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Piecewise-linear models of genetic regulatory networks: equilibria and their stability.

A formalism based on piecewise-linear (PL) differential equations, originally due to Glass and Kauffman, has been shown to be well-suited to modelling genetic regulatory networks. However, the discontinuous vector field inherent in the PL models raises some mathematical problems in defining solutions on the surfaces of discontinuity. To overcome these difficulties we use the approach of Filippov, which extends the vector field to a differential inclusion. We study the stability of equilibria (called singular equilibrium sets) that lie on the surfaces of discontinuity. We prove several theorems that characterize the stability of these singular equilibria directly from the state transition graph, which is a qualitative representation of the dynamics of the system. We also formulate a stronger conjecture on the stability of these singular equilibrium sets.

Genes, Regulator↗

Studies on bacterial conjugational crosses via model populations. II. Genetic studies.

Model populations, simulating progenies obtained from Escherichia coli Hfr x F- crosses, are generated. Linkage relations and exchange frequencies are expressed in these populations in complex, in some cases, even paradoxical manner. It is demonstrated that the origin of the complexities is located in the particular allelic configuration of the genotypes, characteristic for all exconjugant and selected populations.

Chromosomes, Bacterial↗

Using graphical models and genomic expression data to statistically validate models of genetic regulatory networks.

We propose a model-driven approach for analyzing genomic expression data that permits genetic regulatory networks to be represented in a biologically interpretable computational form. Our models permit latent variables capturing unobserved factors, describe arbitrarily complex (more than pair-wise) relationships at varying levels of refinement, and can be scored rigorously against observational data. The models that we use are based on Bayesian networks and their extensions. As a demonstration of this approach, we utilize 52 genomes worth of Affymetrix GeneChip expression data to correctly differentiate between alternative hypotheses of the galactose regulatory network in S. cerevisiae. When we extend the graph semantics to permit annotated edges, we are able to score models describing relationships at a finer degree of specification.

Bayes Theorem↗

Evolving complex dynamics in electronic models of genetic networks.

Ordinary differential equations are often used to model the dynamics and interactions in genetic networks. In one particularly simple class of models, the model genes control the production rates of products of other genes by a logical function, resulting in piecewise linear differential equations. In this article, we construct and analyze an electronic circuit that models this class of piecewise linear equations. This circuit combines CMOS logic and RC circuits to model the logical control of the increase and decay of protein concentrations in genetic networks. We use these electronic networks to study the evolution of limit cycle dynamics. By mutating the truth tables giving the logical functions for these networks, we evolve the networks to obtain limit cycle oscillations of desired period. We also investigate the fitness landscapes of our networks to determine the optimal mutation rate for evolution.

Biological Evolution↗

The "campus syndrome" in pigs: neurological, neurophysiological, and neuropharmacological characterization of a new genetic animal model of high-frequency tremor.

Inherited neurological diseases in animals are of interest to a wide range of scientific disciplines, particularly because such animals may be suited as genetic animal models for respective human disorders. Because the pig has a number of anatomic and physiologic features similar to those of human beings, this species is becoming increasingly popular in biomedical research. The usefulness of pigs as genetic models of neurological diseases is illustrated by the porcine model of malignant hyperthermia (MH), i.e., a frequently fatal myopathic disease in both pigs and humans. In the present study, we describe a new hereditary movement disorder in Pietrain pigs, which may represent a useful genetic animal model of high-frequency tremor. Because the disorder was first detected in the offspring of a boar named "Campus," we use the term "Campus syndrome" in this respect. Segregation analysis of breeding studies indicates that the syndrome is inherited as a monogenic dominant trait. DNA-based testing of the mutation involved in MH myopathy showed that expression of the Campus syndrome in pigs is not dependent on homozygosity for the MH mutation. In affected pigs, the Campus syndrome develops at an average age of 27 days. The syndrome is characterized by muscular weakness and a very intense tremor of the legs when standing and walking but not when at rest in a lying position. The intensity of tremor and muscular weakness progressively increases with age, resulting in pronounced postural instability. Despite these neurological abnormalities, body weight gain in affected pigs does not differ from that in unaffected siblings.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗

Anti-obesity and anti-diabetic effects of brain-derived neurotrophic factor in rodent models of leptin resistance.

