Robert S. Knox

Oxygen consumption and diffusion effects in photodynamic therapy.

Effects of oxygen consumption in photodynamic therapy (PDT) are considered theoretically and experimentally. A mathematical model of the Type II mechanism of photooxidation is used to compute estimates of the rate of therapy-dependent in vivo oxygen depletion resulting from reactions of singlet oxygen (1O2) with intracellular substrate. Calculations indicate that PDT carried out at incident light intensities of 50 mW/cm2 may consume 3O2 at rates as high as 6-9 microM s-1. An approximate model of oxygen diffusion shows that these consumption rates are large enough to decrease the radius of oxygenated cells around an isolated capillary. Thus, during photoirradiation, cells sufficiently remote from the capillary wall may reside at oxygen tensions that are low enough to preclude or minimize 1O2-mediated damage. This effect is more pronounced at higher power densities and accounts for an enhanced therapeutic response in tumors treated with 360 J/cm2 delivered at 50 mW/cm2 compared to the same light dose delivered at 200 mW/cm2. The analysis further suggests that the oxygen depletion could be partially overcome by fractionating the light delivery. In a transplanted mammary tumor model, a regimen of 30-s exposures followed by 30-s dark periods produced significantly longer delays in tumor growth when compared to the continuous delivery of the same total fluence.

Theory of polarization quenching by excitation transfer

Abstract The several modern theories of concentration quenching of fluorescence polarization (cq/tfp) are in fair qualitative agreement with one another, but differ considerably in their physical and statistical assumptions and in their quantitative predictions of the resonance transfer rate from a given set of data. A critical comparison of the theories of Foster, Weber and Jablonski is made and a new theory on excitation transfer within clusters of molecules is outlined. Certain cq/tfp data on phenol, anthracene, fluorescein and chlorophyll a are discussed and reinterpreted on the basis of the theory.

THEORY OF POLARIZED FLUORESCENCE FROM MOLECULAR PAIRS: FÖRSTER TRANSFER AT LARGE ELECTRONIC COUPLING

Polarization properties of the fluorescence from a pair of identical molecules coupled electronically are examined on the basis of a stochastic Liouville equation formalism developed in 1979 by Rahman, Knox and Kenkre. The time development of polarization is calculated for random ensembles of rigid molecule pairs under initial conditions that represent either selective excitation or broad‐band coherent excitation. We hold that the applicability of the Forster mechanism is not limited to cases of weak coupling, and we indicate the rationale and a method for observing it in cases involving large interaction between transition dipoles.

Theory of depolarization of fluorescence in molecular pairs

Abstract Depolarization of fluorescence as a result of energy transfer is studied phenomenologically for a model pair of electronically coupled molecules. The usual rate equations are replaced by the Stochastic Liouville Equations and new radiative terms are included. An expression for the fluorescence polarization for all strengths of electronic coupling between the molecules is obtained. The inclusion of off-diagonal density matrix elements is essential for resolving a paradox arising in the Forster theory of depolarization. The calculation points the way toward using a previously untapped source of information on coherence in complex systems.

On the theory of trapping of excitation in the photosynthetic unit

Abstract Current theories of the primary physical processes in the photosynthetic unit are based on a model in which excitations diffuse throughout a lattice and become trapped at a specialized centre. Despite the apparently well-defined nature of the problem, master equation and random walk calculations have given different answers for the average trapping time, and some doubts have been expressed about the equivalence of the methods. The equivalence is made explicit here, and the two-dimensional random walk solution by ten Bosch & Ruijgrok (1963) is found to be incorrect. The asymptotic dependence of trapping time on N , the number of sites per trap, found to be proportional to N ln N by Pearlstein (1966) and by Robinson (1967) in square networks, has been verified and extended to the triangular case. Some general kinetic considerations are presented and applications to the theory of photosynthesis are briefly discussed.

Thermodynamics and the Primary Processes of Photosynthesis

Numerous discussions of the relationship of the thermodynamics of radiation to photosynthesis have been published, but the results are often in disagreement or at best difficult to compare with one another. The recent treatment of maximal photosynthetic efficiencies by Ross and Calvin is here shown to be directly related to the thermodynamic method of Duysens. A smooth connection between the light and dark conditions is derived, the case of polarized light is considered briefly, and a critique of some other thermodynamic treatments is presented.

Energy transfer and fluorescence mechanisms in photosynthetic membranes

Energy transfer in photosynthetic membranes involves the migration of excitons from light‐harvesting antenna chlorophyll‐protein complexes to the reaction center complexes. Recent efforts have focused on determining the time of arrival of excitons (trapping times) at the reaction centers following excitation with a single picosecond laser pulse. Three different approaches have been utilized: (1) determination of appearance of separated charges within the reaction centers by differential absorbtion spectroscopy, (2) determination of appearance of separated charges by fast photoemf measurements, and (3) kinetics of decay of fluorescence. The first two methods provide more direct information on exciton trapping by reaction centers than fluorescence methods, but are experimentally difficult to realize. Therefore, much activity has centered around the accurate measurement and analysis of fluorescence‐decay profiles by single‐photon counting methods. In green plants, about three different components with lifeti...

Theory of Trapped‐Hole Centers in Rare‐Gas Solids

Experimental evidence suggests that self‐trapping of holes occurs in rare‐gas solids. Formation of an intrinsic diatomic center, similar to the Vk center, is investigated as a possible mechanism. The energy of trapping a valence‐band hole is discussed on the basis of a simple model for the rare‐gas hole center. A method of calculating the relaxation and polarization energies is developed, appropriate parameters for the model estimated, and the method applied to solid argon, krypton, and xenon to determine the degree of relaxation and the contributions to the trapping energy. The results suggest stable trapped‐hole centers at 0°K associated with only small lattice relaxations. The internal molecular binding of the center is found to be the overwhelming factor determining its configuration on this model.

Dipole and Oscillator Strengths of Chromophores in Solution

Abstract A widely published expression for dipole strengths of optical transitions is found to require correction. The proposed adjustment, which involves the refractive index of the solvent in which the strengths are measured, may lead to significant changes in predictions that have been based on the equation. We discuss a closely related issue, the vacuum dipole strength concept, in an empirical context. A simple mapping procedure for estimating index dependence of strengths is advocated as an alternative to effective field corrections. The technique is illustrated for chlorophyll a and bacteriochlorophyll a.

Optical spectra and exciton coherence

Abstract The overlap of donor emission and acceptor absorption spectra has long been known as a determining factor in the rate of excitation transfer. Memory functions capable of providing short time information can be obtained in an equally direct way from spectra. We present several examples derived from both real and model systems to illustrate the effect of spectral linewidth and splitting on the coherence of excitation undergoing transfer.