Safe uses of Hill's model: an exact comparison with the Adair-Klotz model

<p>Abstract</p> <p>Background</p> <p>The Hill function and the related Hill model are used frequently to study processes in the living cell. There are very few studies investigating the situations in which the model can be safely used. For example, it has been shown, at the mean field level, that the dose response curve obtained from a Hill model agrees well with the dose response curves obtained from a more complicated Adair-Klotz model, provided that the parameters of the Adair-Klotz model describe strongly cooperative binding. However, it has not been established whether such findings can be extended to other properties and non-mean field (stochastic) versions of the same, or other, models.</p> <p>Results</p> <p>In this work a rather generic quantitative framework for approaching such a problem is suggested. The main idea is to focus on comparing the particle number distribution functions for Hill's and Adair-Klotz's models instead of investigating a particular property (e.g. the dose response curve). The approach is valid for any model that can be mathematically related to the Hill model. The Adair-Klotz model is used to illustrate the technique. One main and two auxiliary similarity measures were introduced to compare the distributions in a quantitative way. Both time dependent and the equilibrium properties of the similarity measures were studied.</p> <p>Conclusions</p> <p>A strongly cooperative Adair-Klotz model can be replaced by a suitable Hill model in such a way that any property computed from the two models, even the one describing stochastic features, is approximately the same. The quantitative analysis showed that boundaries of the regions in the parameter space where the models behave in the same way exhibit a rather rich structure.</p

A danger of low copy numbers for inferring incorrect cooperativity degree

Background: A dose-response curve depicts fraction of bound proteins as a function of unbound ligands. Dose-response curves are used to measure the cooperativity degree of a ligand binding process. Frequently, the Hill function is used to fit the experimental data. The Hill function is parameterized by the value of the dissociation constant, and the Hill coefficient which describes the cooperativity degree. The use of Hill's model and the Hill function have been heavily criticised in this context, predominantly the assumption that all ligands bind at once, which lead to further refinements of the model. In this work, the validity of the Hill function has been studied from an entirely different point of view. In the limit of low copy numbers the dynamics of the system becomes noisy. The goal was to asses the validity of the Hill function in this limit, and to see in which ways the effects of the fluctuations change the form of the dose-response curves. Results: Dose-response curves were computed taking into account effects of fluctuations. The effects of fluctuations were described at the lowest order (the second moment of the particle number distribution) by using previously developed Pair Approach Reaction Noise EStimator (PARNES) method. The stationary state of the system is described by nine equations with nine unknowns. To obtain fluctuation corrected dose-response curves the equations have been investigated numerically. Conclusions: The Hill function cannot describe dose-response curves in a low particle limit. First, dose-response curves are not solely parameterized by the dissociation constant and the Hill coefficient. In general, the shape of a dose-response curve depends on the variables that describe how an experiment (ensemble) is designed. Second, dose-response curves are multi valued in a rather non-trivial way

Selective complexation of divalent cations by a cyclic α,β-peptoid hexamer: a spectroscopic and computational study

We describe the qualitative and quantitative analysis of the complexation properties towards cations of a cyclic peptoid hexamer composed of alternating α- and β-peptoid monomers, which bear exclusively chiral (S)-phenylethyl side chains (spe) that have no noticeable chelating properties. The binding of a series of monovalent and divalent cations was assessed by 1H NMR, circular dichroism, fluorescence and molecular modelling. In contrast to previous studies on cations binding by 18-membered α-cyclopeptoid hexamers, the 21-membered cyclopeptoid cP1 did not complex monovalent cations (Na+, K+, Ag+) but showed selectivity for divalent cations (Ca2+, Ba2+, Sr2+ and Mg2+). Hexacoordinated C-3 symmetrical complexes were demonstrated for divalent cations with ionic radii around 1 Å (Ca2+ and Ba2+), while 5-coordination is preferred for divalent cations with larger (Ba2+) or smaller ionic radii (Mg2+)

The Terminal Oxidase Cytochrome bd Promotes Sulfide-resistant Bacterial Respiration and Growth

Hydrogen sulfide (H2S) impairs mitochondrial respiration by potently inhibiting the heme-copper cytochrome c oxidase. Since many prokaryotes, including Escherichia (E.) coli, generate H2S and encounter high H2S levels particularly in the human gut, herein we tested whether bacteria can sustain sulfide-resistant O2-dependent respiration. E. coli has three respiratory oxidases, the cyanide-sensitive heme-copper bo3 enzyme and two bd oxidases much less sensitive to cyanide. Working on the isolated enzymes, we found that, whereas the bo3 oxidase is inhibited by sulfide with half-maximal inhibitory concentration IC50=1.1±0.1μM, under identical experimental conditions both bd oxidases are insensitive to sulfide up to 58μM. In E. coli respiratory mutants, both O2-consumption and aerobic growth proved to be severely impaired by sulfide when respiration was sustained by the bo3 oxidase alone, but unaffected by ≤200μM sulfide when either bd enzyme acted as the only terminal oxidase. Accordingly, wild-type E. coli showed sulfide-insensitive respiration and growth under conditions favouring the expression of bd oxidases. In all tested conditions, cyanide mimicked the functional effect of sulfide on bacterial respiration. We conclude that bd oxidases promote sulfide-resistant O2- consumption and growth in E. coli and possibly other bacteria. The impact of this discovery is discussed

Amplification by PCR Artificially Reduces the Proportion of the Rare Biosphere in Microbial Communities

