Pascal Maire

The Hill equation: a review of its capabilities in pharmacological modelling.

The Hill equation was first introduced by A.V. Hill to describe the equilibrium relationship between oxygen tension and the saturation of haemoglobin. In pharmacology, the Hill equation has been extensively used to analyse quantitative drug–receptor relationships. Many pharmacokinetic–pharmacodynamic models have used the Hill equation to describe nonlinear drug dose–response relationships. Although the Hill equation is widely used, its many properties are not all well known. This article aims at reviewing the various properties of the Hill equation. The descriptive aspects of the Hill equation, in particular mathematical and graphical properties, are examined, and related to Hill’s original work. The mechanistic aspect of the Hill equation, involving a strong connection with the Guldberg and Waage law of mass action, is also described. Finally, a probabilistic view of the Hill equation is examined. Here, we provide some new calculation results, such as Fisher information and Shannon entropy, and we introduce multivariate probabilistic Hill equations. The main features and potential applications of this probabilistic approach are also discussed. Thus, within the same formalism, the Hill equation has many different properties which can be of great interest for those interested in mathematical modelling in pharmacology and biosciences.

Six1 and Six4 homeoproteins are required for Pax3 and Mrf expression during myogenesis in the mouse embryo

In mammals, Six5, Six4 and Six1 genes are co-expressed during mouse myogenesis. Six4 and Six5 single knockout (KO) mice have no developmental defects, while Six1 KO mice die at birth and show multiple organ developmental defects. We have generated Six1Six4 double KO mice and show an aggravation of the phenotype previously reported for the single Six1 KO. Six1Six4 double KO mice are characterized by severe craniofacial and rib defects, and general muscle hypoplasia. At the limb bud level, Six1 and Six4 homeogenes control early steps of myogenic cell delamination and migration from the somite through the control of Pax3 gene expression. Impaired in their migratory pathway, cells of the somitic ventrolateral dermomyotome are rerouted, lose their identity and die by apoptosis. At the interlimb level, epaxial Met expression is abolished, while it is preserved in Pax3-deficient embryos. Within the myotome, absence of Six1 and Six4 impairs the expression of the myogenic regulatory factors myogenin and Myod1, and Mrf4 expression becomes undetectable. Myf5 expression is correctly initiated but becomes restricted to the caudal region of each somite. Early syndetomal expression of scleraxis is reduced in the Six1Six4 embryo, while the myotomal expression of Fgfr4 and Fgf8 but not Fgf4 and Fgf6 is maintained. These results highlight the different roles played by Six proteins during skeletal myogenesis.

Altered myogenesis in Six1-deficient mice.

Six homeoproteins are expressed in several tissues, including muscle, during vertebrate embryogenesis, suggesting that they may be involved in diverse differentiation processes. To determine the functions of the Six1 gene during myogenesis, we constructed Six1-deficient mice by replacing its first exon with the lacZ gene. Mice lacking Six1 die at birth because of severe rib malformations and show extensive muscle hypoplasia affecting most of the body muscles in particular certain hypaxial muscles. Six1–/– embryos have impaired primary myogenesis, characterized, at E13.5, by a severe reduction and disorganisation of primary myofibers in most body muscles. While Myf5, MyoD and myogenin are correctly expressed in the somitic compartment in early Six1–/– embryos, by E11.5 MyoD and myogenin gene activation is reduced and delayed in limb buds. However, this is not the consequence of a reduced ability of myogenic precursor cells to migrate into the limb buds or of an abnormal apoptosis of myoblasts lacking Six1. It appears therefore that Six1 plays a specific role in hypaxial muscle differentiation, distinct from those of other hypaxial determinants such as Pax3, cMet, Lbx1 or Mox2.

