Molecular Structure and the Dynamics of the …...email: [email protected] Received December 12,...

ISSN 1990�7931, Russian Journal of Physical Chemistry B, 2014, Vol. 8, No. 4, pp. 524–533. © Pleiades Publishing, Ltd., 2014.Original Russian Text © K.V. Shaitan, 2014, published in Khimicheskaya Fizika, 2014, Vol. 33, No. 7, pp. 53–63.

524

1. INTRODUCTION

Modern period of studies on the conformationaldynamics and functioning of macromolecules has amore than 30�year history. In a brief article it is impos�sible of course to cover all issues of conformationalmobility and its relation to the functioning of macro�molecules. A significant contribution to this work hasbeen made by the Russian scientific schools foundedby M.V. Volkenstein, V.I. Gol’danskii, I.M. Lifshitz,O.B. Ptitsyna, their students, and many other Russianand foreign scientists. We focus only on the essentialproblems of the physics of the conformational mobil�ity of biopolymers. Why have they caused and con�tinue to cause great interest of biophysicists andresearchers from other fields of modern biology?

Here are some features of the dynamic behavior ofbiopolymers:

(1) The tendency to self�organization of the spatialstructure;

(2) The existence of relatively slow and large�scalefunctionally important collective modes;

(3) Substantially time�extended kinetic depen�dences of the processes;

(4) Broad distributions over rate constants andactivation energies;

(5) Nonlinear (non�Kramers) dependences of therate constants of the intraprotein processes on the vis�cosity of the medium;

(6) Memory effects, i.e., the dependence of thestate parameters on the method of preparation;

(7) A very wide spectrum of conformational relax�ation times, etc.

These properties are untypical of simple systems,but individually are sometimes found in objects stud�ied in classical physical chemistry. At first glance,these properties seem very dissimilar, but, beingassembled together in objects of the same type, makeone wonder what is the matter here. Since the middleof last century, it is known that the physicochemicalproperties of polymers and biopolymers are largelyassociated with relatively low energy barriers to rota�tions about single C–C bonds. This is a consequenceof the electronic structure of the carbon atom, inwhich the four electrons in its outermost shell areprone to form a state with four equivalent bondsdirected to the vertices of a tetrahedron. In what fol�lows, we will see that these potentials of the internalrotors give rise to a great diversity of the dynamicbehavior of polymers and biopolymers, a feature thatmakes them fundamentally different from rigidmolecular systems, such as crystals. It should not bebelieved that, for the conformational degrees of free�

Molecular Structure and the Dynamics of the Functioning of Conformationally Mobile Systems

K. V. Shaitana, b

a Lomonosov Moscow State University, Moscow, Russiab Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia

e�mail: [email protected] December 12, 2013

Abstract—The state of art of research on the dynamics of biomacromolecules and complexes thereof isbriefly outlined. Emphasis is placed on the work conduced over the last 30 years at Lomonosov Moscow StateUniversity and Semenov Institute of Chemical Physics RAS. The physical mechanisms of fluctuationdynamics on the angstrom and subangstrom levels in condensed matter are considered based on Mössbauerspectroscopy and molecular dynamics modeling. The results of all�atom simulations of the functioning of ionchannels obtained on a “Lomonosov” supercomputer (MSU) are reported. The self�organizing dynamics ofmacromolecular structures is examined for model polymer structures and nanostructures. The topology ofmultidimensional energy surfaces for conformationally mobile systems and its influence on the dynamicproperties of objects are considered. In conclusion, the dynamics of functioning of simple molecularmachines based on catenanes and rotaxanes and the role of conformational mobility in ensuring their oper�ation are discussed.

Keywords: molecular dynamics, conformational mobility, the Mössbauer effect in proteins, X�ray lasers,molecular machines

DOI: 10.1134/S1990793114040083

CHEMICAL PHYSICS OF BIOLOGICAL PROCESSES

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 8 No. 4 2014

MOLECULAR STRUCTURE AND THE DYNAMICS OF THE FUNCTIONING 525

dom to manifest themselves in the dynamics and phys�ical properties of macromolecules, the respectiveatomic groups must be free to rotate around the chem�ical bonds.

