SUMMARYCytokines are key regulators of ovarian physiology, particularly in relation to folliculogenesis and ovulation, where they contribute to creating an environment supporting follicle selection and growth. Their manifold functions include regulating cellular proliferation/differentiation, follicular survival/atresia, and oocyte maturation. Several cytokines, such as TGF-b-superfamily members, are involved at all stages of folliculogenesis while the production of others is stage-dependent. This review draws upon evidence from both human and animal models to highlight the species-specific roles at each milestone of follicular development. Given these pivotal roles and their ease of detection in follicular fluid, cytokines have been considered as attractive biomarkers of oocyte maturational status and of successful assisted reproductive outcome. Despite this, our understanding of cytokines and their interactions remains incomplete, and is still frequently limited to overly simplistic descriptions of their interrelationships. Given our increased appreciation of cytokine activity in complex and highly regulated networks, we put forward the case for using Bayesian modelling approaches to describe their hierarchical relationships in order to predict causal physiological interactions in vivo.Mol. Reprod. Dev. 81: 284À314,

The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However, molecular networks give rise, through mass-action kinetics, to polynomial dynamical systems, whose steady states are zeros of a set of polynomial equations. These equations may be analysed by algebraic methods, in which parameters are treated as symbolic expressions whose numerical values do not have to be known in advance. For instance, an "invariant" of a network is a polynomial expression on selected state variables that vanishes in any steady state. Invariants have been found that encode key network properties and that discriminate between different network structures. Although invariants may be calculated by computational algebraic methods, such as Gröbner bases, these become computationally infeasible for biologically realistic networks. Here, we exploit Chemical Reaction Network Theory (CRNT) to develop an efficient procedure for calculating invariants that are linear combinations of "complexes", or the monomials coming from mass action. We show how this procedure can be used in proving earlier results of Horn and Jackson and of Shinar and Feinberg for networks of deficiency at most one. We then apply our method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity regulator and the mammalian 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator, whose networks have deficiencies up to four. We show that bifunctionality leads to different forms of concentration control that are robust to changes in initial conditions or total amounts. Finally, we outline a systematic procedure for using complex-linear invariants to analyse molecular networks of any deficiency.

Background: Covalent modification cycles are widely used as regulatory switches. Results: Mathematical analysis reveals, under very general assumptions, an unavoidable trade-off between switching efficiency and cell-to-cell coherence. Conclusion: Enzyme bifunctionality offers a way to circumvent this trade-off. Significance: This may explain the bifunctionality of PFK-2/FBPase-2 in controlling the switch between glycolysis and gluconeogenesis in the mammalian liver.Covalent modification provides a mechanism for modulating molecular state and regulating physiology. A cycle of competing enzymes that add and remove a single modification can act as a molecular switch between "on" and "off" and has been widely studied as a core motif in systems biology. Here, we exploit the recently developed "linear framework" for time scale separation to determine the general principles of such switches. These methods are not limited to Michaelis-Menten assumptions, and our conclusions hold for enzymes whose mechanisms may be arbitrarily complicated. We show that switching efficiency improves with increasing irreversibility of the enzymes and that the on/off transition occurs when the ratio of enzyme levels reaches a value that depends only on the rate constants. Fluctuations in enzyme levels, which habitually occur due to cellular heterogeneity, can cause flipping back and forth between on and off, leading to incoherent mosaic behavior in tissues, that worsens as switching becomes sharper. This trade-off can be circumvented if enzyme levels are correlated. In particular, if the competing catalytic domains are on the same protein but do not influence each other, the resulting bifunctional enzyme can switch sharply while remaining coherent. In the mammalian liver, the switch between glycolysis and gluconeogenesis is regulated by the bifunctional 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/ FBPase-2). We suggest that bifunctionality of PFK-2/FBPase-2 complements the metabolic zonation of the liver by ensuring coherent switching in response to insulin and glucagon.An enzyme-catalyzed modification cycle is illustrated in Fig. 1A. The forward enzyme, E, catalyzes the covalent addition of an M moiety (phosphoryl, methyl, acetyl, etc.), carried by the donor, D-M, to form the modified substrate, S 1 , from the unmodified substrate, S 0 . The reverse enzyme, F, catalyzes the removal of M, returning S 1 to S 0 . Background metabolic processes continually replenish D-M from D and M. The substrate, S, can be any molecule, protein or otherwise.Such cycles can function as biological switches, in which the proportion of S 1 at steady state can be varied from low ("off") to high ("on") by altering properties of the cycle, such as the enzyme levels (1, 2). They are regarded as core motifs in cellular information processing (3,4) and have been the subject of much analysis (5-9).Application of these results to specific biological examples has been hampered, however, by the universal assumption that the enzymes E and F follow the Mich...