Bibliography
121
alfa1B = Raccess / (omega * Taubuff);
alfa1 = -(alfa1A + alfa1B) / (omega * domega); % Eq.(7.6)
alfa2A = Rm / (1 + (omega * Taum) 2 );
alfa2B = Raccess;
alfa2 = (alfa2A + alfa2B) / (omega * domega); % Eq.(7.7)
alfasquare = (alfa1 2 ) + (alfa2 2 ); PMFsqOmega = (2 * kT * alfa2) / (alfasquare *
omega);% Eq.(7.9)
integral = integral + deltaOmega * PMFsqOmega; % Eq. (7.10)*pi w(i)=omega;
PMFsqw(i)=PMFsqOmega;
end
figure(1); plot(w, PMFsqw);grid;
PMFsq = integral / pi % Eq(10)
MPMF = 1000*sqrt(PMFsq) %Mean PMF fluctuation “mV”
Bibliography
1. Procopio, J., Fornés, J.A.: Fluctuations of the proton-electromotive force across the inner
mitochondrial membrane. Phys. Rev. E 55(5), 6285–6288 (1997)
2. Lehninger, A.L., Nelson, D.L., Cox, M.M.: Principles of Biochemistry. Worth Publishers, Inc.,
New York (1993)
3. Procopio, J., Fornés, J.A.: Fluctuation-dissipation theorem imposes high-voltage fluctuations
in biological ionic channels. Phys. Rev. E. 51, 829 (1995)
4. Läuger, P.: Electrogenic Ion Pumps. Sinauer Associates, Inc. Publishers, Sunderland (1990)
5. Lill, H., Althoff, G., Junge, W.: Analysis of ionic channels by a flash spectrophotometric
technique applicable to thylakoid membranes: CF0, the proton channel of the chloroplast ATP
synthase, and, for comparison, Gramicidin. J. Membrane Biol. 98, 69 (1987)
6. Stein, W.D., Läuger, P.: Kinetic properties of F0F1-ATPases. Theoretical predictions from
alternating-site models. Biophys. J. 57, 255 (1990)
7. Kasianowicz, J.J., Bezrukov, S.: Protonation dynamics of the alpha-toxin ion channel from
spectral analysis of pH-dependent current fluctuations. Biophys. J. 69, 94 (1995)
8. Marrink, S.J., Jahnig, F., Berendsen, J.C.: Proton transport across transient single-file water
pores in a lipid membrane studied by molecular dynamics simulations. Biophys. J. 71, 632
(1996)
9. Deame, D.W., Nichols, J.W.: Proton flux mechanisms in model and biological membranes. J.
Membrane Biol. 107, 91 (1989)
10. Woodhull, A.M.: Ionic blockage of sodium channels in nerve. J. Gen. Physiol. 61, 687 (1973)
11. Gutman, M., Kotlyar, A.B., Borovok, N., Nachliel, E.: Reaction of bulk protons with a
mitochondrial inner membrane preparation: time-resolved measurements and their analysis.
Biochemistry 32, 2942 (1993)
12. DeCoursey, E., Cherny, V.V.: Effects of buffer concentration on voltage-gated H+ currents:
does diffusion limit the conductance? Biophys. J. 71, 182 (1996)
13. Nagle, J.F., Morowitz, H.J.: Molecular mechanisms for proton transport in membranes. Proc.
Natl. Acad. Sci. USA 75, 298 (1978)
14. Heberle, J., Riesle, J., Thiedemann, G., Oesterhelt, D.N.A., Dencher, N.A.: Proton migration
along the membrane surface and retarded surface to bulk transfer. Nature 370, 379 (1994)
121
alfa1B = Raccess / (omega * Taubuff);
alfa1 = -(alfa1A + alfa1B) / (omega * domega); % Eq.(7.6)
alfa2A = Rm / (1 + (omega * Taum) 2 );
alfa2B = Raccess;
alfa2 = (alfa2A + alfa2B) / (omega * domega); % Eq.(7.7)
alfasquare = (alfa1 2 ) + (alfa2 2 ); PMFsqOmega = (2 * kT * alfa2) / (alfasquare *
omega);% Eq.(7.9)
integral = integral + deltaOmega * PMFsqOmega; % Eq. (7.10)*pi w(i)=omega;
PMFsqw(i)=PMFsqOmega;
end
figure(1); plot(w, PMFsqw);grid;
PMFsq = integral / pi % Eq(10)
MPMF = 1000*sqrt(PMFsq) %Mean PMF fluctuation “mV”
Bibliography
1. Procopio, J., Fornés, J.A.: Fluctuations of the proton-electromotive force across the inner
mitochondrial membrane. Phys. Rev. E 55(5), 6285–6288 (1997)
2. Lehninger, A.L., Nelson, D.L., Cox, M.M.: Principles of Biochemistry. Worth Publishers, Inc.,
New York (1993)
3. Procopio, J., Fornés, J.A.: Fluctuation-dissipation theorem imposes high-voltage fluctuations
in biological ionic channels. Phys. Rev. E. 51, 829 (1995)
4. Läuger, P.: Electrogenic Ion Pumps. Sinauer Associates, Inc. Publishers, Sunderland (1990)
5. Lill, H., Althoff, G., Junge, W.: Analysis of ionic channels by a flash spectrophotometric
technique applicable to thylakoid membranes: CF0, the proton channel of the chloroplast ATP
synthase, and, for comparison, Gramicidin. J. Membrane Biol. 98, 69 (1987)
6. Stein, W.D., Läuger, P.: Kinetic properties of F0F1-ATPases. Theoretical predictions from
alternating-site models. Biophys. J. 57, 255 (1990)
7. Kasianowicz, J.J., Bezrukov, S.: Protonation dynamics of the alpha-toxin ion channel from
spectral analysis of pH-dependent current fluctuations. Biophys. J. 69, 94 (1995)
8. Marrink, S.J., Jahnig, F., Berendsen, J.C.: Proton transport across transient single-file water
pores in a lipid membrane studied by molecular dynamics simulations. Biophys. J. 71, 632
(1996)
9. Deame, D.W., Nichols, J.W.: Proton flux mechanisms in model and biological membranes. J.
Membrane Biol. 107, 91 (1989)
10. Woodhull, A.M.: Ionic blockage of sodium channels in nerve. J. Gen. Physiol. 61, 687 (1973)
11. Gutman, M., Kotlyar, A.B., Borovok, N., Nachliel, E.: Reaction of bulk protons with a
mitochondrial inner membrane preparation: time-resolved measurements and their analysis.
Biochemistry 32, 2942 (1993)
12. DeCoursey, E., Cherny, V.V.: Effects of buffer concentration on voltage-gated H+ currents:
does diffusion limit the conductance? Biophys. J. 71, 182 (1996)
13. Nagle, J.F., Morowitz, H.J.: Molecular mechanisms for proton transport in membranes. Proc.
Natl. Acad. Sci. USA 75, 298 (1978)
14. Heberle, J., Riesle, J., Thiedemann, G., Oesterhelt, D.N.A., Dencher, N.A.: Proton migration
along the membrane surface and retarded surface to bulk transfer. Nature 370, 379 (1994)