The least squares method is commonly used to find the parameters and sum of exponentials that form molecular fluorescence decay kinetics. However, the method usually fails to lead to a global minimum of approximation, and more reliable methods are therefore necessary for finding the sum N of exponentials that form the fluorescence decay kinetics. If the sum of the exponentials is not greater than 8 and the signal-to-noise ratio is higher than a critical ratio, which depends on N, then it is possible to calculate the sum of exponentials that form fluorescence decay kinetics. A direct, noniterative method was developed to solve the problem.

A method was proposed for multi-exponential approximation of the fluorescence decay kinetics. Unlike the well-known Prony technique, the method is suitable for analyzing large-scale experimental data arrays. The method differs from the Pade–Laplace approximation applied previously in that the Pade coefficients are calculated more accurately. The exponential parameters can be found if the following four conditions are satisfied: (1) there are no more than eight exponentials in the kinetic curve, (2) τa < 0.125T, (3) τi > 4h, and (4) the noise level is kept below a critical value. It is noteworthy that the critical value depends on the sum N of exponentials, i.e., the greater the sum N is, the lower the noise level is. T is the time domain for which the kinetic curve has been measured; h = T/n; n is the number of points that represent the kinetic curve; τa = max (τ1, τ2, …, τN); τi = min (τ1, τ2, …, τN); τk is the time constant for the kth exponential; and k = 1, 2, …, N.

The process of irreversible photochemical charge separation in photosynthetic bacterial reaction centers is proposed to be characterized by the effective rate constant. A formula to compute this effective rate constant is derived. Similar rate constant was previously considered by R.A. Marcus (Marcus R.A. 1956. J. Chem. Phys. 24, 966–978) in order to describe nonphotochemical intermolecular electron transfer. The effective rate constant of the irreversible charge separation in photosynthetic bacterial reaction centers is shown to depend on the temperature. In contrast, rate constants of the forward electron transfer from the excited singlet primary donor to the bacteriochlorophyll and from its ion-radical to the bacteriopheophytin acceptor do not depend on temperature.

An effective rate constant for the irreversible photochemical charge separation in photosynthetic bacterial reaction centers is introduced into consideration. A formula to compute this effective rate constant is derived. Similar rate constant was previously considered by R.A. Marcus (Marcus R.A. 1956. On the theory of oxidation-reduction reactions involving electron transfer. J. Chem. Phys. 24, 966-978) in order to describe non-photochemical intermolecular electron transfer. The effective rate constant of the irreversible charge separation in photosynthetic bacterial reaction centers is shown to depend on the temperature. In contrast, rate constants of the forward electron transfer from the excited primary donor to the bacteriochlorophyll and from its ion-radical to the bacteriopheophytin acceptor do not depend on temperature.

Frequencies and normal vibrational modes of bacteriochlorophyll are calculated using the semiempirical quantum-mechanical MNDO-PM3 method. To analyze the structure of normal modes, the indices of delocalization of the vibrations and the distribution functions of normal modes over atoms in the molecule are introduced. It is shown that normal vibrational modes of bacteriochlorophyll in the region from 3 to 20 cm −1 represent “intermolecular” vibrational modes of phytol and tetrapyrrole macrocycle. As the vibrational frequency increases, the normal modes delocalized both on phytol and tetrapyrrole atoms alternate with the modes that are delocalized only on phytol atoms or only on tetrapyrrole atoms. The structural properties of some modes are considered in the aspect of their possible involvement in the formation of absorption spectra of the pigments of reaction centers in photosynthesis and in the formation in them of the coordinate of a primary reaction of the intermolecular electron transfer.