In a dense condensed medium, in a protein glob�ule, rotations occur not independently for each bond,but due to collectively tuned movements, which resultin the freeing of the space required for atomic dis�placements. Back in 1979, the authors of [1], usingmolecular dynamics simulations, demonstrated that,in a dense protein structure, where there is no freerotation of atomic groups, the activation energy for thediffusion of ligands is critically dependent on the magni�tude of the internal rotation barriers. At very large barrierheights, at which actually no rotations about chemicalbonds occur, only torsional oscillations, the activationenergy for the diffusion of ligands (more specifically, oxy�gen and carbon monoxide in myoglobin) increases to 100kcal/mol, a value typical of diffusion in crystalline solids,which have no conformational degrees of freedom. For arealistic height of the potential barrier to internal rota�tions (2–3 kcal/mol), the activation energy for diffusionreduces to 5–10 kcal/mol, in agreement with experi�mental values. This numerical experiment, carried outat the dawn of the age of protein dynamics computersimulations showed that the physics of the dynamicorganization of a dense protein globule differs sub�stantially from that of crystals with a similar density.This fact is of considerable interest in its own right.

There is, however, a far more important circum�stance, consisting in the fact that the functioning of

biopolymers is closely related to the conformationalmobility of their structure. This has been establishednot only for the diffusion of ligands, but also for a vastvariety of biomolecular processes, including electrontransfer, photoreceptor processes, enzymatic catalysis,operation of ion channels and membrane receptors,genetic information reading, etc. It is these circum�stances that motivate interest in the conformationalmobility of macromolecules and its physical aspects.

2. PHYSICS OF THE CONFORMATIONAL MOBILITY OF MACROMOLECULES

Let us briefly consider the methods for studying thephysics of conformational mobility and related func�tional activity, notably, the most powerful and directmethods, except, perhaps, a very powerful NMRmethod, which deserves a separate article.

One of the most efficient methods of studying thephysics of conformational mobility is Mössbauerspectroscopy. The matter is that the line shape of theMössbauer spectrum is directly related to the timedependence of the mean square displacement of theatoms, and what is more, the parameters of Mössbaueremitters fall into a very favorable range of values: awavelength of ~1 Å and a characteristic time of move�ment to which the line shape is sensitive is ~10–100 ns.This provides both a good spatial and temporal resolu�tion for atomic displacements. The method has a recordenergy resolution, ~10–9 eV, a feature that makes it a

Fig. 1. Molecular oscillator (at the center) in an aqueous medium.

526


SHAITAN

unique tool for studying the fine mechanisms of confor�mational motions in macromolecules [2].

It is the application of Mössbauer spectroscopy tostudying the dynamics of proteins that caused a resur�gence of interest in the physics of the conformationaldynamics of biopolymers in the late 1970s and early1980s. There is no possibility to list the numerousworks in this direction performed at R. M?ssbauer’sand V.I. Gol’danskii’s laboratories and by other teams(see, e.g., [2–4] and references therein).

As a result of these studies, it became clear thateven micro�conformational motions with amplitudesof ~0.5 Å occur quite differently from the vibrations ofthe atoms in a crystal lattice. Not without somedebate, the concept of restricted diffusion for confor�mational movements has been adopted [3, 5]. Twentyyears on after these discussions, capitalizing on theprogress in molecular modeling capabilities, we havecarried out a numerical experiment [6], which veryclearly shows the point.

A molecular oscillator, two atoms linked by avalence bond (thought of as a spring) was placed in amedium of water molecules (Fig. 1). At normal tem�perature and fluid density, the molecular dynamics ofthe whole system was simulated to calculate the timedependence of the mean square displacement of themolecular oscillator atoms with respect to each other.It was found that, with decreasing stiffness of thespring (accordingly, increasing amplitude of the ther�mal motion of the oscillator), a threshold amplitude isreached at which an abrupt change of the regime ofmotion takes place (Fig. 2). At an amplitude of fluctu�ations of ~0.4 Å, the oscillatory mode disappears, giv�ing way to the stochastic motion (limited diffusion) ofthe oscillator atoms relative to each other (Fig. 2c).This behavior is both qualitatively and quantitativelysimilar to that observed in proteins by means of Möss�bauer spectroscopy (Fig. 3). A motion amplitude of0.3–0.4 Å in a condensed medium corresponds to asharp increase in friction, which in a condensedmedium has the same nature as diffusion: in bothcases, thermally activated density fluctuations areneeded for atomic motions to occur with requiredamplitude.