Model-based, goal-oriented, individualised drug therapy : Linkage of population modelling, new 'multiple model' dosage design, Bayesian feedback and individualised target goals

SummaryThis article examines the use of population pharmacokinetic models to store experiences about drugs in patients and to apply that experience to the care of new patients. Population models are the Bayesian prior. For truly individualised therapy, it is necessary first to select a specific target goal, such as a desired serum or peripheral compartment concentration, and then to develop the dosage regimen individualised to best hit that target in that patient.One must monitor the behaviour of the drug by measuring serum concentrations or other responses, hopefully obtained at optimally chosen times, not only to see the raw results, but to also make an individualised (Bayesian posterior) model of how the drug is behaving in that patient. Only then can one see the relationship between the dose and the absorption, distribution, effect and elimination of the drug, and the patient’s clinical sensitivity to it; one must always look at the patient. Only by looking at both the patient and the model can it be judged whether the target goal was correct or needs to be changed. The adjusted dosage regimen is again developed to hit that target most precisely starting with the very next dose, not just for some future steady state.Nonparametric population models have discrete, not continuous, parameter distributions. These lead naturally into the multiple model method of dosage design, specifically to hit a desired target with the greatest possible precision for whatever past experience and present data are available on that drug — a new feature for this goal-oriented, model-based, individualised drug therapy. As clinical versions of this new approach become available from several centres, it should lead to further improvements in patient care, especially for bacterial and viral infections, cardiovascular therapy, and cancer and transplant situations.

Improved clinical outcome of paediatric bone marrow recipients using a test dose and Bayesian pharmacokinetic individualization of busulfan dosage regimens.

In order to control busulfan pharmacokinetic variability and toxicity, a specific monitoring protocol was instituted in our bone marrow transplant BMT paediatric patients including a test dose, daily Bayesian forecasting of busulfan plasma levels, and Bayesian individualization of busulfan dosage regimens. Twenty-nine children received BMT after a busulfan-based conditioning regimen. Individual pharmacokinetic parameters were obtained following a 0.5 mg*kg test dose and were used for daily individualization of dosage regimens during the subsequent 4-day course of treatment. Doses were adjusted to reach a target mean AUC per 6 h between 4 and 6 μg.h.ml+1. Plasma busulfan assays were performed by liquid chromatography. Pharmacokinetic analysis used the USC*PACK software. The performance of the test dose to predict AUC during the busulfan regimen was evaluated. Incidence of toxicity, chimerism and relapse, overall Kaplan–Meier survival, and VOD-free survival were compared after matching our patients (group A) with patients conditioned by using standard doses of busulfan (group B). Busulfan doses were decreased in 69% of patients compared to conventional doses. Expected AUC was significantly correlated with observed AUC and predictability of the test dose was 101.9 ± 17.9%. Incidence of VOD in group A was 3.4% vs 24.1% in group B, while the incidence of stomatitis was similar. Engraftment was successful in all patients in group A. The rate of full engraftment at 3 months post-BMT was higher in group A (P = 0.012). Long-term overall survival did not differ between the two groups, in contrast to the 90-day survival. VOD-free survival was higher in group A (P = 0.026). Pharmacokinetic monitoring and individualization of busulfan dosage regimen are useful in improving clinical outcome and reducing early mortality in paediatric bone marrow transplant recipients. Bone Marrow Transplantation (2001) 28, 743–751.

Six proteins regulate the activation of Myf5 expression in embryonic mouse limbs

Myf5, a member of the myogenic regulatory factor family, plays a major role in determining myogenic cell fate at the onset of skeletal muscle formation in the embryo. Spatiotemporal control of its expression during development requires multiple enhancer elements spread over >100 kb at the Myf5 locus. Transcription in embryonic limbs is regulated by a 145-bp element located at −57.5 kb from the Myf5 gene. In the present study we show that Myf5 expression is severely impaired in the limb buds of Six1−/− and Six1−/−Six4−/+ mouse mutants despite the presence of myogenic progenitor cells. The 145-bp regulatory element contains a sequence that binds Six1 and Six4 in electromobility shift assays in vitro and in chromatin immunoprecipitation assays with embryonic extracts. We further show that Six1 is able to transactivate a reporter gene under the control of this sequence. In vivo functionality of the Six binding site is demonstrated by transgenic analysis. Mutation of this site impairs reporter gene expression in the limbs and in mature somites where the 145-bp regulatory element is also active. Six1/4 therefore regulate Myf5 transcription, together with Pax3, which was previously shown to be required for the activity of the 145-bp element. Six homeoproteins, which also directly regulate the myogenic differentiation gene Myogenin and lie genetically upstream of Pax3, thus control hypaxial myogenesis at multiple levels.

