Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps

Aim. In this work we developed a novel technique of obtaining the spectrum of conformational relaxations in a solvated protein using non-equilibrium molecular dynamics simulation. Methods. Structural relaxations in the protein are initiated by the abrupt jump of pressure in the NPT simulations. The...

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Дата:	2012
Автори:	Yesylevskyy, S.O., Hushcha, T.O.
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Опубліковано:	Інститут молекулярної біології і генетики НАН України 2012
Назва видання:	Вiopolymers and Cell
Теми:	Molecular Biophysics
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Цитувати:	Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps / S.O. Yesylevskyy, T.O. Hushcha // Вiopolymers and Cell. — 2012. — Т. 28, № 6. — С. 486-492. — Бібліогр.: 29 назв. — англ.

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spelling	irk-123456789-1568562019-06-20T01:28:58Z Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps Yesylevskyy, S.O. Hushcha, T.O. Molecular Biophysics Aim. In this work we developed a novel technique of obtaining the spectrum of conformational relaxations in a solvated protein using non-equilibrium molecular dynamics simulation. Methods. Structural relaxations in the protein are initiated by the abrupt jump of pressure in the NPT simulations. The change of the protein volume after the jump is monitored and the Maximum Entropy Method is used for spectral decomposition of the volume relaxation curve. The human serum albumin (HSA) is used as a test case. Results. The obtained relaxation spectrum of HSA contains one component attributed to the bulk water and five components caused by the relaxations of the protein globule and its hydration shell. All relaxation components are in good agreement with the available experimental data obtained by the time-resolved spectroscopy and the broadband acoustic spectroscopy of HSA. Conclusions. The developed technique allows obtaining spectra of conformational relaxations of soluble proteins in a range of time scales from ~0.1 ps to ~50 ns utilizing single non-equilibrium molecular dynamics simulation. Keywords: protein relaxations, molecular dynamics, maximum entropy method, pressure jump, HSA. Мета. Розробка методики, що дозволяє отримувати спектри конформаційних релаксацій сольватованого білка методом нерівноважної молекулярної динаміки. Методи. Структурну релаксацію білка ініціювали різкою зміною тиску у процесі розрахунку в NPT- ансамблі. Проведено спектральну декомпозицію кривої зміни об’єму білка після стрибка тиску методом максимальної ентропії. Результати. Одержаний спектр релаксацій містить один компонент, що належить до чистої води, і п’ять компонентів, віднесених до білка та його гідратної оболонки. Конформації всіх компонентів відповідають структурам, отриманим методами оптичної і акустичної спектроскопії. Висновки. Розроблена методика дозволяє розраховувати спектри структурної релаксації сольватованих білків у діапазоні часів від ~0,1 пс до ~50 нс з однієї траєк- торії, одержаної методом нерівноважної молекулярної динаміки. Ключові слова: релаксація білка, молекулярна динаміка, метод максимальної ентропії, стрибки тиску, сироватковий альбумін людини. Цель. Разработка новой методики получения спектра конформационных релаксаций сольватированного белка методом неравновесной молекулярной динамики. Методы. Структурную релаксацию белка инициировали резким изменением давления в процессе расчета в NPT-ансамбле. Проведена спектральная декомпозиция кривой изменения объема белка после скачка давления методом максимальной энтропии. В качестве тестового объекта использован сывороточный альбумин человека. Результаты. Полученный спектр релаксаций содержит один компонент, принадлежащий чистой воде, и пять компонентов, относящихся к белку и его гидратной оболочке. Конформации всех компонентов соответствуют таковым, полученным методами оптической и акустической спектроскопии. Выводы. Разработанная методика позволяет рассчитывать спектры конформационных релаксаций сольватированных белков в диапазоне времен от ~0,1 пс до ~50 нс из единственной траектории, вычисленной методом неравновесной молекулярной динамики. Ключевые слова: релаксация белка, молекулярная динамика, метод максимальной энтропии, скачки давления, сывороточный альбумин человека. 2012 Article Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps / S.O. Yesylevskyy, T.O. Hushcha // Вiopolymers and Cell. — 2012. — Т. 28, № 6. — С. 486-492. — Бібліогр.: 29 назв. — англ. 0233-7657 DOI: http://dx.doi.org/10.7124/bc.00013B http://dspace.nbuv.gov.ua/handle/123456789/156856 577.322 en Вiopolymers and Cell Інститут молекулярної біології і генетики НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Molecular Biophysics Molecular Biophysics
spellingShingle	Molecular Biophysics Molecular Biophysics Yesylevskyy, S.O. Hushcha, T.O. Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps Вiopolymers and Cell
description	Aim. In this work we developed a novel technique of obtaining the spectrum of conformational relaxations in a solvated protein using non-equilibrium molecular dynamics simulation. Methods. Structural relaxations in the protein are initiated by the abrupt jump of pressure in the NPT simulations. The change of the protein volume after the jump is monitored and the Maximum Entropy Method is used for spectral decomposition of the volume relaxation curve. The human serum albumin (HSA) is used as a test case. Results. The obtained relaxation spectrum of HSA contains one component attributed to the bulk water and five components caused by the relaxations of the protein globule and its hydration shell. All relaxation components are in good agreement with the available experimental data obtained by the time-resolved spectroscopy and the broadband acoustic spectroscopy of HSA. Conclusions. The developed technique allows obtaining spectra of conformational relaxations of soluble proteins in a range of time scales from ~0.1 ps to ~50 ns utilizing single non-equilibrium molecular dynamics simulation. Keywords: protein relaxations, molecular dynamics, maximum entropy method, pressure jump, HSA.
