Computational simulation of the reactive oxygen species and redox network in the regulation of chloroplast metabolism.

Gerken M, Kakorin S, Chibani K, Dietz K-J. Computational simulation of the reactive oxygen species and redox network in the regulation of chloroplast metabolism. PLoS computational biology. 2020;16(1): e1007102.Cells contain a thiol redox regulatory network to coordinate metabolic and developmental activities with exogenous and endogenous cues. This network controls the redox state and activity of many target proteins. Electrons are fed into the network from metabolism and reach the target proteins via redox transmitters such as thioredoxin (TRX) and NADPH-dependent thioredoxin reductases (NTR). Electrons are drained from the network by reactive oxygen species (ROS) through thiol peroxidases, e.g., peroxiredoxins (PRX). Mathematical modeling promises access to quantitative understanding of the network function and was implemented by using published kinetic parameters combined with fitting to known biochemical data. Two networks were assembled, namely the ferredoxin (FD), FD-dependent TRX reductase (FTR), TRX, fructose-1,6-bisphosphatase (FBPase) pathway with 2-cysteine PRX/ROS as oxidant, and separately the FD, FD-dependent NADP reductase (FNR), NADPH, NTRC-pathway for 2-CysPRX reduction. Combining both modules allowed drawing several important conclusions of network performance. The resting H2O2 concentration was estimated to be about 30 nM in the chloroplast stroma. The electron flow to metabolism exceeds that into thiol regulation of FBPase more than 7000-fold under physiological conditions. The electron flow from NTRC to 2-CysPRX is about 5.32-times more efficient than that from TRX-f1 to 2-CysPRX. Under severe stress (30 muM H2O2) the ratio of electron flow to the thiol network relative to metabolism sinks to 1:251 whereas the ratio of e- flow from NTRC to 2-CysPRX and TRX-f1 to 2-CysPRX rises up to 1:67. Thus, the simulation provides clues on experimentally inaccessible parameters and describes the functional state of the chloroplast thiol regulatory network

Revision of Boltzmann statistics for a finite number of particles

Kakorin S. Revision of Boltzmann statistics for a finite number of particles. AMERICAN JOURNAL OF PHYSICS. 2009;77(1):48-53.The Stirling approximation, ln(N!)approximate to N ln(N)-N, is used in the literature to derive the exponential Boltzmann distribution. We generalize the latter for a finite number of particles by applying the more exact Stirling formula and the exact function ln(N!). A more accurate and analytical formulation of Boltzmann statistics is found in terms of the Lambert W-function. The Lambert-Boltzmann distribution is shown to be a very good approximation to the exact result calculated by numerical inversion of the Digamma-function. For a finite number of particles N the exact distribution yields results that differ from the usual exponential Boltzmann distribution. As an example, the exact Digamma-Boltzmann distribution predicts that the constant-volume heat capacity of an Einstein solid decreases with decreasing N. The exact Digamma-Boltzmann distribution imposes a constraint on the maximum energy of the highest populated state, consistent with the finite total energy of the microcanonical ensemble

Electrooptics of membrane electroporation and vesicle shape deformation

Neumann E, Kakorin S. Electrooptics of membrane electroporation and vesicle shape deformation. CURRENT OPINION IN COLLOID & INTERFACE SCIENCE. 1996;1(6):790-799.Electrooptical and conductometric methods continue to reveal new and more detailed information on the dynamic properties of membranes in electric fields. In particular, the electric pore formation in lipid vesicles, doped with optical probes, has been successfully investigated with electrooptical techniques thus providing new insight into the lipid rearrangements underlying membrane electroporation (ME) and vesicle deformation. Progress in understanding the molecular mechanism of ME and related phenomena, such as electrofusion of cells or electroinsertion of foreign proteins into membranes, is crucially important for the numerous applications of ME, for example, direct electroporative gene transfer and drug delivery in the new medical discipline of electroporative chemotherapy

Electrooptical relaxation spectrometry of membrane electroporation in lipid vesicles

Kakorin S, Neumann E. Electrooptical relaxation spectrometry of membrane electroporation in lipid vesicles. In: Colloids and Surfaces A: Physicochemical and Engineering Aspects. COLLOIDS AND SURFACES. A, PHYSICOCHEMICAL AND ENGINEERING ASPECTS. Vol 209. ELSEVIER SCIENCE BV; 2002: 147-165.The classical interpretation of the experimental electric turbidity and absorbance dichroisms has been extended to account for chemical contributions to the dichroitic signal caused by changes in the immediate neighborhood of the scattering centers or chromophores. In diluted suspensions of lipid bilayer vesicles (Lecithin (20%), concentration I mM) of radius a = 90 nm, doped with diphenylhexatrienyl-phosphatidylcholine (beta-DPH pPC, 5 muM), the chemical modes refer to the entrance of water into the head-group region of the lipids in the bilayer and into those membrane parts constituting the electropores. We propose here, an extended analytical approach to correctly analyze turbidity and absorbance relaxation data on membrane electroporation (ME) and electro-elongation of lipid vesicles. It is shown that the combination of turbidity and absorbance data provides a tool to quantify molecular order and rapid motion of optical probes within the vesicle bilayer in terms of order parameters. (C) 2002 Elsevier Science B.V. All rights reserved