The microbial world has been shown to hold an unimaginable diversity. The use of rRNA genes and PCR amplification to assess microbial community structure and diversity present biases that need to be analyzed in order to understand the risks involved in those estimates. Herein, we show that PCR amplification of specific sequence targets within a community depends on the fractions that those sequences represent to the total DNA template. Using quantitative, real-time, multiplex PCR and specific Taqman probes, the amplification of 16S rRNA genes from four bacterial species within a laboratory community were monitored. Results indicate that the relative amplification efficiency for each bacterial species is a nonlinear function of the fraction that each of those taxa represent within a community or multispecies DNA template. Consequently, the low-proportion taxa in a community are under-represented during PCR-based surveys and a large number of sequences might need to be processed to detect some of the bacterial taxa within the ‘rare biosphere’. The structure of microbial communities from PCR-based surveys is clearly biased against low abundant taxa which are required to decipher the complete extent of microbial diversity in nature

At the Biological Modeling and Simulation Frontier

We provide a rationale for and describe examples of synthetic modeling and simulation (M&S) of biological systems. We explain how synthetic methods are distinct from familiar inductive methods. Synthetic M&S is a means to better understand the mechanisms that generate normal and disease-related phenomena observed in research, and how compounds of interest interact with them to alter phenomena. An objective is to build better, working hypotheses of plausible mechanisms. A synthetic model is an extant hypothesis: execution produces an observable mechanism and phenomena. Mobile objects representing compounds carry information enabling components to distinguish between them and react accordingly when different compounds are studied simultaneously. We argue that the familiar inductive approaches contribute to the general inefficiencies being experienced by pharmaceutical R&D, and that use of synthetic approaches accelerates and improves R&D decision-making and thus the drug development process. A reason is that synthetic models encourage and facilitate abductive scientific reasoning, a primary means of knowledge creation and creative cognition. When synthetic models are executed, we observe different aspects of knowledge in action from different perspectives. These models can be tuned to reflect differences in experimental conditions and individuals, making translational research more concrete while moving us closer to personalized medicine

Mathematical Model of Plasmid-Mediated Resistance to Ceftiofur in Commensal Enteric Escherichia coli of Cattle

Antimicrobial use in food animals may contribute to antimicrobial resistance in bacteria of animals and humans. Commensal bacteria of animal intestine may serve as a reservoir of resistance-genes. To understand the dynamics of plasmid-mediated resistance to cephalosporin ceftiofur in enteric commensals of cattle, we developed a deterministic mathematical model of the dynamics of ceftiofur-sensitive and resistant commensal enteric Escherichia coli (E. coli) in the absence of and during parenteral therapy with ceftiofur. The most common treatment scenarios including those using a sustained-release drug formulation were simulated; the model outputs were in agreement with the available experimental data. The model indicated that a low but stable fraction of resistant enteric E. coli could persist in the absence of immediate ceftiofur pressure, being sustained by horizontal and vertical transfers of plasmids carrying resistance-genes, and ingestion of resistant E. coli. During parenteral therapy with ceftiofur, resistant enteric E. coli expanded in absolute number and relative frequency. This expansion was most influenced by parameters of antimicrobial action of ceftiofur against E. coli. After treatment (>5 weeks from start of therapy) the fraction of ceftiofur-resistant cells among enteric E. coli, similar to that in the absence of treatment, was most influenced by the parameters of ecology of enteric E. coli, such as the frequency of transfer of plasmids carrying resistance-genes, the rate of replacement of enteric E. coli by ingested E. coli, and the frequency of ceftiofur resistance in the latter

A local glucose-and oxygen concentration-based insulin secretion model for pancreatic islets

<p>Abstract</p> <p>Background</p> <p>Because insulin is the main regulator of glucose homeostasis, quantitative models describing the dynamics of glucose-induced insulin secretion are of obvious interest. Here, a computational model is introduced that focuses not on organism-level concentrations, but on the quantitative modeling of local, cellular-level glucose-insulin dynamics by incorporating the detailed spatial distribution of the concentrations of interest within isolated avascular pancreatic islets.</p> <p>Methods</p> <p>All nutrient consumption and hormone release rates were assumed to follow Hill-type sigmoid dependences on local concentrations. Insulin secretion rates depend on both the glucose concentration and its time-gradient, resulting in second-and first-phase responses, respectively. Since hypoxia may also be an important limiting factor in avascular islets, oxygen and cell viability considerations were also built in by incorporating and extending our previous islet cell oxygen consumption model. A finite element method (FEM) framework is used to combine reactive rates with mass transport by convection and diffusion as well as fluid-mechanics.</p> <p>Results</p> <p>The model was calibrated using experimental results from dynamic glucose-stimulated insulin release (GSIR) perifusion studies with isolated islets. Further optimization is still needed, but calculated insulin responses to stepwise increments in the incoming glucose concentration are in good agreement with existing experimental insulin release data characterizing glucose and oxygen dependence. The model makes possible the detailed description of the intraislet spatial distributions of insulin, glucose, and oxygen levels. In agreement with recent observations, modeling also suggests that smaller islets perform better when transplanted and/or encapsulated.</p> <p>Conclusions</p> <p>An insulin secretion model was implemented by coupling local consumption and release rates to calculations of the spatial distributions of all species of interest. The resulting glucose-insulin control system fits in the general framework of a sigmoid proportional-integral-derivative controller, a generalized PID controller, more suitable for biological systems, which are always nonlinear due to the maximum response being limited. Because of the general framework of the implementation, simulations can be carried out for arbitrary geometries including cultured, perifused, transplanted, and encapsulated islets.</p