Predicting lung exposure of intramuscular niclosamide as an antiviral agent: Power-law based pharmacokinetic modeling

Niclosamide, a potent anthelmintic agent, has emerged as a candidate against COVID-19 in recent studies. Its formulation has been investigated extensively to address challenges related to systemic exposure. In this study, niclosamide was formulated as a long-acting intramuscular injection to achieve systemic exposure in the lungs for combating the virus. To establish the dose-exposure relationship, a hamster model was selected, given its utility in previous COVID-19 infection studies. Pharmacokinetic (PK) analysis was performed using NONMEM and PsN. Hamsters were administered doses of 55, 96, 128, and 240 mg/kg with each group comprising five animals. Two types of PK models were developed, linear models incorporating partition coefficients and power-law distributed models, to characterize the relationship between drug concentrations in the plasma and lungs of the hamsters. Numerical and visual diagnostics, including basic goodness-of-fit and visual predictive checks, were employed to assess the models. The power-law-based PK model not only demonstrated superior numerical performance compared with the linear model but also exhibited better agreement in visual diagnostic evaluations. This phenomenon was attributed to the nonlinear relationship between drug concentrations in the plasma and lungs, reflecting kinetic heterogeneity. Dose optimization, based on predicting lung exposure, was conducted iteratively across different drug doses, with the minimum effective dose estimated to be ~1115 mg/kg. The development of a power-law-based PK model proved successful and effectively captured the nonlinearities observed in this study. This method is expected to be applicable for investigating the drug disposition of specific formulations in the lungs.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Renormalization group approach to power-law modeling of complex metabolic networks

In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations.

A biological interpretation of transient anomalous subdiffusion. II. Reaction kinetics

Reaction kinetics in a cell or cell membrane is modeled in terms of the first passage time for a random walker at a random initial position to reach an immobile target site in the presence of a hierarchy of nonreactive binding sites. Monte Carlo calculations are carried out for the triangular, square, and cubic lattices. The mean capture time is expressed as the product of three factors: the analytical expression of Montroll for the capture time in a system with a single target and no binding sites; an exact expression for the mean escape time from the set of lattice points; and a correction factor for the number of targets present. The correction factor, obtained from Monte Carlo calculations, is between one and two. Trapping may contribute significantly to noise in reaction rates. The statistical distribution of capture times is obtained from Monte Carlo calculations and shows a crossover from power-law to exponential behavior. The distribution is analyzed using probability generating functions; this analysis resolves the contributions of the different sources of randomness to the distribution of capture times. This analysis predicts the distribution function for a lattice with perfect mixing; deviations reflect imperfect mixing in an ordinary random walk.

Integration of kinetic information on yeast sphingolipid metabolism in dynamical pathway models

For the first time, kinetic information from the literature was collected and used to construct integrative dynamical mathematical models of sphingolipid metabolism. One model was designed primarily with kinetic equations in the tradition of Michaelis and Menten whereas the other two models were designed as alternative power-law models within the framework of Biochemical Systems Theory. Each model contains about 50 variables, about a quarter of which are dependent (state) variables, while the others are independent inputs and enzyme activities that are considered constant. The models account for known regulatory signals that exert control over the pathway. Standard mathematical testing, repeated revisiting of the literature, and numerous rounds of amendments and refinements resulted in models that are stable and rather insensitive to perturbations in inputs or parameter values. The models also appear to be compatible with the modest amount of experimental experience that lends itself to direct comparisons. Even though the three models are based on different mathematical representations, they show dynamic responses to a variety of perturbations and changes in conditions that are essentially equivalent for small perturbations and similar for large perturbations. The kinetic information used for model construction and the models themselves can serve as a starting point for future analyses and refinements.

Metabolic modeling: a tool of drug discovery in the post-genomic era

The Human Genome Project, DNA microarrays, proteome chips and metabolic profiles, among others, are generating unprecedented amounts of valuable information about the genetic and metabolic responses of organisms to stimuli. This wealth of information poses a great scientific challenge, namely the development of novel, effective methods for functional analysis and interpretation. It is proposed here that biomathematical systems models must accompany data generation and management. A particularly effective framework for this purpose is canonical modeling based on Biochemical Systems Theory. The key concept of this theory is the formulation of biological phenomena as systems of differential equations, in which all processes are represented as products of power-law functions.

Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways

Recent evidence has shown that elementary bimolecular reactions under dimensionally-restricted conditions, such as those that might occur within cells when reactions are confined to two-dimensional membranes and one-dimensional channels, do not follow traditional mass-action kinetics, but fractal kinetics. The power-law formalism, which provides the context for examining the kinetics under these conditions, is used here to examine the implications of fractal kinetics in a simple pathway of reversible reactions. Starting with elementary chemical kinetics, we proceed to characterise the equilibrium behaviour of a simple bimolecular reaction, derive a generalised set of conditions for microscopic reversibility, and develop the fractal kinetic rate law for a reversible Michaelis-Menten mechanism. Having established this fractal kinetic framework, we go on to analyse the steady-state behaviour and temporal response of a pathway characterised by both the fundamental and quasi-steady-state equations. These results are contrasted with those for the fundamental and quasi-steady-state equations based on traditional mass-action kinetics. Finally, we compare the accuracy of three local representations based on both fractal and mass-action kinetics. The results with fractal kinetics show that the equilibrium ratio is a function of the amount of material in a closed system, and that the principle of microscopic reversibility has a more general manifestation that imposes new constraints on the set of fractal kinetic orders. Fractal kinetics in a biochemical pathway allow an increase in flux to occur with less accumulation of pathway intermediates and a faster temporal response than is the case with traditional kinetics. These conclusions are obtained regardless of the level of representation considered. Thus, fractal kinetics provide a novel means to achieve important features of pathway design.