format	Article
author	Yesylevskyy, S.O. Hushcha, T.O.
author_facet	Yesylevskyy, S.O. Hushcha, T.O.
author_sort	Yesylevskyy, S.O.
title	Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps
title_short	Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps
title_full	Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps
title_fullStr	Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps
title_full_unstemmed	Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps
title_sort	conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps
publisher	Інститут молекулярної біології і генетики НАН України
publishDate	2012
topic_facet	Molecular Biophysics
url	http://dspace.nbuv.gov.ua/handle/123456789/156856
citation_txt	Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps / S.O. Yesylevskyy, T.O. Hushcha // Вiopolymers and Cell. — 2012. — Т. 28, № 6. — С. 486-492. — Бібліогр.: 29 назв. — англ.
series	Вiopolymers and Cell
work_keys_str_mv	AT yesylevskyyso conformationalrelaxationsofhumanserumalbuminstudiedbymoleculardynamicssimulationswithpressurejumps AT hushchato conformationalrelaxationsofhumanserumalbuminstudiedbymoleculardynamicssimulationswithpressurejumps
first_indexed	2025-07-14T09:10:37Z
last_indexed	2025-07-14T09:10:37Z
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fulltext	MOLECULAR BIOPHYSICS UDC 577.322 Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps S. O. Yesylevskyy1, T. O. Hushcha2 1Institute of Physics, NAS of Ukraine 46, Prospect Nauki, Kyiv, Ukraine, 03039 2Institute of Bioorganic Chemistry and Petrochemistry, NAS of Ukraine 1, Murmans’ka Str., Kyiv, Ukraine, 02094 yesint4@gmail.com Aim. In this work we developed a novel technique of obtaining the spectrum of conformational relaxations in a solvated protein using non-equilibrium molecular dynamics simulation. Methods. Structural relaxations in the protein are initiated by the abrupt jump of pressure in the NPT simulations. The change of the protein volume af- ter the jump is monitored and the Maximum Entropy Method is used for spectral decomposition of the volume re- laxation curve. The human serum albumin (HSA) is used as a test case. Results. The obtained relaxation spectrum of HSA contains one component attributed to the bulk water and five components caused by the relaxations of the protein globule and its hydration shell. All relaxation components are in good agreement with the available ex- perimental data obtained by the time-resolved spectroscopy and the broadband acoustic spectroscopy of HSA. Conclusions. The developed technique allows obtaining spectra of conformational relaxations of soluble proteins in a range of time scales from ~0.1 ps to ~50 ns utilizing single non-equilibrium molecular dynamics simulation. Keywords: protein relaxations, molecular dynamics, maximum entropy method, pressure jump, HSA. Introduction. It is well known that the dynamics of pro- tein globules extents from femtoseconds to seconds and even minutes [1]. It is not surprising that none of exist- ing experimental techniques is able to study the whole spectrum of motions in proteins. Various time-resolved spectroscopic methods could detect motions at the pico- seconds to nanoseconds time scale [2]. Other techniqu- es, such as broadband acoustic spectroscopy, can cover characteristic times from nanoseconds to microseconds and larger [3]. The majority of available experimental techniques are based on measuring relaxations in protein globules initiated by various factors, such as excitation of the chromophore in optical spectroscopy or local chan- ges of pressure in acoustic measurements. Although ve- ry different stimuli may trigger relaxation in the system the general picture of the protein dynamics remains mo- stly consistent in different experimental techniques. Spatial resolution of optical spectroscopy is limited by the position of chromophore, while acoustic spectrosco- py is a completely integral method, which is unable to focus on particular parts of protein structure. Thus, rela- xation components are quite hard to attribute to particu- lar conformational changes in the protein globules. Molecular Dynamics (MD) simulations are now con sidered as an important complementary method, which allows interpreting experimental data in terms of detailed atomistic model and mapping them into the protein structure [4]. MD is particularly successful in re- producing the data of time-resolved spectroscopy by computing equilibrium fluctuations of atoms in the vici- nity of chromophores [5–7]. To our knowledge no at- tempt was made to obtain the general spectrum of struc- tural relaxations of a whole solvated protein in MD si- mulations. Such spectrum would provide a global over- view of protein dynamics at very different time scales and could be compared with the results of integral tech- 486 ISSN 0233–7657. Biopolymers and Cell. 2012. Vol. 28. N 6. P. 486–492 doi 10.7124/bc.00013B  Institute of Molecular Biology and Genetics, NAS of Ukraine, 2012 niques, such as acoustic spectroscopy. The origin of re- laxation components could be determined later and map- ped to particular conformational changes in the globule. The goal of this work is developing a technique for obtaining the spectrum of conformational relaxations of a whole protein globule in the wide range of time sca- les in MD simulations. Instead of computing the equili- brium fluctuations of atoms and