Shuvalov, V. A., A. V. Klevanik, A. V. Sharkov, P. G. Kryukov and B. Ke, Picosecond spectroscopy of photosystem I reaction centers (1979) FEBS Letters 107, 313-316. The following correction may be observed in the above article: page 3 13, line 2 should read: V. A. SHUVALOV, A. V. KLEVANIK, A. V. SHARKOV+, P. G. KRYUKOV+ and Bacon KE* instead of: V. A. SHUVALOV, A. V. KLEVANIK, A. V. SHARKOV+, P. G. KRYUKOV+ and BACON K. E.*

The spectrum of vibrations and normal model for the Mg piropheophorbide-histidine complex was calculated using the MNDO-PM3 (MOPAC) semiempirical quantum chemical method. The delocalization index and the distribution function were introduced to describe the shape of normal vibrations. The greatest part (approximately 65%) of the low-frequency vibrations (1-400 cm-1) was shown to delocalize over both the His and Mg piropheophorbide molecules. Leu, Met, and Asp were also studied as the fifth ligand to the Mg piropheophorbide molecule. It is concluded that the fifth amino acid ligand to porphyrin molecules causes marked geometrical distortions in porphyrin, and induces a new, compared to four coordinated pigment, spectrum of normal modes.

Shuvalov, V. A., A. V. Klevanik, A. V. Sharkov, P. G. Kryukov and B. Ke, Picosecond spectroscopy of photosystem I reaction centers (1979) FEBS Letters 107, 313-316. The following correction may be observed in the above article: page 3 13, line 2 should read: V. A. SHUVALOV, A. V. KLEVANIK, A. V. SHARKOV+, P. G. KRYUKOV+ and Bacon KE* instead of: V. A. SHUVALOV, A. V. KLEVANIK, A. V. SHARKOV+, P. G. KRYUKOV+ and BACON K. E.*

The low-temperature absorption spectra of the Chlorobium tepidum FMO bacteriochlorophyll-protein complex at various pressures have been calculated within the framework of mini-exciton theory. The dependences of the Qy transition energies of the monomeric pigments on pressure have been found by means of functional minimization. This functional includes the parameters of both theoretical and experimental absorption spectra at low temperatures and various pressures. The dependences obtained are compared with those derived for the exciton transition energies, which have been obtained by deconvoluting absorption spectra with seven Gaussian components at each pressure. The pressure increase has been shown to result in the increased coupling energy between both the pigment molecules themselves and pigments and amino acid residues. The pigment molecules capable of binding histidines and water molecules have been shown to have the greatest and smallest responses to increased pressure, respectively. The couplings of Bchl molecules with the surrounding amino acid residues have been shown to change both the exciton delocalization index and the exciton distribution between the pigment molecules within the protein subunit; the increased pressure does not change these parameters significantly.

Reliability of the hydropathy method to predict the formation of membrane-spanning alpha-helices by integral membrane proteins and peptides whose structure is known from X-ray crystallography is analysed. It is shown that Kyte-Doolittle hydropathy plots do not predict accurately 22 transmembrane alpha-helices in the reaction centres (RC) of the photosynthetic bacteria Rhodopseudomonas viridis and Rhodobacter sphaeroides (R-26). The accuracy of prediction for these proteins was improved using an optimised Kyte-Doolittle hydrophobicity scale. However, this hydrophobicity scale did not improve the predictions for the alphabeta-peptides of the B800-850 (LH2) complexes of the photosynthetic bacteria Rhodopseudomonas acidophila and Rhodospirillum molischianum, which were excluded from the optimisation procedure. The best and worst predictions of membrane-spanning alpha-helices for the RC proteins and LH2 peptides, respectively, were obtained with a propensity scale (PRC) calculated from the amino acid sequences and X-ray data for the RC proteins. A propensity scale (PLH) obtained using the amino acid sequences and X-ray data for the alphabeta-peptides of the LH2 complexes did not give an acceptable prediction of the transmembrane segments in the LH2 peptides; moreover, it markedly contradicted the PRC scale. Amino acids have been concluded to have no significant preference to localisation in transmembrane segments. Therefore, the predictive ability of the hydropathy methodology appears to be limited: the number of transmembrane segments can be correctly calculated for the best case only, and the lengths and positions of membrane-spanning alpha-helices in a protein amino acid sequence can not be predicted exactly.

