecular profile data is proposed as a mechanism for predicting the physiological function of genes in instances when comparative sequence analysis proves uninformative, such as with human and yeast translationally controlled tumour protein. Graphical models and SVMs hold promise as the foundations for developing decision support systems for diagnosis, prognosis, and monitoring as well as inferring biological networks.

From genotype to phenotype: buffering mechanisms and the storage of genetic information

DNA sequence variation is abundant in wild populations. While molecular biologists use genetically homogeneous strains of model organisms to avoid this variation, evolutionary biologists embrace genetic variation as the material of evolution since heritable differences in fitness drive evolutionary change. Yet, the relationship between the phenotypic variation affecting fitness and the genotypic variation producing it is complex. Genetic buffering mechanisms modify this relationship by concealing the effects of genetic and environmental variation on phenotype. Genetic buffering allows the build-up and storage of genetic variation in phenotypically normal populations. When buffering breaks down, thresholds governing the expression of previously silent variation are crossed. At these thresholds, phenotypic differences suddenly appear and are available for selection. Thus, buffering mechanisms modulate evolution and regulate a balance between evolutionary stasis and change. Recent work provides a glimpse of the molecular details governing some types of genetic buffering.

Modeling stochastic gene expression: implications for haploinsufficiency

There is increasing recognition that stochastic processes regulate highly predictable patterns of gene expression in developing organisms, but the implications of stochastic gene expression for understanding haploinsufficiency remain largely unexplored. We have used simulations of stochastic gene expression to illustrate that gene copy number and expression deactivation rates are important variables in achieving predictable outcomes. In gene expression systems with non-zero expression deactivation rates, diploid systems had a higher probability of uninterrupted gene expression than haploid systems and were more successful at maintaining gene product above a very low threshold. Systems with relatively rapid expression deactivation rates (unstable gene expression) had more predictable responses to a gradient of inducer than systems with slow or zero expression deactivation rates (stable gene expression), and diploid systems were more predictable than haploid, with or without dosage compensation. We suggest that null mutations of a single allele in a diploid organism could decrease the probability of gene expression and present the hypothesis that some haploinsufficiency syndromes might result from an increased susceptibility to stochastic delays of gene initiation or interruptions of gene expression.