In principle, radiation scattering could provide notonly dynamic but also structural information aboutthe protein. Ideally, it would be desirable to producesomething like a “molecular movie”. In the 1980s, thisdream went under the name Mössbauergraphy [8].However, the sources of Mössbauer radiation werevery weak to solve this problem. After 30 years, thisdream seems to start to come true due to the develop�ment of X�ray free electron lasers, the brightness ofwhich tens of orders of magnitude higher than eventhat of synchrotron sources [9]. In particular, in Ger�many (Hamburg), with the participation of Russia, anX�ray free�electron laser is under construction, with awavelength of ~1 Å, pulse duration of about tens offemtoseconds, and brightness of ~1023 W/cm2 [10].

–8100 2 4 6 8

–6

–4

–2

0

2

4

6

8

10

–62.00 0.5 1.0 1.5

–4

–2

0

2

4

6

8

–0.2100 2 4 6 8

0

0.2

0.4

0.6

0.8

×10–3

×10–3

Aut

ocor

rela

tion

fun

ctio

n,

Å2

Aut

ocor

rela

tion

fun

ctio

n,

Å2

Aut

ocor

rela

tion

fun

ctio

n,

Å2

t, ps

t, ps

t, ps

(a)

(b)

(c)

Fig. 2. Autocorrelation function for a molecular oscillatorin an aqueous medium at various values of the force con�stant K (kcal/(mol Å2): (a) 264 (typical of the C–C bond),(b) 74, and (c) 0.02.



The brightness of an X�ray laser flash is such that,within 10–14 s, the electrons are actually blown off themacromolecule, making it experience a Coulombexplosion. However, before the protein macromole�cule collapses, a diffraction pattern from it can berecorded and used to recover an instantaneous struc�ture of the protein. In [11], a diffraction pattern froma nanocrystals and the structure of the complex ofphotosystem 1 were obtained. A huge advantage of thistechnique is the possibility to determine the instanta�neous structure of single protein macromolecules andtheir complexes and shoot a “molecular movie” of thefunctional processes accompanied by conformationalchanges.

3. PROSPECTS OF USING X�RAY LASERSIN STUDYING THE STRUCTURE

OF BIOMACROMOLECULES AND THE DYNAMICS

OF FUNCTIONAL PROCESSES

The use of X�ray lasers opens a new era in structuralbiology and very harmoniously fits into the futuredevelopment of post�genomic technologies. The levelof development of modern biology, biomedicine, andpharmacology requires knowledge of the mechanismsof biological processes in norm and pathology with anatomic precision. Currently, the databases containinformation on only about 90 thousands of the morethan 6 millions of protein structures. In most cases,this information has been obtained from X�ray diffrac�tion (XRD) measurements, and it refers to crystallinestructures of proteins in some local�equilibrium con�formations. Unfortunately, a large number of proteinstructures are uncrystallizable, or their crystals have ananometer size and strong defects, factors that make itdifficult to use classical X�ray analysis. In addition,classical XRD is practically useless for studying thestructure and dynamics of biomacromolecules in tran�sient functionally active states.

Using X�ray free�electron laser (XFEL) offers fun�damentally new opportunities for the structural analy�sis of biological objects and for studying their func�tional structural dynamics. A combination of a hugeflash brightness (focused on an area of 100 nm2) andfemtosecond duration impart to this tool quite uniquecapabilities. On the one hand, with such radiationpower, the electric field strength on the molecule issuch that, within ~10 fs, it is subjected to deep ioniza�

tion, leading later to a Coulomb explosion. However,up to this point, it is possible to record the X�ray scat�tering pattern, which gives information of the electron

0.1

800 20 40 60

0.2

1

2

3

t

⟨[Δx(t)]2⟩

⟨xa2⟩

⟨[x(t) – x(0)]2⟩, Å2

t, ns

293 К

253 К

245 К

238 К

203 К

183 К

(a)

(b)

223 К

Fig. 3. (a) Qualitative dependence of the mean square dis�placement for (1) weakly damped vibrations, (2) diffusion,and (3) restricted diffusion in a potential well. (b) The timeevolution of the mean square displacement in a polymermatrix at various temperatures as measured by MössbauerFourier spectroscopy.

