The paper presents a differential equation model for the feedback mechanisms between gonadotropin-releasing hormone (GnRH), follicle-stimulating hormone (FSH), luteinizing hormone (LH), development of follicles and corpus luteum, and the production of estradiol (E2), progesterone (P4), inhibin A (IhA), and inhibin B (IhB) during the female menstrual cycle. Compared to earlier human cycle models, there are three important differences: The model presented here (a) does not involve any delay equations, (b) is based on a deterministic modeling of the GnRH pulse pattern, and (c) contains less differential equations and less parameters. These differences allow for a faster simulation and parameter identification. The focus is on modeling GnRH-receptor binding, in particular, by inclusion of a pharmacokinetic/pharmacodynamic (PK/PD) model for a GnRH agonist, Nafarelin, and a GnRH antagonist, Cetrorelix, into the menstrual cycle model. The final mathematical model describes the hormone profiles (LH, FSH, P4, E2) throughout the menstrual cycle of 12 healthy women. It correctly predicts hormonal changes following single and multiple dose administration of Nafarelin or Cetrorelix at different stages in the cycle.

This model is according to the paper of A model for the dynamics of human weight cycling by A. Goldbeter 2006.The figure3 (A) and (B) have been reproduced by Copasi 4.0.19(development) and SBMLodeSolver.The writer of the paper did not specify any units for the metabolites, so the creator of the model did not define the units as well.Both Q and R are normalized to vary between 0 and 1.

In genetic disorders associated with premature neuronal death, symptoms may not appear for years or decades. This delay in clinical onset is often assumed to reflect the occurrence of age-dependent cumulative damage. For example, it has been suggested that oxidative stress disrupts metabolism in neurological degenerative disorders by the cumulative damage of essential macromolecules. A prediction of the cumulative damage hypothesis is that the probability of cell death will increase over time. Here we show in contrast that the kinetics of neuronal death in 12 models of photoreceptor degeneration, hippocampal neurons undergoing excitotoxic cell death, a mouse model of cerebellar degeneration and Parkinson's and Huntington's diseases are all exponential and better explained by mathematical models in which the risk of cell death remains constant or decreases exponentially with age. These kinetics argue against the cumulative damage hypothesis; instead, the time of death of any neuron is random. Our findings are most simply accommodated by a 'one-hit' biochemical model in which mutation imposes a mutant steady state on the neuron and a single event randomly initiates cell death. This model appears to be common to many forms of neurodegeneration and has implications for therapeutic strategies.