Electroporation of curved lipid membranes in ionic strength gradients

Neumann E, Kakorin S. Electroporation of curved lipid membranes in ionic strength gradients. BIOPHYSICAL CHEMISTRY. 2000;85(2-3):249-271.A thermodynamic theory for the membrane electroporation of curved membranes such as those of lipid vesicles and cylindrical membrane tubes has been developed. The theory covers in particular the observation that electric pore formation and shape deformation of vesicles and cells are dependent on the salt concentration of the suspending solvent. It is shown that transmembrane salt gradients can appreciably modify the electrostatic part of Helfrich's spontaneous curvature, elastic bending rigidity and Gaussian curvature modulus of charged membranes. The Gibbs reaction energy of membrane electroporation can be explicitely expressed in terms of salt gradient-dependent contributions of bending, the ionic double layers and electric surface potentials and dielectric polarisation of aqueous pores. In order to cover the various physical contribution to the chemical process of electroporation-resealing, we have introduced a generalised chemophysical potential covering all generalised forces and generalised displacements in terms of a transformed Gibbs energy formalism. Comparison with, and analysis of, the data of electrooptical relaxation kinetic studies show that the Gibbs reaction energy terms can be directly determined from turbidity dichroism (Planck's conservative dichroism). The approach also quantifies the electroporative cross-membrane material exchange such as electrolyte release, electrohaemolysis of red blood cells or uptake of drugs and dyes and finally gene DNA by membrane electroporation. (C) 2000 Elsevier Science B.V. All rights reserved

Ionic conductivity of electroporated lipid bilayer membranes

Kakorin S, Neumann E. Ionic conductivity of electroporated lipid bilayer membranes. In: Bioelectrochemistry. BIOELECTROCHEMISTRY. Vol 56. ELSEVIER SCIENCE SA; 2002: 163-166.The ionic conductivity of lipid membrane pores has been theoretically analysed in terms of electrostatic interactions of the transported ions with the low-dielectric pore wall for a commonly encountered case of unequal concentrations of electrolyte on the two sides of curved lipid membranes. Theoretical analysis of the data on the conductivity of the electroporated membrane of lipid vesicles (Lecithin 20%) of radius a=90 nm yields the molar energy of interaction of a small monovalent ion with a pore wall w(0)=9+/-1 RT (or w(0)=22+/-kJ mol(-1)), corresponding to a mean pore radius of (r) over bar (p)=0.56+/-0.05 nm. The proposed theoretical approach provides a tool for the analysis and description of the nonlinear current-voltage dependencies in membrane pores and channels. (C) 2002 Published by Elsevier Science B.V

Assessment of Michaelis-Menten parameters by analysis of single time courses of enzyme-catalyzed reactions

Schleeger M, Heberle J, Kakorin S. Assessment of Michaelis-Menten parameters by analysis of single time courses of enzyme-catalyzed reactions. In: EBEC Abstract Book. Biochimica et Biophysica Acta (BBA) - Bioenergetics. Vol 1797. Elsevier; 2010

Membrane electroporation: chemical thermodynamics and flux kinetics revisited and refined

Neumann E, Kakorin S. Membrane electroporation: chemical thermodynamics and flux kinetics revisited and refined. EUROPEAN BIOPHYSICS JOURNAL WITH BIOPHYSICS LETTERS. 2018;47(4):373-387.The chemical thermodynamic concept for membrane electroporation is critically revisited. The hysteresis in the electric field dependence of the rapid in-field electroporation events (on the in-field hysteresis branch) and the slower post-field pore resealing process (zero-field hysteresis branch) is a typical ensemble property involving rapid single-pore opening-closing events that are temporally and spatially distributed. In the case of spherical membrane shells in homogeneous external fields, the acting local field is dependent on the polar-angular position. Hence, the experimental state distribution constant and the ensemble rate coefficients are statistical position averages; they are cosine square averages of the polar angle. Advanced flux analysis uses the concept of time-dependent flux coefficients reflecting the kinetics of the rate-limiting structural processes of electroporation and membrane resealing. The explicit integral flux equations rationalize the sigmoid onset of the in-field kinetics and quantify the post-field-stretched exponentials as exponentials of exponentials. Finally, the new analytical proposal for the evaluation of the electric field strength dependence of global cell electroporation data starts with the low-field range and continues with iterative parameter optimisation over the entire field strength range

Digression on membrane electroporation and electroporative delivery of drugs and genes.

Neumann E, Kakorin S. Digression on membrane electroporation and electroporative delivery of drugs and genes. Radiol Oncol. 1998;32:7-17

Conductometric study of the surface conductivity of colloidal particles of palygorskite in water

Voitylov V, Kakorin S, Trusov A. Conductometric study of the surface conductivity of colloidal particles of palygorskite in water. Colloid. J. 1990;52:15-20