OBJECTIVE: Obesity in rodents and humans is mostly associated with elevated plasma leptin concentrations, suggesting a new pathological concept of 'leptin resistance'. We have demonstrated that brain-derived neurotrophic factor (BDNF) can improve obesity and diabetes of C57BL/KsJ db/db (db/db) mice. In this study, we investigated whether or not BDNF is effective in two different models of leptin resistance, an acquired model and a genetic model. DESIGN: C57BL/6J mice rendered obese by consumption of a high-fat diet (diet-induced obesity (DIO) mice) were used as an acquired model and lethal yellow agouti mice (KKA(y) mice) as a genetic model of leptin resistance. Food intake and glucose metabolism were studied after acute or repetitive administration of BDNF. RESULTS: Intraperitoneal administration of BDNF (10 mg/kg, twice/day) significantly reduced cumulative food intake of DIO and KKA(y) mice, whereas they were unresponsive to leptin administration. Repetitive subcutaneous administration of BDNF (10 mg/kg daily for 6 days) reduced food intake and improved impaired glucose tolerance in DIO mice. Pair feeding of vehicle-treated DIO mice with the same amount of chow consumed by the BDNF-treated group did not improve the impaired glucose homeostasis, indicating that the antidiabetic effect is not due to decreased food intake. We also observed that BDNF is effective in improving obesity and diabetes of KKA(y) mice. CONCLUSION: This study demonstrated antiobesity and antidiabetic effects of BDNF in two different models of leptin resistance, thereby suggesting the therapeutic potential of BDNF in the treatment of leptin-resistant obesity and diabetes.

Animals↗

Genetic animal models of epilepsy as a unique resource for the evaluation of anticonvulsant drugs. A review.

Genetic animal models of epilepsy comprise genetically predisposed animal species in which seizures either occur spontaneously or in response to sensory stimulation. The major advantage of these naturally occurring epilepsies in animals as models of human epilepsy is that they simulate the clinical situation more closely than any other experimental epilepsy. Models with idiopathic spontaneous recurrent seizures are epileptic dogs, tottering mice, and rats with spike-wave absence (petit mal) seizures. In dogs, the most common seizure type are generalized tonic-clonic (grand mal) seizures. Recent epidemiological and antiepileptic drug efficacy studies strongly suggest that epileptic dogs offer a valuable model for human grand mal epilepsy. In tottering mice, two types of spontaneous recurrent seizures occur: spike-wave absence seizures and focal motor seizures. Both types differ in sensitivity to common antiepileptic drugs, which closely resembles the absence and focal types of epilepsy in humans. Spontaneously recurrent spike-wave absence seizures in rats can be selectively blocked by drugs effective in petit mal (absence) epilepsy in man, demonstrating the validity of this new petit mal model for anticonvulsant drug screening. Models with reflex seizures comprise photosensitive baboons (Papio papio) and fowl, audiogenic seizure susceptible mice and rats, and gerbils with seizures in response to different sensory stimuli. With respect to seizure types and drug efficacies in these species, rats and chickens may represent suitable models for grand mal epilepsy, whereas baboons offer a useful model of photomyoclonic seizures. Gerbils can be subdivided into animals with minor (myoclonic) and major (mostly generalized tonic-clonic) seizures, which respond differently to antiepileptic drugs and seem to provide interesting models for petit mal and grand mal epilepsy in man. In conclusion, the data summarized in this review emphasize that genetic animal models of epilepsy offer unique approaches to the evaluation of antiepileptic drugs used or usable in man.

Acoustic Stimulation↗

Long-term antidepressant treatment restores clonidine's effect on growth hormone secretion in a genetic animal model of depression.

We have recently demonstrated that various doses of clonidine failed to increase growth hormone (GH) in Fawn-hooded (FH) rats (a rat strain suggested to represent a genetic model of depression). In the present study, we investigated whether long-term antidepressant treatment might normalize clonidine's effect on GH secretion in male FH rats. Long-term (16 days) treatment with the tricyclic antidepressant, imipramine (5 mg/kg/day), the 5-HT uptake inhibiting antidepressant, fluoxetine (2.5 mg/kg/day), and the noradrenergic uptake inhibiting antidepressant, desipramine (5 mg/kg/day), accentuated clonidine's effect on GH levels. On the other hand, long-term treatment with the monoamine oxidase type-A inhibiting antidepressant, clorgyline (1 mg/kg/day) and the alpha 2-noradrenergic antagonists, yohimbine and 1-phenylpiperazine (1 mg/kg/day, each) did not modify clonidine's effect. These findings suggest enhancement of 5-HT2c receptor-mediated function following long-term treatment with uptake inhibiting antidepressants in a genetic animal model of depression.

Adrenergic alpha-2 Receptor Agonists↗

Equivalence of the mixed and regressive models for genetic analysis. I. Continuous traits.

