1. Charge transfer by nonlinear excitations in DNA Institute of mathematical problems of biology RAS V.D.Lakhno

2. Basic linear biopolymer - DNA Relative space positions of Н – bounds and stacking interactions in DNA Space DNA structure

3. Mechanical DNA models Ковалентная связь ~ 3,6 эВ Стэкинговое взаимодействие ~ 0,14  0,63 эВ Водородная связь ~ 0,13  0,26 эВ

4. Peyrard – Bishop – Dauxois model J.-X Zhu etal, J. of Phys. 19, (2007), 136203

5. Peyrard – Bishop – Dauxois model with excess charge basis  Thimin (Т) Cytozin (С) Adenin (А) Guanin (G) 0,66 eV 0,45 eV 0

6. Electron motion in Electric field in harmonic approach. Holstein model. Motion equatioon:

7. Fast motion of localized excitations on large distance in strong electric field

8. Super fast motion of localized excitations in strong electric field.

9. Nonlinear fast moving non equalibrium excitation. A.N.Korshunova, V.D.Lakhno Physica E, 60 (2014), 206-209

10. Computer expenditure For the chain with N = 10 3 ÷ 10 5 the requested time on IMPB RAS cluster ( processing power 1,2 Tfl ) is about 240 hours of continual calculations (~10 9 integration steps). The main problem is a number of parameters: Initial data ξ Electric field E Chain length N

11. Nonlinear oscillations and waves in DNA without electron, excited by external influence Formation of standing breather under excitation of one chain particle by initial impulse (,, ). On the left hand side, a), time evolution of velocity distribution, on the right hand side, б), fragment of distribution of displacements (red) and particle velocities (green) at the end of simulation. Breather frrequency Excitation by weak impulse:

12. DNA excitation by strong impulse Chain excitation by strong initial impulse of one particle The time evolution of distribution of particle velocities, а), and displacements distribution (red) and velocities (green) in several successive moments, b)–g). b) t = 0 c) t = 50 d) t = 100 e) t = 200 f) t = 300 g) t = 400 a)

13. DNA excitation by periodic influence Chain excitation by periodic (harmonic) influence of the velocity of one particle. The time evolution particle velocities is shown

14. Interaction of an electron with nonlinear localized waves in DNA. (initial impulse of one site) Bubble and breather excitation by initial impulse of one particle ( ) and electron capture ( ). The time evolution of probability function to observe the electron in the chain is shown, а), distribution of probability density (b) and displacement q n (red) and velocities v n (green) ofparticles (c) along the chain at the end of simulation at a) b) c)

15. Periodic influence (one site) Excitation of babble and breather by external periodic perturbation of velocity of one particle and electron capture. The time evolution of probability function to observe the electron in the chain is shown, а), distribution of probability density (b) and displacement q n (red) and particle velocities v n (green) (c) along the chain at the end of simulation at. Other parameters have the values, indicated above ( ). a) b) c)

16. Directed motion. Periodic influence on 4-sites with phase shift. Babble exitation by periodic external influence on the velocities of four particls ( ) and electron capture. The evolution of probability distribution function of electron is shown (left) and fragment of probability distribution function along the chain (right) in the moment before the breaking of bound state

17. Polaron interaction by babbles I. Attraction of polaron to babble. Polaron motion due to breather or babble excitation. Time evolution of electron probability density distribution is shown, а), c) probability density distribution of electron, b), d), displacements (red) and velocities (green), e), f) along the chain at the end of simulation. On the left hand side – weak influence ( ), on the right hand side – strong influence ( ). а) b) e) c) d) f)

18. Interaction of polaron with babbles II. Repulson of polaron from babble. Polaron motion due to breather excitation by weak external influence (i.e. originaly polaron moves from the breather), а), electron probability distribution on n-th site, b), and displacements (red) and velocities (green), c), at the end of simulation. N = 200, а) b) c)

19. Conclusions. 1.The problem of low mobility of charge carriers in DNA can be overcome. 2.The special initial conditions can be constructed. 3.The external force can influence on charge motion by creation the nonlinear excitation in DNA.