Low-temperature heterogeneous absorption and circular dichroism spectra of the Rb. sphaeroides LH2 complexes are calculated within the framework of the mini-exciton theory and diagonal static random disorder for the pure electronic transitions of the monomeric Bchl molecules. The coupling of Bchl molecules with the surrounding amino acid residues has been shown to change both the exciton distribution between the pigment molecules in each of the exciton states. The value of the delocalization index depends on the excitation wavelength and varies between 2-6 Bchl molecules. The optical transitions occurring at 780-790 and 820 nm have been found to be strongly mixed so that all Bchl molecules of the LH2 complex predetermine absorption in these spectral regions. On the other hand, absorption at 800 and 850 nm is mainly determined by the cycles of 9 and 18 Bchl molecules, respectively. Thus, the light energy absorbed by the B800 molecules at 800 nm is transferred to the B850 molecules by the interlevel exciton relaxation processes due to the population of the heavily mixed 820-nm exciton levels. The width of the heterogeneous absorption band for the cyclic monomeric aggregate has been shown to decrease as compared with the monomeric absorption band by square root(Ndel) time, where Ndel is the mean number of pigments over which the exciton is delocalized within the excited absorption band.

Low-temperature heterogeneous absorption and circular dichroism spectra of the Prosthecochloris aestuarii FMO complex are calculated within the framework of the mini-exciton theory including both the inhomogeneous distribution of exciton line frequencies and static random disorder of the pure electronic transitions of Bchl molecules. The frequencies of the Q(y) pure electronic transitions of Bchl molecules immobilized by the FMO complex polypeptides are found by minimization of a functional that links the parameters of the theoretical and experimental optical spectra. The interactions of Bchl molecules with surrounding amino acid residues has been shown to change both the exciton delocalization index and exciton distribution between the pigment molecules in each of exciton energetic state. As a consequence the interlevel exciton relaxation processes, being accompanied by an essential changes in the exciton distribution between pigment molecules, lead to the energy transfer within the FMO complex. The model spectra calculations within the framework of the static random disorder approach have been shown to give unacceptable results.

Within the framework of the exciton theory, the absorption spectrum and differential Stark spectrum are calculated for the bacteriochlorophyll-protein complex found in the photosynthetic bacterium Prosthecochloris aestuarii, whose structure was established earlier by the X-ray diffraction method. The change in the static dipole moment of a monomer bacteriochlorophyll a (BChl-a) molecule is found upon its transition to the first excited singlet state as well as changes in the static dipole moments for each exciton absorption band of the bacteriochlorophyll-protein complex consisting of seven bacteriochlorophyll molecules.

A possible structural and functional organization of the antenna chromophore protein complexes (CPC) in the Rhodopseudomonas viridis membranes was considered in terms of structural models proposed by Zuber and Brunisholz (in Chlorophylls, ed. H. Scheer (Boca Raton: CRC Press, 1991):626-703). Analysis of the absorption spectra led to the conclusion that the number of the antenna bacteriochlorophyll molecules per reaction center (RC) is 30 +/- 3 both for chromophores and quantasomes of Rps. viridis. It implies a multicentral organization of the CPCs around RCs, when the CPC of cyclic structure is formed by (alpha beta gamma)4 polypeptides. A multicentral model predicts an almost linear dependence of the antenna fluorescence yield on the oxidized primary donor concentration if the antenna fluorescence lifetimes are assumed to be 60-70 and 110-120 ps for the open and closed RCs, respectively, which is in agreement with the experimental observations. We conclude that the Rps. viridis membrane domain consists of 4-6 RCs surrounded by 6-22 CPCs, and both of these protein subsystems are packed into a hexagonal array.