Reverse smoothing: a model-free data smoothing algorithm

Biophysical chemistry experiments, such as sedimentation-equilibrium analyses, require computational techniques to reduce the effects of random errors of the measurement process. The existing approaches have primarily relied on assumption of polynomial models and least-squares approximation. Such models by constraining the data to remove random fluctuations may distort the data and cause loss of information. The better the removal of random errors the greater is the likely introduction of systematic errors through the constraining fit itself. An alternative technique, reverse smoothing, is suggested that makes use of a more model-free approach of exponential smoothing of the first derivative. Exponential smoothing approaches have been generally unsatisfactory because they introduce significant data lag. The approaches given here compensates for the lag defect and appears promising for the smoothing of many experimental data sequences, including the macromolecular concentration data generated by sedimentation-equilibria experiments. Test results on simulated sedimentation-equilibrium data indicate that a 4-fold reduction in error may be typical over standard analyses techniques.