Actual capabilities of supercomputers in modeling dynamic trajectories [14]

Size 2004 2008 2012 (прогноз)@

0.1 million atoms (aquaporine, K�channel) 4 ns/day 100 ns/day 10 мкс/day* @1 million atoms (ribosome) – 10 ns/day 1 мкс/day* @10 million atoms (poliovirus) – 1 ns/day 100 ns/day

* The range of times characteristic of physiological processes.

528


SHAITAN

density distribution in the molecule, which, in turn,can be used to reconstruct the atomic structure of theprotein.

At present, a very topical problem is to developalgorithms, software, and protocols for analysis andintegration of X�ray data (including synchrotron� andlaser�produced) scattering, electron microscopy, andmolecular modeling techniques to study the structureand dynamics of biological macromolecules and theircomplexes (see, e.g., [12]).

4. MOLECULAR DYNAMICS OF FUNCTIONAL PROCESSES

Currently, the leading method in studying confor�mational mobility is molecular modeling on super�computers. The conformational movements and func�tional processes involving heavy (non�hydrogen)atoms have been successfully investigated using classi�cal molecular dynamics methods. For processesinvolving protons and electrons necessary, it is neces�sary to use QM/MM hybrid methods [13].

(a)

5

0–3 –2 –1 0 1 2 3 4 5

10

15

20

25

30

3.04.

59.

6

18.0

4.5

Z�axis coordinate, Å

Mea

n fo

rce

pote

nti

al,

kcal

/mol

1

2

3

(b)

Fig. 4. Simulations of the functional dynamics of the operation of a KCSA potassium channel [24]. (a) The ion channel is builtin a biomembrane and the system is immersed in water. The number of atoms is more than 100000. The trajectory length is 100ns (“Lomonosov” supercomputer (MSU)). (b) Mean force potential profiles for the triple potassium ions in a selective filter atvarious values of the transmembrane potential (mV): (1) 0, (2) 80, and (3) 150. Illustrated at the bottom is the event of ion passage.



Table 1 shows the forecast of the development ofmolecular modeling methods up to 2012, made a fewyears ago [14]. While eight years ago, the most power�ful supercomputers could confidently simulate thedynamics of objects such as ion channels over timeintervals of ~100 ns, the forecast for 2012 predicted theextension of this interval to a microsecond and even asubmillisecond range. Now we must acknowledge thatthis prediction has come true. A supercomputer sys�tem with a special processor architecture wasdesigned, which enabled to cover time intervals ofhundreds of microseconds, i.e., reach physiologicallyrelevant times and to simulate the entire cycle of oper�ation of a potential�dependent ion channel (includingopening and closing the channel) [15].

Of Particular interest are functionally significantand relatively large�scale slow collective movementsthat cause the opening and closing of the channel. Thistype of modes undoubtedly has great significance forcontrolling the function, being critical areas for exter�nal influences through mutations or ligand binding.

Along with record achievements, modern super�computers enable to solve scientific problems relatedto the dynamics of functional processes [16–25]. Inparticular, it is the operation of ion channels. Figure 4shows the result of an all�atom simulation of a potas�sium channel in a biological membrane (Fig. 4). Thetransport of potassium ions occurs under the action ofa ~500�mV electric field. There is also a concentrationgradient for the potassium chloride solutions at theopposite sides of the membrane, ~0.1 M. The dynam�ics of the process clearly exhibits conformationalchanges of the channel during the passage of ions. It isalso seen that the ionic interaction has a direct influ�ence on the kinetics. The entry of an additional ionthrough the ion channel gate causes the ejection ofanother ion through the channel exit.

It is worthwhile to mention a common beautifulpattern. An ion in solution is typically hydrated withsix water molecules. Such a hydration complex cannotpass through the ion channel gate. This is one of thefoundations of ion selectivity. This means that the hydra�tion complex should lose some of the water molecules.Energetically, it can cost more than 100 kcal/mol.Therefore, what is needed is a very strict energy bal�ance in replacing the hydration water by amino acidresidues in the interior of the channel. Figure 5 showsthe process of mirroring of the energy of interaction ofthe sodium cation with the hydration shell moleculesand amino acid residues for a very simple channelformed by gramicidin A. In this case, the energy ofhydration with four water molecules is compensated inthe channel by the energy of interaction of the cationwith partially negatively charged carbonyl�group oxy�gens. The same principles are operative in other chan�nels we studied [16–25]. By mutations in the interiorof the channel, it is possible to significantly change theselectivity of its functioning and even transform ancationic into an anionic channel, and vice versa.