Aminoglycoside Nephrotoxicity: Modeling, Simulation, and Control

ABSTRACT The main constraints on the administration of aminoglycosides are the risks of nephrotoxicity and ototoxicity, which can lead to acute, renal, vestibular, and auditory toxicities. In the present study we focused on nephrotoxicity. No reliable predictor of nephrotoxicity has been found to date. We have developed a deterministic model which describes the pharmacokinetic behavior of aminoglycosides (with a two-compartment model), the kinetics of aminoglycoside accumulation in the renal cortex, the effects of aminoglycosides on renal cells, the resulting effects on renal function by tubuloglomerular feedback, and the resulting effects on serum creatinine concentrations. The pharmacokinetic parameter values were estimated by use of the NPEM program. The estimated pharmacodynamic parameter values were obtained after minimization of the least-squares objective function between the measured and the calculated serum creatinine concentrations. A simulation program assessed the influences of the dosage regimens on the occurrence of nephrotoxicity. We have also demonstrated the relevancy of modeling of the circadian rhythm of the renal function. We have shown the ability of the model to fit with 49 observed serum creatinine concentrations for a group of eight patients treated for endocarditis by comparison with 49 calculated serum creatinine concentrations (r2 = 0.988; P < 0.001). We have found that for the same daily dose, the nephrotoxicity observed with a thrice-daily administration schedule appears more rapidly, induces a greater decrease in renal function, and is more prolonged than those that occur with less frequent administration schedules (for example, once-daily administration). Moreover, for once-daily administration, we have demonstrated that the time of day of administration can influence the incidence of aminoglycoside nephrotoxicity. The lowest level of nephrotoxicity was observed when aminoglycosides were administered at 1:30 p.m. Clinical application of this model might make it possible to adjust aminoglycoside dosage regimens by taking into account both the efficacies and toxicities of the drugs.

Population Modeling and Monte Carlo Simulation Study of the Pharmacokinetics and Antituberculosis Pharmacodynamics of Rifampin in Lungs

ABSTRACT Little information exists on the pulmonary pharmacology of antituberculosis drugs. We used population pharmacokinetic modeling and Monte Carlo simulation to describe and explore the pulmonary pharmacokinetics and pharmacodynamics of rifampin (RIF; rifampicin). A population pharmacokinetic model that adequately described the plasma, epithelial lining fluid (ELF), and alveolar cell (AC) concentrations of RIF in a population of 34 human volunteers was made by use of the nonparametric adaptive grid (NPAG) algorithm. The estimated concentrations correlated well with the measured concentrations, and there was little bias and good precision. The results obtained with the NPAG algorithm were then imported into Matlab software to perform a 10,000-subject Monte Carlo simulation. The ability of RIF to suppress the development of drug resistance and to induce a sufficient bactericidal effect against Mycobacterium tuberculosis was evaluated by calculating the proportion of subjects achieving specific target values for the maximum concentration of drug (Cmax)/MIC ratio and the area under the concentration-time curve from time zero to 24 h (AUC0-24)/MIC ratio, respectively. At the lowest MIC (0.01 mg/liter), after the administration of one 600-mg oral dose, the rates of target attainment for Cmax/MIC (≥175) were 95% in ACs, 48.8% in plasma, and 35.9% in ELF. Under the same conditions, the target attainment results for the killing effect were 100% in plasma (AUC0-24/MIC ≥ 271) but only 54.5% in ELF (AUC0-24/MIC ≥ 665). The use of a 1,200-mg RIF dose was associated with better results for target attainment. The overall results suggest that the pulmonary concentrations obtained with the standard RIF dose are too low in most subjects. This work supports the need to evaluate higher doses of RIF for the treatment of patients with tuberculosis.

