Direct analysis of continuous relaxation spectra.

The dynamic response of a complex biological or chemical system to a perturbation must often be described by an integral over an effectively continuous relaxation spectrum. Because of its well known instability to experimental error, the direct estimation of the spectrum is generally considered unfeasible. However, we show that good estimates can be obtained by constraining the spectrum to be the smoothest one that is consistent with the data. Also constraining the spectrum to be non-negative, if there is a priori knowledge of this, can further increase its accuracy. The method is completely automatic in that no initial estimates or assumptions about the functional form of the spectrum are necessary. Therefore models can be tested more rigorously and objectively since the functional form that they predict for the spectrum need not be assumed at the outset of the analysis as with parameter-fitting procedures. The method is illustrated on simulated data on the photodissociation of CO from heme proteins at low temperatures. The nonuniqueness of the solutions is discussed.