Quantitative analysis of cytosolic free calcium oscillations in neutrophils by mathematical modelling

Mathematical models are often used to elucidate mechanisms behind cytosolic Ca 2+ oscillations. We have evaluated the use of mathematical modelling to analyse and quantify Ca 2+ signal patterns, in single, adherent human neutrophils (PMN) after stimulation by the bacterial peptide N-formyl-methionyl-leucyl-phenylalanine (fMLP). The cells were loaded with Fura-2 and fluctuations in cytosolic Ca 2+ recorded with a video based digital imaging system. A new indirect intracellular calibration method was introduced to avoid the uncertainty in obtaining an equilibrium between the extracellular and intracellular calcium concentrations. Two different approaches to mathematical modelling were used. First, we applied a sensitivity analysis with a two-pool model by assuming an optimal situation using reliable a priori estimates of all structural parameters (e.g. Hill coefficients and dissociation constants). We found that the a priori estimates of the other 5 more variable parameters must lie within the range of 25–400% of the postulated true parameter values to be reliable in a parameter estimation method. Small changes (less than 5%) in those variable parameter values induced very different types of signal patterns which may have some relevance in evaluating a possible functional significance to the oscillatory signals. Second, we employed a one-pool, non oscillatory model integrated with a power spectrum method as a tool to quantify the dose dependency between fMLP (1–1000 nM) and parameters describing the biphasic process of calcium signalling and parameters describing only the oscillatory components. We conclude that the frequency of the observed oscillations assembled around one characteristic frequency independent of fMLP concentration, and sinusoidal oscillations were observed most frequently in PMN stimulated to a moderate peak [Ca 2+] i level.