–300

–200

–100

0

(a)

–300

–200

–100

0

(b)

–400

Fig. 5. Change of the energy of interaction (kJ/mol) of asodium ion with (a) the interior of the channel and (b)water during its passage through the channels formed in abiomembrane by gramicidin A. The bottom panel showshow the coordinate of the ion is related to its position inthe channel.

530


SHAITAN

5. DYNAMICS OF THE SELF�ORGANIZATION OF MOLECULAR STRUCTURES

Let us return to the specifics of the conformationaldynamics of biopolymers. One of the challengingproblems is that of folding or self�organization of thespatial structure of biopolymers. There are a lot of the�oretical developments and achievements in this field[26]. Herein, we would like to draw attention to somerelatively simple patterns typical of systems with geo�metric and kinematic relations. We have studied an

example of a simple polymer chain (Fig. 6a) with anartificially increased attraction between units. Thechain spontaneously folds into a helical structure [27].For two chains with the attraction between units of thedifferent chains stronger than that between the samechains, the system spontaneous folds into a doublehelix structure (Fig. 6b).

A more complicated case is a real polymer speciallybuilt from amino acids with thiophene side groups,which interact strongly enough with their aromatic

(a)

(b)

Fig. 6. Spontaneous folding of model polymer chains: (a) homopolymer chain forms a helix at a ratio of the van der Waals diam�eter of the node to the chemical bond length equal to 2.5. (b) The formation of a double helix from two chains.

Fig. 7. Self�assembly of a molecular syringe. Polyalanine spontaneously packs itself in the form of a helix into a carbon nanotubeby overcoming an activation barrier bear the nanotube entrance.



rings. The fibril is built from beta�strands, forming asuperhelix [28–31].

Analysis of such situations shows that the ratio ofthe geometric parameters of the polymer chain units,more specifically, the van der Waals diameter r of thechain node to the chemical bond length b quiteclearly influences the shape of the structure formedduring self�assembly [32]. This involves the forma�tion of various helical configurations, which resem�ble those found in biopolymers. Note also that thedynamics of folding proceeds not sequentially, fromunit to unit, but encompasses large segments of thechain. The region of influence of the geometric andkinematic relations on the dynamics of folding is lit�tle studied, but these effects are undoubtedly impor�tant.

Here is another example of spontaneous self�assembly: the formation of a polyalanine (PA) alpha�helix induced by interaction with a carbon nanotube(CNT) [33, 34]. At the start, the PA coil is adsorbed onthe CNT surface, but then, once occurring near theentrance to the nanotube, it efficiently transforms intoa helix and spontaneously packs itself into the tube(Fig. 7). It is clear that the energy of the PA in the heli�cal conformation inside the CNT tube is lower, but theease with which it twists in a helix is apparently associ�ated with geometric and kinematic relations betweenthe rotations about C–C bonds. Clearly, the dynamicsof self�organization is closely connected with thestructure of the multidimensional energy surface.Some aspects of this problem are related to Morse the�ory [35] and presented in [36–40].

6. DYNAMICS OF MOLECULAR MACHINES

In conclusion, let us discuss some aspects ofmolecular machines in terms of organization of con�formational mobility dynamics. Figure 8 shows a sim�ple machine based on rotaxane structure [41]. Theattachment and detachment of a proton changes thepotential energy profile the interaction with the ring,and the latter changes its position according to thelaws of restricted diffusion.

This is a perfect illustration of an electron�confor�mational transition. In mathematical terms, the sys�tem is described by two coupled Fokker–Planck�typeequations with additional terms describing chemicalreactions [36–40, 42].

Consider another example, a switch based on cat�enane, two topologically interlocked rings. The switchoperates due to a change in the resistance of a layer ofthese molecules upon application of a voltage, whichalters the charge on the functional groups [43]. Thisinvolves a turn of the rings to a new equilibrium posi�tion. This process is similar to the aforementioned. Aninteresting question is how these rings rotate. Notethat one ring is rigid whereas the other is flexible, con�formationally mobile. Molecular modeling shows thatthe tetrathiafulvalene ring (Fig. 9) rotates, which hasgreater flexibility. [44]

From the viewpoint of a macroscopic machine,this is quite unexpected; however, the situation is dif�ferent for molecular machines. Movements occur bydiffusion due to conformational mobility. A rigidmolecular structure in motion will necessarily enterinto a steric conflict with the environment, whereas aconformationally flexible structure has the ability tofix the steric conflict and take a new equilibrium posi�tion.