Six and Eya expression during human somitogenesis and MyoD gene family activation.

This report describes the characterisation of the expression profile of several myogenic determination genes during human embryogenesis. The data were obtained from axial structures and limb buds of human embryos aged between 3 and 8 weeks of development. Using in situ hybridisation to detect Pax3 and MyoD gene family mRNAs, and immunochemistry to follow Six and Eya protein accumulation, we have been able to establish the chronology of accumulation of these gene products. As in mouse, the first transcripts detected in myotomes of 3 week-old embryos are Pax3 and Myf5, followed by the expression of myogenin. MyoD appears to be activated well after Myf5, myogenin and MRF4 in the early myotome, whereas, in limb bud muscles, the presence of all four of these mRNAs is concomitant from 6 weeks. Six1, Six4 and Six5 homeoproteins are detected later than Myf5 activation. These Six homeoproteins are first observed in the cytoplasm of myogenin expressing cells. At later stages of development, Six1 and Six5, but not Six4, are translocated into the nuclei of myogenic cells, concomitantly with MyHCemb expression. Eya1 and Eya2 proteins, potential Six cofactors, were also detected in myogenin positive cells, but their accumulation was delayed and was mainly cytoplasmic. These results preclude that early activation of Myf5, myogenin and MRF4 is under the control of Six and Eya proteins, while Six and Eya proteins would be involved in later steps of myogenic differentiation.

Dosage Regimens of Antibacterials

SummaryA prominent trend in optimising anti-infective therapy is to prescribe time-dependent antibacterials (e.g. β-lactams, glycopeptides) using short dosing intervals, but to prescribe concentration-dependent antibacterials (e.g. aminoglycosides, quinolones) using widely spaced intervals — even once daily. However, the currently prevailing notion that the clinical efficacy of concentration-dependent antibacterials can be improved by lengthening the dosing interval has not been well established. We integrated the differential equations of a pharmacokinetic/pharmacodynamic model describing the fate of a bacterial population in the presence of an antibacterial agent. We studied the variations of predicted efficacy, using a 1-compartment pharmacokinetic model with intravenous administration, according to the ratio between the dosing interval and the half-life of the drug, for a given daily dose. Simulations were performed using the published in vitro killing curve data of Pseudomonas aeruginosa obtained with tobramycin and ticarcillin. The results suggest that, independent of the time- or concentration-dependent nature of the antibacterial agent and the susceptibility of the pathogen, steady-state efficacy will decrease as the dosing interval increases, and therefore all antibacterials should ideally be administered at relatively short dosing intervals compared with their half-life, so that concentrations are below the minimum inhibitory concentration (MIC) as little as possible. Some arguments support the use of a large loading dose for concentration-dependent antibacterials, to rapidly reach steady-state at the infection site (this is also valid for time-dependent antibacterials), and to avoid the emergence of resistant mutants. Aminoglycosides are a special case within the class of concentration-dependent antibacterials, because of the possibility of adaptive resistance in terms of efficacy and of saturable target-organ uptake in terms of toxicity, both of which may support the concept of a long administration interval for these agents. Widely spaced administration of large doses of antibacterials with little dose-dependent toxicity may remain a valuable option, for reasons of cost and convenience, in the case of high susceptibility of the pathogen. However, in difficult situations (e.g. short drug half-life, high MIC of the pathogen, compromised host defences), optimising therapy using short dosing intervals should be most beneficial, especially when both the dose and the dose interval are adjusted for each patient (bodyweight, renal function, etc.) to achieve and maintain specific peak and trough concentrations selected according to the infecting organism and its susceptibility to the drug.