Hill functions follow from the equilibrium state of the reaction in which n ligands simultaneously bind a single receptor. This result if often employed to interpret the Hill coefficient as the number of ligand binding sites in all kinds of reaction schemes. Here, we study the equilibrium states of the reactions in which n ligand bind a receptor sequentially, both non-cooperatively and in a cooperative fashion. The main outcomes of such analysis are that: n is not a good estimate, but only an upper bound, for the Hill coefficient; while the Hill coefficient depends quite strongly on the cooperativity level among ligands. We finally use these results to discuss the feasibility and constrains of using Hill functions to model the regulatory functions in mathematical models of gene regulatory networks.

A mathematical model for regulation of the tryptophan operon is presented. This model takes into account repression, feedback enzyme inhibition, and transcriptional attenuation. Special attention is given to model parameter estimation based on experimental data. The model's system of delay differential equations is numerically solved, and the results are compared with experimental data on the temporal evolution of enzyme activity in cultures of Escherichia coli after a nutritional shift (minimal + tryptophan medium to minimal medium). Good agreement is obtained between the numeric simulations and the experimental results for wild-type E. coli , as well as for two different mutant strains.

Understanding the principles that govern community assemblages is a central goal of ecology. There is limited experimental evidence in natural settings showing that microbial assembly in communities are influenced by antagonistic interactions. We, therefore, analyzed antagonism among bacterial isolates from a taxonomically related bacterial guild obtained from five sites in sediments from a fresh water system. We hypothesized that if antagonistic interactions acted as a shaping force of the community assembly, then the frequency of resistance to antagonism among bacterial isolates originating from a given site would be higher than the resistance to conspecifics originating from a different assemblage. Antagonism assays were conducted between 78 thermoresistant isolates, of which 72 were Bacillus spp. Sensitive, resistant and antagonistic isolates co-occurred at each site, but the within-site frequency of resistance observed was higher than that observed when assessed across-sites. We found that antagonism results from bacteriocin-like substances aimed at the exclusion of conspecifics. More than 6000 interactions were scored and described by a directed network with hierarchical structure that exhibited properties that resembled a food chain, where the different Bacillus taxonomic groups occupied specific positions. For some tested interacting pairs, the unidirectional interaction could be explained by competition that inhibited growth or completely excluded one of the pair members. This is the first report on the prevalence and specificity of Bacillus interactions in a natural setting and provides evidence for the influence of bacterial antagonist interactions in the assemblage of a taxonomically related guild in local communities.