1

�

��

��

��

��

I

I

x

W1(x) U1(x)W2(x)U2(x)

(a)

(b)

Fig. 8. (a) Simplest pH�dependent molecular machine based on rotaxane. When a proton attaches, the ring shifts to the left, shift�ing rightwards when a proton detaches. (b) Energy profiles of the ring (I) for the protonated U2(x) and deprotonated U1(x) statesof the system. The vertical arrows indicate the transitions between the states of the system for protonation and deprotonation.

532


SHAITAN

–100° –50° 0° 50° 100°

–100°

–50°

0°

50°

100°

–150° 150°Rotation angle, tetrathiafulvalene ring

Rot

atio

n a

ngl

e, c

yclo

phan

e ri

ng

S S

S S

OO

OO

O

O

O

OOO

+N N+

N++N

–e–

+e–

(a)

–100° –50° 0° 50° 100°

–100°

–50°

0°

50°

100°

Rotation angle,

Rot

atio

n a

ngl

e, c

yclo

phan

e ri

ng

tetrathiafulvalene ring

(b)

(c)

Fig. 9. Molecular switch based on catenane. (a) Structure and conformational transition; the folding of the rings is shown at theright. (b, c) Probability density maps for the realization of catenane conformations at (b) 300 K and (c) 2000 K. Higher probabil�ities occur in the upper part of the maps, which corresponds to rotations of the tetrathiafulvalene ring.

11



7. CONCLUSIONS

To conclude this brief review of the functionaldynamics of macromolecules, we would like to notethat the rapid development of supercomputers with acapacity expectedly reaching tens flops in the comingyears, as well as the introduction of femtosecond X�raylasers into structural biology and materials science,will undoubtedly lead to a new level of understandingof biological and physicochemical processes, withatomic and subatomic precision. The progressachieved to date in the field of functional conforma�tional dynamics makes it possible to group conforma�tional transitions in proteins and other molecularmachines into a class of collective motions occurringby restricted diffusion mechanisms. Moreover, unlikemacroscopic machines, the mobility of flexible (con�formationally labile) elements is much higher com�pared to rigid segments of a macromolecule or molec�ular structure.

ACKNOWLEDGMENTS

This work was supported by the Ministry of Educa�tion and Science of the Russian Federation and theRussian Foundation for Basic Research.

REFERENCES

1. D. A. Case and M. Karplus, J. Mol. Biol. 132, 343(1979).

2. R. L. Moessbauer, Hyperfine Interact. 33, 199 (1987).3. K. V. Shaitan and A. B. Rubin, Mol. Biol. 14, 1323

(1980).4. Yu. F. Krupyanskii and V. I. Gol’danskii, Phys. Usp. 45,

1131 (2002).5. K. V. Shaitan and A. B. Rubin, Biofizika 25, 796 (1980).6. K. V. Shaitan and S. S. Saraikin, Biophysics 45, 397

(2000).7. K. V. Shaitan, M. G. Mikhailyuk, A. S. Plachinda, and

V. I. Khromov, Russ. Chem. Bull. 51, 2196 (2002).8. A. V. Belyakov and R. N. Kuz’min, Mössbauerography

(Znanie, Moscow, 1979) [in Russian].9. http://xfel.desy.de/

10. K. V. Shaitan, M. P. Kirpichnikov, V. S. Lamzin, et al.,Vestn. RFFI, No. 4, 22 (2013).

11. H. N. Chapman, P. Fromme, A. Barty, et al., Nature470, 73 (2011).

12. K. V. Shaitan, A. K. Shaitan, D. V. Bagrov, et al.,Nanostrukt. Mat. Fiz. Model. 9 (2), 33 (2013).13.http://link.springer.com/chapter/10.1007%2F128_2006_084?LI=true#

