Scaling and critical-like behavior in multidimensional diffusive dynamics

Antigen-antibody binding kinetics for biosensor applications. A dual-fractal analysis

The diffusion-limited binding kinetics of antigen (or antibody) in solution to antibody (or antigen) immobilized on a biosensor surface is analyzed within a fractal framework. The fit obtained by a dual-fractal analysis is compared with that obtained from a single-fractal analysis. In some cases, the dual-fractal analysis provides an improved fit when compared with a single-fractal analysis. This was indicated by the regression analysis provided by Sigmaplot (San Rafael, CA). These examples are presented. It is of interest to note that the state of disorder (or the fractal dimension) and the binding rate coefficient both increase (or decrease, a single example is presented for this case) as the reaction progresses on the biosensor surface. For example, for the binding of monoclonal antibody MAb 49 in solution to surface-immobilized antigen, a 90.4% increase in the fractal dimension (Df1 to Df2) from 1.327 to 2.527 leads to an increase in the binding rate coefficient (k1 to k2) by a factor of 9.4 from 11.74 to 110.3. The different examples analyzed and presented together provide a means by which the antigen-antibody reactions may be better controlled by noting the magnitude of the changes in the fractal dimension and in the binding rate coefficient as the reaction progresses on the biosensor surface.

A fractional calculus approach to self-similar protein dynamics

Relaxation processes and reaction kinetics of proteins deviate from exponential behavior because of their large amount of conformational substrates. The dynamics are governed by many time scales and, therefore, the decay of the relaxation function or reactant concentration is slower than exponential. Applying the idea of self-similar dynamics, we derive a fractal scaling model that results in an equation in which the time derivative is replaced by a differentiation (d/dt)beta of non-integer order beta. The fractional order differential equation is solved by a Mittag-Leffler function. It depends on two parameters, a fundamental time scale tau 0 and a fractional order beta that can be interpreted as a self-similarity dimension of the dynamics. Application of the fractal model to ligand rebinding and pressure release measurements of myoglobin is demonstrated, and the connection of the model to considerations of energy barrier height distributions is shown.

Ligand binding to heme proteins: the effect of light on ligand binding in myoglobin

Extended illumination slows the rebinding of CO to myoglobin after photodissociation at cryogenic temperatures. Two types of models have been put forward to explain the effect: motions of the CO within the heme pocket or conformational transitions of the protein. To resolve this ambiguity, we have studied the effect of extended illumination on ligand binding to horse and sperm whale myoglobin (hMb and swMb) with temperature-derivative spectroscopy, monitoring the reaction in the CO stretch bands in the infrared and the conformation-sensitive band III near 760 nm. The experiments show that the stretch frequency of the photodissociated CO does not change upon illumination, implying that the slowing of the CO rebinding is caused by conformational relaxation of Mb from the bound state toward the deoxy structure. The light-induced relaxation (LIR) depends on the number of photons absorbed but not on the light intensity or duration separately. LIR occurs on photon absorption in either the bound or photodissociated state and depends on the temperature at which the MbCO is illuminated. The LIR proceeds in jumps through a small number of conformational substates. The effective barrier for rebinding increases with each step. The substates populated are similar to those found in the thermally-induced relaxation (TIR) that is observed above 160 K. LIR depends markedly on the structural details; it differs for swMbCO and hMbCO and even for the three A substates of swMbCO. Pronounced differences exist between the effects in MbCO and MbO2. The similarity of LIR and TIR leads to a revised model for ligand binding to swMbCO and hMbCO, in which the relaxation is crucial for the escape of the ligand from the pocket, as was first suggested by Friedman [Friedman, J. M. (1985) Science 228, 1273-1280].

The transition from inhomogeneous to homogeneous kinetics in CO binding to myoglobin

Heme proteins react inhomogeneously with ligands at cryogenic temperatures and homogeneously at room temperature. We have identified and characterized a transition from inhomogeneous to homogeneous behavior at intermediate temperatures in the time dependence of CO binding to horse myoglobin. The turnover is attributed to a functionally important tertiary protein relaxation process during which the barrier increases dynamically. This is verified by a combination of theory and multipulse measurements. A likely biological significance of this effect is in the autocatalysis of the ligand release process.