Sensitivity analysis and error structure of progress curves

In vitro models of axon regeneration

A variety of in vitro models have been developed to understand the mechanisms underlying the regenerative failure of central nervous system (CNS) axons, and to guide pre-clinical development of regeneration-promoting therapeutics. These range from single-cell based assays that typically focus on molecular mechanisms to organotypic assays that aim to recapitulate in vivo behavior. By utilizing a combination of models, researchers can balance the speed, convenience, and mechanistic resolution of simpler models with the biological relevance of more complex models. This review will discuss a number of models that have been used to build our understanding of the molecular mechanisms of CNS axon regeneration.

Rapid determination of enzyme kinetics from fluorescence: overcoming the inner filter effect

Fluorescence change is convenient for monitoring enzyme kinetics. Unfortunately, it loses linearity as the absorbance of the fluorescent substrate increases with concentration. When the sum of absorbance at excitation and emission wavelengths exceeds 0.08, this inner filtering effect (IFE) alters apparent initial velocities, K(m), and k(cat). The IFE distortion of apparent initial velocities can be corrected without doing fluorophore dilution assays. Using the substrate's extinction coefficients at excitation and emission wavelengths, the inner filter effect can be modeled during curve fitting for more accurate Michaelis-Menten parameters. A faster and simpler approach is to derive k(cat) and K(m) from progress curves. Strategies to obtain reliable and reproducible estimates of k(cat) and K(m) from only two or three progress curves are illustrated using matrix metalloproteinase 12 and alkaline phosphatase. Accurate estimates of concentration of enzyme-active sites and specificity constant k(cat)/K(m) (from one progress curve with [S]<<K(m)) confer accuracy, freedom of choices of [S], and robustness to k(cat) and K(m) globally fitted to a few progress curves. The economies of the progress curve approach make accurate k(cat) and K(m) more accessible from fluorescence measurements.

Detection of competitive enzyme inhibition with end point progress curve data

A model for a dimensionless factor, the inhibition detection limit (IDL), which describes the limit of detection of competitive inhibition for end point assays as a function of the proportion of substrate converted into product, has been developed. For a given end point enzymatic assay, the IDL function has a maximum that is dependent on the error structure parameters (four parameters) of the assay, the value of [S]o/K(ms), and the extent of product inhibition (K(ms)/K(mp)). Accordingly, the substrate conversion level that maximized the ability to detect samples with high Ki/[I] ratios was predicted for each member of a population of simulated assays. Furthermore, we identified a consensus substrate conversion level where the probability of a near-optimal robustness and detection limit for all the members of the assay population is maximal. Unlike the optimal substrate conversion level for individual assays, this consensus substrate conversion level was dependent only on [S]o/K(m), K(ms)/K(mp), and whether the signal increases or decreases during the course of the reaction. Consensus substrate conversion levels were beyond the initial velocity range for almost all the analyzed assay populations. It was shown that the IDL factor was a more informative indicator of assay quality than the popular Z' factor.