14. E. H. Lee, J. Hsin, M. Sotomayor, et al., Structure 17,1295 (2009).

15. M. O. Jensen, V. Jogini, D. W. Borhani, et al., Science336, 229 (2012).

16. K. V. Shaitan, E. V. Turlei, D. N. Golik, et al., Zh. Ross.Khim. Obshch. 50 (2), 53 (2006).

17. K. V. Shaitan, E. V. Turlei, D. N. Golik, et al., Khim.Fiz. 25 (9), 31 (2006).

18. D. Yu. Mordvitsev, Ya. L. Polyak, D. A. Kuzmin, et al.,Comput. Biol. Chem. 31, 72 (2007).

19. K. V. Shaitan, A. Li, K. B. Tereshkina, andM. P. Kirpichnikov, Biophysics 52, 301 (2007).

20. K. V. Shaitan, M. Yu. Antonov, E. V. Turlei, et al., Biol.Membr. 25, 75 (2008).

21. A. V. Popinako, O. V. Levtsova, M. Yu. Antonov, et al.,Biophysics 56, 1078 (2011).

22. O. V. Levtsova, I. D. Davletov, O. S. Sokolova, andK. V. Shaitan, Biophysics 56, 220 (2011).

23. K. V. Shaitan, M. Yu. Antonov, A. K. Shaitan, et al.,Nanostrukt. Mat. Fiz. Model. 6 (1–2), 61 (2011).

24. O. S. Sokolova, K. V. Shaitan, A. V. Grizel’, et al.,Bioorg. Khim. 38, 177 (2012).

25. K. V. Shaitan, O. S. Sokolova, A. K. Shaytan, et al.,Mosc. Univ. Biolog. Sci. Bull. 68, 8 (2013).

26. A. V. Finkel’shtein and O. B. Ptitsyn, Physics of Proteins(KDU, Moscow, 2002) [in Russian].

27. K. V. Shaitan and I. V. Fedik, Biophysics 53, 44 (2008).28. M. Yolamanova, C. Meier, A. K. Shaytan, et al., Nature

Nanotechnol. 8, 130 (2013).29. A. K. Shaytan, E.�K. Schillinger, P. G. Khalatur, et al.,

ACS Nano 5, 6894 (2011).30. A. K. Shaitan, P. G. Khalatur, and A. R. Khokhlov, in

Supercomputer Technologies in Science, Education, andIndustry, Ed. by V. A. Sadovnichii, G. I. Savin, andV. V. Voevodin (Mosk. Gos. Univ., Moscow, 2009),p. 51 [in Russian].

31. A. K. Shaytan, A. R. Khokhlov, and P. G. Khalatur, SoftMatter 6, 1453 (2010).

32. K. V. Shaitan, E. V. Turlei, D. N. Golik, et al., Vestn.Biotekhnol. Fiz.�Khim. Biol. 1, 66 (2005).

33. K. V. Shaitan, Y. V. Tourleigh, D. N. Golik, andM. P. Kirpichnikov, J. Drug Delivery Sci. Technol. 16,253 (2006).

34. K. V. Shaitan, Y. V. Tourleigh, and M. P. Kirpichnikov,J. Qafqaz Univ., No. 21, 3 (2007).

35. J. Milnor, Morse Theory, Annals of Mathematic StudiesAM�51 (Princeton University Press, Princeton, 1963;Mir, Moscow, 1965).

36. K. V. Shaitan, Biofizika 9, 949 (1994).37. K. V. Shaitan, Macromol. Symp. 106, 321 (1996).38. K. V. Shaitan, Russ. J. Electrochem. 39, 198 (2003).39. K. V. Shaitan, A. A. Belyakov, K. M. Leont’ev, et al.,

Khim. Fiz. 22 (2), 57 (2003).40. K. V. Shaitan, Stochastic Dynamics of Reacting Biomol�

ecules, Ed. by W. Ebeling, L. Schimansky�Gefer, andY. M. Romanovsky (World Scientific, Singapore, 2003),p. 283.

41. http://en.wikipedia.org/wiki/Rotaxane/42. K. V. Shaitan and A. B. Rubin, Mol. Biol. 16, 1004

(1982).43. C. P. Collier, G. Mattersteig, E. W. Wong, et al., Science

289, 1172 (2000).44. Ye. V. Tourleigh and K. V. Shaitan, Defect Diffus.

Forum 237–240, 1174 (2005).

Translated by V. Smirnov

SPELL: 1. OK

Molecular Structure and the Dynamics of the …...email: [email protected] Received December 12,...

Documents

Transcript of Molecular Structure and the Dynamics of the …...email: [email protected] Received December 12,...