Collective oscillation period of inter-coupled biological negative cyclic feedback oscillators

A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from that of an autonomous oscillator. Based on cyclic feedback oscillators, we analyze the collective oscillation pattern of coupled cellular oscillators. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior. Then we estimate the collective oscillation period based on a novel multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design.Comment: arXiv admin note: substantial text overlap with arXiv:1203.125

Seasonal reproduction in a fluctuating energy environment: Insolation-driven synchronized broadcast spawning in corals

*Background/Question/Methods:* Colonies of spawning corals reproduce in mass-spawning events, in which polyps within each colony release sperm and eggs for fertilization in the water column, with fertilization occurring only between gametes from different colonies. Participating colonies synchronize their gamete release to a window of a few hours once a year (for the species Acropora digitifera we study experimentally). This remarkable synchrony is essential for successful coral reproduction and thus, maintenance of the coral reef ecosystem that is currently under threat from local and global environmental effects such as pollution, global warming and ocean acidification. The mechanisms determining this tight synchrony in reproduction are not well understood, although several influences have been hypothesized and studied including lunar phase, solar insolation, and influences of temperature and tides. Moreover, most corals are in a symbiotic relationship with photosynthetic algae (Symbiodinium spp.) that live within the host tissue. Experiments supported by detailed bioenergetic modeling of the coral-algae symbiosis have shown that corals receive >90% of their energy needs from these symbionts. We develop a bioenergetic integrate-and-fire model in order to investigate whether annual insolation rhythms can entrain the gametogenetic cycles that produce mature gametes to the appropriate spawning season, since photosynthate is their primary source of energy. We solve the integrate-and-fire bioenergetic model numerically using the Fokker-Planck equation and use analytical tools such as rotation number to study entrainment.

*Results/Conclusions:* In the presence of short-term fluctuations in the energy input, our model shows that a feedback regulatory mechanism is required to achieve coherence of spawning times to within one lunar cycle, in order for subsequent cues such as lunar and diurnal light cycles to unambiguously determine the “correct” night of spawning. Entrainment to the annual insolation cycle is by itself not sufficient to produce the observed coherence in spawning. The feedback mechanism can also provide robustness against population heterogeneity due to genetic and environmental effects. We also discuss how such bioenergetic, stochastic, integrate-and-fire models are also more generally applicable: for example to aquatic insect emergence, synchrony in cell division and masting in trees

A Conic Sector-Based Methodology for Nonlinear Control Design

A design method is presented for the analysis and synthesis of robust nonlinear controllers for chemical engineering systems. The method rigorously treats the effect of unmeasured disturbances and unmodeled dynamics on the stability and performance properties of a nonlinear system. The results utilise new extensions of structured singular value theory for analysis and recent synthesis results for approximate linearisation

Quantitative performance metrics for robustness in circadian rhythms

Motivation: Sensitivity analysis provides key measures that aid in unraveling the design principles responsible for the robust performance of biological networks. Such metrics allow researchers to investigate comprehensively model performance, to develop more realistic models, and to design informative experiments. However, sensitivity analysis of oscillatory systems focuses on period and amplitude characteristics, while biologically relevant effects on phase are neglected. Results: Here, we introduce a novel set of phase-based sensitivity metrics for performance: period, phase, corrected phase and relative phase. Both state- and phase-based tools are applied to free-running Drosophila melanogaster and Mus musculus circadian models. Each metric produces unique sensitivity values used to rank parameters from least to most sensitive. Similarities among the resulting rank distributions strongly suggest a conservation of sensitivity with respect to parameter function and type. A consistent result, for instance, is that model performance of biological oscillators is more sensitive to global parameters than local (i.e. circadian specific) parameters. Discrepancies among these distributions highlight the individual metrics' definition of performance as specific parametric sensitivity values depend on the defined metric, or output. Availability: An implementation of the algorithm in MATLAB (Mathworks, Inc.) is available from the authors. Contact: [email protected] Supplementary information: Supplementary Data are available at Bioinformatics onlin

Iterative approach to model identification of biological networks

BACKGROUND: Recent advances in molecular biology techniques provide an opportunity for developing detailed mathematical models of biological processes. An iterative scheme is introduced for model identification using available system knowledge and experimental measurements. RESULTS: The scheme includes a state regulator algorithm that provides estimates of all system unknowns (concentrations of the system components and the reaction rates of their inter-conversion). The full system information is used for estimation of the model parameters. An optimal experiment design using the parameter identifiability and D-optimality criteria is formulated to provide "rich" experimental data for maximizing the accuracy of the parameter estimates in subsequent iterations. The importance of model identifiability tests for optimal measurement selection is also considered. The iterative scheme is tested on a model for the caspase function in apoptosis where it is demonstrated that model accuracy improves with each iteration. Optimal experiment design was determined to be critical for model identification. CONCLUSION: The proposed algorithm has general application to modeling a wide range of cellular processes, which include gene regulation networks, signal transduction and metabolic networks

Robust Controller Design for a Nonlinear CSTR

A design methodology is presented for the analysis and synthesis of robust linear controllers for a nonlinear continuous stirred tank reactor. Regions are defined in the phase plane in which the maintenance of robust stability and the achievement of robust performance levels are guaranteed. The results are based upon new extensions of the structured singular value theory to a class of nonlinear and time-varying systems

Polygenic risk associated with post-traumatic stress disorder onset and severity.

Post-traumatic stress disorder (PTSD) is a psychiatric illness with a highly polygenic architecture without large effect-size common single-nucleotide polymorphisms (SNPs). Thus, to capture a substantial portion of the genetic contribution, effects from many variants need to be aggregated. We investigated various aspects of one such approach that has been successfully applied to many traits, polygenic risk score (PRS) for PTSD. Theoretical analyses indicate the potential prediction ability of PRS. We used the latest summary statistics from the largest published genome-wide association study (GWAS) conducted by Psychiatric Genomics Consortium for PTSD (PGC-PTSD). We found that the PRS constructed for a cohort comprising veterans of recent wars (n = 244) explains a considerable proportion of PTSD onset (Nagelkerke R2 = 4.68%, P = 0.003) and severity (R2 = 4.35%, P = 0.0008) variances. However, the performance on an African ancestry sub-cohort was minimal. A PRS constructed with schizophrenia GWAS also explained a significant fraction of PTSD diagnosis variance (Nagelkerke R2 = 2.96%, P = 0.0175), confirming previously reported genetic correlation between the two psychiatric ailments. Overall, these findings demonstrate the important role polygenic analyses of PTSD will play in risk prediction models as well as in elucidating the biology of the disorder