Solute transport with Michaelis-Menten kinetics for in vitro cell culture.

A traditional method of in vitro cell culture involves a monolayer of cells at the base of a petri dish filled with culture medium. While the primary role of the culture medium is to supply nutrients to the cells, drug or other solutes may be added, depending on the purpose of the experiment. Metabolism by cells of oxygen, nutrients and drug is typically governed by Michaelis-Menten (M-M) kinetics. In this paper, a mathematical model of solute transport with M-M kinetics is developed. Upon non-dimensionalization, the reaction/diffusion system is re-characterized in terms of Volterra integral equations, where a parameter $\beta $, the ratio of the initial solute concentration to the M-M constant, proves important: $\beta \ll 1$ is relevant to drug metabolism for the liver, whereas $\beta \gg 1$ is more appropriate in the case of oxygen metabolism. Regular perturbation expansions for both cases are obtained. A small-time expansion and steady-state solution are also presented. All results are compared against the numerical solution of the Volterra integral equations, and excellent agreement is found. The utility of the model and analytical solutions are discussed in the context of assisting experimental researchers to better understand the environment within in vitro cell culture experiments.

Mathematical modelling of fluid flow and solute transport to define operating parameters for in vitro perfusion cell culture systems.

In recent years, there has been a move away from the use of static in vitro two-dimensional cell culture models for testing the chemical safety and efficacy of drugs. Such models are increasingly being replaced by more physiologically relevant cell culture systems featuring dynamic flow and/or three-dimensional structures of cells. While it is acknowledged that such systems provide a more realistic environment within which to test drugs, progress is being hindered by a lack of understanding of the physical and chemical environment that the cells are exposed to. Mathematical and computational modelling may be exploited in this regard to unravel the dependency of the cell response on spatio-temporal differences in chemical and mechanical cues, thereby assisting with the understanding and design of these systems. In this paper, we present a mathematical modelling framework that characterizes the fluid flow and solute transport in perfusion bioreactors featuring an inlet and an outlet. To demonstrate the utility of our model, we simulated the fluid dynamics and solute concentration profiles for a variety of different flow rates, inlet solute concentrations and cell types within a specific commercial bioreactor chamber. Our subsequent analysis has elucidated the basic relationship between inlet flow rate and cell surface flow speed, shear stress and solute concentrations, allowing us to derive simple but useful relationships that enable prediction of the behaviour of the system under a variety of experimental conditions, prior to experimentation. We describe how the model may used by experimentalists to define operating parameters for their particular perfusion cell culture systems and highlight some operating conditions that should be avoided. Finally, we critically comment on the limitations of mathematical and computational modelling in this field, and the challenges associated with the adoption of such methods.

Development of an in vitro media perfusion model of Leishmania major macrophage infection.

BACKGROUND: In vitro assays are widely used in studies on pathogen infectivity, immune responses, drug and vaccine discovery. However, most in vitro assays display significant differences to the in vivo situation and limited predictive properties. We applied medium perfusion methods to mimic interstitial fluid flow to establish a novel infection model of Leishmania parasites. METHODS: Leishmania major infection of mouse peritoneal macrophages was studied within the Quasi Vivo QV900 macro-perfusion system. Under a constant flow of culture media at a rate of 360µl/min, L. major infected macrophages were cultured either at the base of a perfusion chamber or raised on 9mm high inserts. Mathematical and computational modelling was conducted to estimate medium flow speed, shear stress and oxygen concentration. The effects of medium flow on infection rate, intracellular amastigote division, macrophage phagocytosis and macropinocytosis were measured. RESULTS: Mean fluid speeds at the macrophage cell surface were estimated to be 1.45 x 10-9 m/s and 1.23 x 10-7 m/s for cells at the base of the chamber and cells on an insert, respectively. L. major macrophage infection was significantly reduced under both media perfusion conditions compared to cells maintained under static conditions; a 85±3% infection rate of macrophages at 72 hours in static cultures compared to 62±5% for cultures under slow medium flow and 55±3% under fast medium flow. Media perfusion also decreased amastigote replication and both macrophage phagocytosis (by 44±4% under slow flow and 57±5% under fast flow compared with the static condition) and macropinocytosis (by 40±4% under slow flow and 62±5% under fast flow compared with the static condition) as measured by uptake of latex beads and pHrodo Red dextran. CONCLUSIONS: Perfusion of culture medium in an in vitro L. major macrophage infection model (simulating in vivo lymphatic flow) reduced the infection rate of macrophages, the replication of the intracellular parasite, macrophage phagocytosis and macropinocytosis with greater reductions achieved under faster flow speeds.

In vitro Liver Zonation of Primary Rat Hepatocytes.

The ability of the liver to simultaneously carry out multiple functions is dependent on the metabolic heterogeneity of hepatocytes spatially located within a liver lobule spanning from the portal triad to the central vein. This complex zonal architecture of the liver, however, makes accurate in vitro modeling a challenge and often standard culture systems assume a homogenous model which may lead to inaccurate translatability of results. Here, we use a combination of mathematical modeling and experimental data to demonstrate a readily constructible in vitro flow system capable of liver zonation in primary rat hepatocytes. We show the differential expression of zonation markers, enhanced functionality when compared to standard static cultures and zone-specific metabolism and cell damage in the presence of paracetamol, a known zone-specific toxin. This type of advanced system provides a more in-depth and essential understanding of liver physiology and pathophysiology as well as the accurate evaluation of pharmacological interventions at a zone-specific level.