The mixed model of segregation analysis specifies major gene effects and partitions the residual variance into polygenic and environmental components. The model explains familial correlations essentially in terms of genetic causation. The regressive model, on the other hand, is constructed by successively conditioning on ancestral phenotypes and major genes. Familial patterns of dependence are described in terms of correlations without necessarily introducing a particular scheme of causal relationship. These two approaches are compared both theoretically and numerically through computer simulations for the case of continuous traits on nuclear families. The class D regressive model, which is characterized by equal sib-sib correlations, is mathematically and numerically equivalent to the mixed model. The simpler class A regressive model, which is also characterized by equal sib-sib correlations determined in this case by the common parentage, provides good estimates of the mixed model parameters: major gene parameters and residual polygenic heritability, derived from the parent-offspring correlation. However, in the absence of a major gene, the restriction imposed by the class A model on the sibling correlation can affect the conclusions of segregation analysis: False inference of a major gene was observed in two out of ten replicates. Our simulations also indicate that the mixed model allowing for different heritabilities in adults and children leads to correct estimates of the major gene parameters and residual familial correlations (parent-offspring and sib-sib) as specified by the class A model. For all the models studied, major gene effects, when present, are correctly detected and estimated.

Adult↗

Evaluation of histo-blood group ABO genotyping in a Danish population: frequency of a novel O allele defined as O2.

Traditional blood group ABO serology is based on immunoreactivity with the carbohydrate determinants A, B and H antigens. Recent advances at the DNA level of the ABO genes have provided a molecular genetic model for the ABO polymorphism. This genetic model has to date only been tested on a limited basis. The present study was initiated to evaluate the universality of the proposed genetic model on a larger group of serologically defined ABO phenotypes. Three hundred healthy Danish blood donors were analysed (A:50, B:50, AB:50, O:150) by PCR amplification followed by diagnostic restriction enzyme cutting. In all cases A, B, and AB at least one allele of correctly predicted status was found. However, in O phenotype individuals, 11 out of 150 carried one allele discordant to the proposed genetic model. This novel O allele (3.7% allele frequency) was further characterized by diagnostic restriction enzyme analysis in two positions divergent between A and B alleles and by DNA sequencing of the two major exons. The novel O allele is termed O2 as it typed as B in nucleotide position 526 and as A in positions 703, 796, and 803, in contrast to the most predominant O allele termed O1, which types as A in all 4 positions. The structural defect in the O2 allele appears to be an additional substitution at nucleotide position 802. The results clearly demonstrate that with the addition of the two distinctly different O alleles, O1, O2, the previously proposed molecular genetic basis of the ABO polymorphism is quite valid.(ABSTRACT TRUNCATED AT 250 WORDS)

ABO Blood-Group System↗

Modeling quantitative trait Loci and interpretation of models.

A quantitative genetic model relates the genotypic value of an individual to the alleles at the loci that contribute to the variation in a population in terms of additive, dominance, and epistatic effects. This partition of genetic effects is related to the partition of genetic variance. A number of models have been proposed to describe this relationship: some are based on the orthogonal partition of genetic variance in an equilibrium population. We compare a few representative models and discuss their utility and potential problems for analyzing quantitative trait loci (QTL) in a segregating population. An orthogonal model implies that estimates of the genetic effects are consistent in a full or reduced model in an equilibrium population and are directly related to the partition of the genetic variance in the population. Linkage disequilibrium does not affect the estimation of genetic effects in a full model, but would in a reduced model. Certainly linkage disequilibrium would complicate the detection of QTL and epistasis. Using different models does not influence the detection of QTL and epistasis. However, it does influence the estimation and interpretation of genetic effects.

Gene Frequency↗

CCL2 polymorphisms are associated with serum monocyte chemoattractant protein-1 levels and myocardial infarction in the Framingham Heart Study.

BACKGROUND: Monocyte chemoattractant protein-1 (MCP-1) is a chemokine strongly implicated in promoting atherosclerosis in animal models, but human genetic evidence is contradictory. METHODS AND RESULTS: We analyzed the association of genetic variation in the MCP-1 gene (CCL2) with prevalent myocardial infarction and serum MCP-1 levels in the community-based Framingham Heart Study Offspring Cohort (50% women; mean age, 62 years). MCP-1 levels and CCL2 genotypes were determined in 3236 and 1797 individuals, respectively. Significant clinical correlates of MCP-1 levels were age, cigarette smoking, triglycerides, body mass index, and waist-to-hip ratio. The MCP-1-2578G allele located in the CCL2 regulatory region was significantly associated with both higher serum MCP-1 levels in a recessive genetic model (358+/-10 versus 328+/-3 pg/mL; P=0.002) and higher prevalence of myocardial infarction in a dominant genetic model (adjusted odds ratio, 2.0; 95% CI, 1.2 to 3.3; P=0.005). We also defined the linkage disequilibrium structure at the CCL2 locus and observed 6 common haplotypes in whites. We performed haplotype-based association analysis and found that only the most frequent haplotype, defined by the MCP-1-2578G allele, was associated with prevalent MI. CONCLUSIONS: Our data are consistent with the hypothesis that MCP-1 is involved in the pathogenesis of human atherosclerosis and myocardial infarction.

