Noise-induced phenomena in condensed matter and in complex systems

Scientific results

(i) Physical model of molecular machines based on the Kolmogorov-Fokker-Planck equations.

(ii) Theoretical model of the 2D and 3D Brownian motion for simulation of protein dynamics in water.

(iii) Stochastic, probability, and spectrum characteristics of the Brownian motion obtained using numerical methods and computer simulation.

(iv) Raman spectroscopy data on enzyme (chymotrypsin) and enzyme-substrate complex and their interpretation using numerical and analytical results.

In more details, the results obtained are as follows. We developed a stochastic model of molecular motor (F1-ATPase) making it possible to describe the hydrolysis of Mg-ATP molecules. In the model, we employ a dynamic equation for gamma-subunit representing a rotor and equations for probabilities of ATP and ADP binding in the catalytic centers of ATPase at various conformations. It is demonstrated that the potentials of the enzyme-substrate complex calculated for all conformations allow for 98% efficiency of the molecular motor. The model enables us to interpret the experimentally observed stepwise random rotations of the rotor by 30 and 90 degrees independent of the ATP concentration in the surrounding medium. The model makes it possible to analyze F0-ATPase complex. Using molecular dynamics, we studied statistical characteristics of hydrogen bonds at room temperature in a liquid drop containing 265 water molecules.

We employ a three-point potential to characterize the interaction of elastic water molecules. For computer simulation, we use Modyp computer codes developed by KAMA Group and MSU Molecular Design and Modeling Laboratory. Based on the results of calculations, we obtain the statistical characteristics of angles and lengths of hydrogen bonds. The lifetimes of hydrogen bonds are about 10 ps. This result is in agreement with the existing data obtained for the models with rigid water molecules. The aforesaid system can be used to analyze the interaction of water molecules with the surface of protein molecule and biomembrane and the motion of small molecules (Brownian particles) in water. We studied the effect of the Fermi resonance on the increase in the probability of potential barrier crossing for Brownian particles in a two-well potential (the Fermi-resonance conditions are satisfied for both particles). It is demonstrated that the transition time exhibits a several-fold decrease at low friction coefficients. The notion of statistically asymmetric noise is considered, i.e. random signal with zero mean, small correlation time and different probabilities of positive and negative pulses. The mechanism and conditions for such noise in Brownian motion are investigated. The reason for statistical asymmetry is the deviation from molecular chaos hypothesis. A conditional probability distribution of the velocities of particles given they are able to collide with the Brownian particle is obtained. The distribution differs considerably from the Maxwell density for the Brownian particle velocities values near the velocities of particles of medium. Possibility for statistically nonsymmetrical noise to influence the time of boundary crossing in free random motion is examined. Statistically asymmetric noise is employed to interpret the processes in molecular machines. It is demonstrated that FPE cannot be used to analyze the processes affected by asymmetric noise.

We introduced a new kind of noise, which we called noise with memory. This noise represents a set of random pulses that appear at random time moments but with a certain delay. Changing the delay time we can obtain white noise, periodical process, or a quasi-random process. The spectrum density and correlation function are calculated. Multiplying this noise by a periodic function yields switches. This noise is useful in modeling population dynamics and for solving epidemiological problems. Using the methods of Raman scattering spectroscopy and polarization-sensitive coherent anti-Stokes Raman scattering spectroscopy, we performed a comparative analysis of the conformation-sensitive bands of free enzyme (chymotrypsin) and liganded enzyme (chymotrypsin anthranilate). We analyze the bands of tyrosine and tryptophan residues, disulfide bridges, and the bands amide I and amide III. The ligandation of enzyme by anthranilic acid results in substantial changes of the secondary structure. Ligandation results in a decrease of the ?С-helix content and an increase of the content of ?Т-sheet, whereas the relative amount of random coil remains virtually unchanged. In the case of anthranilated chymotrypsin, tyrosines are stronger proton acceptors in H-bonds formed with the neighboring groups of the protein globule than in the case of free enzyme. Ligandation of enzyme results in a decrease of the content of the gauche-gauche-gauche isomers of disulfide bridges and a corresponding increase in the content of trans-gauche-trans isomers.

Based on the results obtained, we conclude that the local substrate binding in the active site results in substantial conformational changes of enzyme molecule as a whole.

List of references

1. A. V. Kargovsky, O. P. Khodjer, and Yu. M. Romanovsky, Functional dynamics of hydrolytic enzymes, Proc. SPIE, v. 5068, pp. 16-26 (2003).

2. A. F. Pogrebnaya, Yu. M. Romanovsky, and A. N. Tikhonov, Electrostatic interactions in catalytic centers of F1-ATPase, Proc. SPIE, v. 5068, pp. 27-35 (2003).

3. O. A. Chichigina, A. V. Netrebko, and Yu. M. Romanovsky, A model of oscilations of subglobular moleculel with anomalous quality factor, Fluctuations and Noise Letters, v.3, no. 3, pp. L205-L211 (2003).

4. A. N. Tikhonov, A. F. Pogrebnaya, and Yu. M. Romanovsky, Electrostatic interactions in catalytic centers of F1-ATPase, Biofizika, v. 48, no. 6, pp. 1052-1070 (2003) (in Russian).

5. N. N. Brandt, A. Yu. Chikishev, and I. K. Sakodinskaya. Raman spectroscopy of tris-(hydroxymethyl)aminomethane as a model system for the studies of chymotrypsin activation by crown ether in organic solvents, J. Molecular Structure, v. 648, no. 3, pp.177-182 (2003).

6. N. R. Arutyunyan, N. N. Brandt, A. Yu. Chikishev, and S. I. Lebedenko, Laser Raman spectroscopy of proteins: problem of the broadband background, Italian-Russian Laser Symposium, Book of Abstratcs, p. 79 (2003).

7. W. Ebeling, A. Kargovsky, A. Netrebko, and Yu. Romanovsky, Fermi resonance - new applications of an old effect, Fluctuations and Noise Letters, v. 4, no. 1, pp. L195-L205 (2004).

8. A. F. Pogrebnaya, Yu. M. Romanovsky, and A. N. Tikhonov, Proc. SPIE, v. 5330, pp. 120-131 (2004).

9. A. F. Pogrebnaya, Yu. M. Romanovsky, and A. N. Tikhonov, Stochastic dynamics of F1ATPase molecular motor, III All-Russia Congress of Biophysicists, Book of Abstracts, v. 1, pp. 85-86 (2004) (in Russian).

10. E. V. Shuvalova and Yu. M. Romanovsky, Proton transfer in catalytic site of chymotrypsin, III All-Russia Congress of Biophysicists, Book of Abstracts, v. 1, pp. 127-128 (2004) (in Russian).

11. V. Mitrofanov, Yu. Romanovsky, and A. Netrebko, On the structure and dynamics of hydrogen bonds in liquid water, Proc. SPIE (in press).

12. V. V. Belik, Yu. M. Romanovsky, and O. A. Chichigina, Statistically nonsymmetric noise upon Brownian motion, Topical Problems of Radiophysics, A. N. Malakhov Memorial Issue, (2004) (in Russian) (in press).

13. N. N. Brandt, A. Yu. Chikishev, A. I. Chulichkov, P. A. Ignatiev, S. I. Lebedenko, and O.V. Voronina, Raman spectra comparison method, Laser Physics, (2004) (in press).

14. N. R. Arutyunyan, N. N. Brandt, A. Yu. Chikishev, S. I. Lebedenko, and Yu. M. Romanovsky, Nature of the broadband background in Raman spectra of aqueous solutions of chymotrypsin, Laser Physics, v.14 (2004) (in press).