Aged↗

The heritability of breast cancer: a Bayesian correlated frailty model applied to Swedish twins data.

The aim of this study was to investigate the role of genes and environment in susceptibility to breast cancer and to give an estimate of heritability in the propensity to develop the disease. To do this we applied an interdisciplinary approach, merging models developed in the field of demography and survival analysis - so-called frailty models - and models coming from quantitative genetics and epidemiology, namely genetic models. In our study, the inferential problem was solved in a Bayesian framework and the numerical work was carried out using MCMC methods. We used the special information coming from twin data, particularly breast cancer data, from the Swedish Twin Register. The application of a correlated log-normal frailty model leads to a very large estimate of the population heterogeneity (sigma = 6.7), and relatively small correlations between co-twins' frailties - around 0.3 for monozygotic and 0.1 for dizygotic twins. Comparing three different genetic models (an ACE, an AE and an ADE model), we furthermore concluded that genetic effects would explain globally almost 30% of the total variability of propensity to breast cancer. Environmental effects would be predominant in determining breast cancer susceptibility and these effects would be primarily individual-specific, that is, non-shared effects. Finally, a model which includes dominance genetic effects (ADE model) is preferred for genetic and statistical reasons.

Bayes Theorem↗

Lentiviral nigral delivery of GDNF does not prevent neurodegeneration in a genetic rat model of Parkinson's disease.

Viral delivery of glial cell line-derived neurotrophic factor (GDNF) currently represents one of the most promising neuroprotective strategies for Parkinson's Disease (PD). However, the effect of this neurotrophic factor has never been tested in the newly available genetic models of PD based on the viral expression of mutated alpha-synuclein. In this study, we evaluated the ability of lentiviral vectors coding for GDNF (lenti-GDNF) to prevent nigral dopaminergic degeneration associated with the lentiviral mediated expression of the A30P mutant human alpha-synuclein (lenti-A30P). This virally based rat model develops a progressive and selective loss of dopamine neurons associated with the appearance of alpha-synuclein containing inclusions, thus recapitulating the major hallmarks of PD. Lenti-GDNF was injected in the substantia nigra 2 weeks before nigral administration of lenti-A30P. Although a robust expression of GDNF was observed in the whole nigrostriatal pathway due to retrograde and/or anterograde transport, lenti-GDNF did not prevent the alpha-synuclein-induced dopaminergic neurodegeneration in the lentiviral-based genetic rat model of PD. These results suggest that sustained GDNF treatment cannot modulate the cellular toxicity related to abnormal folded protein accumulation as mutated human alpha-synuclein.

Animals↗

Chemical models of genetic toggle switches.

We study by mean-field analysis and stochastic simulations chemical models for genetic toggle switches formed from pairs of genes that mutually repress each other. To determine the stability of the genetic switches, we make a connection with reactive flux theory and transition state theory. The switch stability is characterized by a well-defined lifetime tau. We find that tau grows exponentially with the mean number N of transcription factor molecules involved in the switching. In the regime accessible to direct numerical simulations, the growth law is well-characterized by tau approximately N(alpha) exp(bN), where alpha and b are parameters. The switch stability is decreased by phenomena that increase the noise in gene expression, such as the production of multiple copies of a protein from a single mRNA transcript (shot noise) and fluctuations in the number of proteins produced per transcript. However, robustness against biochemical noise can be drastically enhanced by arranging the transcription factor binding domains on the DNA such that competing transcription factors mutually exclude each other on the DNA. We also elucidate the origin of the enhanced stability of the exclusive switch with respect to that of the general switch; while the kinetic prefactor is roughly the same for both switches, the "barrier" for flipping the switch is significantly higher for the exclusive switch than that for the general switch.

Animals↗

[Kinetic developmental genetics analysis of Hibiscus cannabinus plant height and stem diameter].

By using quantitative traits additive-dominance genetics model and developmental genetics model, this paper analyzed the developmental behaviors of gene expression for Hibiscus cannabinu plant height and stem diameter at its different growth stages. The results showed that at different growth stages, the unconditional and conditional genetics effects of plant height all showed dominance, while the additive effect was weak. No additive effect was found for stem diameter, but dominance effect was significant at each growth stage. Plant height and stem diameter all had active gene expression from July 28 to August 9, and from September 2 to September 14. There was no additive correlation between plant height and stem diameter, but positive dominance correlation was significant after August 21. The unconditional and conditional genetics effects of plant height and stem diameter were not completely the same. According to practice, conditional genetic analysis could indicate the gene expression more truly in the whole growth period. The ecological and genetics variation patterns of Hibiscus cannabinus plant height and stem diameter at different space-time growth stages implied by our research was of significance in Hibiscus cannabinus genetics and breeding in both theory and practice.

Genes, Plant↗