deducing relaxation ti- mes from them we put the whole system into highly non- equilibrium conditions and record relaxations directly. The Human Serum Albumin (HSA) was used as a test protein. Relaxation dynamics of this protein is stu- died by various experimental techniques such as broad- band acoustic spectroscopy [8, 9] and time-resolved op- tical spectroscopy [10–13]. This makes it an ideal test object for our technique. The major goal of this study is developing a consis- tent methodology of detecting volume relaxations in MD simulations rather then detailed study of a particu- lar protein. Materials and methods. Molecular dynamics si- mulations. S i m u l a t i o n s e t u p. All MD simu- lations were performed with the GROMACS suit of pro- grams (versions 4.0.2 and 4.5.1) [14, 15]. The GRO- MOS force fields G53A6 was used [17]. The long-ran- ge electrostatic interactions were computed using the fourth-order PME method with a Fourier spacing of 0.15 nm. The cut-offs of 1.4 nm and 1.0 nm were used for the short-range Coulomb and the Lennard-Jones in- teractions respectively. Bond lengths within the protein were constrained using the LINCS algorithm [18]. The water molecules were constrained using SETTLE [19]. The usage of heavy hydrogens [20] allowed the time step of 4 fs in all simulations. Initial structure of the hu- man serum albumin was extracted from the PDB entry 1AO6:A. The protein was solvated by 23504 SPC water mo- lecules [21] in rectangular periodic box. Necessary num- ber of the counter ions was added to neutralize the sys- tem. The protein and the water with counter ions were coupled to independent heat bathes at 300 K using v-re- scale thermostat with a coupling constant of τt = 0.1 ps. Berendsen barostat with a coupling constant of τp =1.0 ps was used for isotropic pressure coupling. E q u i l i b r a t i o n. Initial equilibration of the sys- tem at pressure of 1 atm was monitored by the Cα RMSD of the protein relative to the starting frame and the se- condary structure content. Fig. 1 shows that equilibrati- on takes about 100 ns before both parameters could be considered fluctuating around settled equilibrium values. P r e s s u r e j u m p s e t u p. In order to initiate re- laxations in the system the reference pressure of the ba- rostat τp was changed abruptly and the simulation was continued with the coordinates and velocities of the atoms, which were recorded before the jump. After that the simulation continues at new pressure and the volu- me of the simulation box relaxes to new equilibrium va- lue. The relaxation of the volume of the protein globule dominates this process because the water is rather in- compressible and relaxes quickly. Thus, analyzing the relaxation of the box volume one could extract infor- mation about the relaxation of the protein globule. The individual exponential components of this relaxation will correspond to particular structural rearrangements in the protein globule. This technique is related to the well known fluctuation-dissipation theorem [22]. 487 CONFORMATIONAL RELAXATIONS OF HUMAN SERUM ALBUMIN STUDIED BY MD SIMULATIONS 0 20 40 60 80 100 120 140 Equilibration time, ns 390 410 430 450 470 0.25 0.35 0.45 0.55 A B N u m b er o f re si d u es R M S D ,n m Fig. 1. Evolution of the seconda- ry structure content (A) and the Cα RMSD with the starting structure (B) in the course of equilibration MD run In order to make the relaxation detectable we increa- sed the pressure from 1 atm to 10000 atm in MD. This does not lead to any significant changes in the secon- dary structure content, which convinces us that the pro- tein is not unnaturally distorted by the pressure jump. P r o d u c t i o n s i m u l a t i o n s. In order to resolve relaxation components, which are scattered in time over several orders of magnitude, the coordinates were sa- ved with increasing intervals. For the interval from 0 to 1 ps the coordinates were saved each 0.002 ps. For the times from 1 ps to 10 ps each 0.02 ps. For the times from 10 ps to 100 ps 0.2 ps, etc. The longest part of trajec- tory from 100 ns to 175 ns was saved each 800 ps. Such setup provided enough data points for all covered time scales. The volume of the simulation box was compu- ted for each saved frame. P u r e w a t e r r e f e r e n c e. In order to distinguish the relaxation of the protein globule from the response of bulk water the reference simulations of pure SPC water were performed. The same number of water molecules presenting in the system with solvated protein (23504) was placed into the cubic box and simulated using the same protocol with the pressure jump for 10 ns. The maximum entropy method. The major problem in the analysis of volume relaxations is decomposition of relaxation curves into exponential components. One of the most successful techniques of such decompo- sition is the Maximum Entropy Method (MEM) [23, 24]. MEM is widely used in such areas as time-resolved spectroscopy [24, 25], neutron scattering [26] and ima- ge processing in astronomy [27] and tomography [28]. In this work we provide the first application of MEM to the analysis of volume relaxations in proteins. Let us consider the abstract problem of fitting de- caying curve G(x) by exponential spectral components exp(–t/τ): G t A t d fit ( ) ( exp( / min max = ⋅ −∫ τ) τ) τ, τ τ (1) where A(τ) is a continuous spectrum of experimental sig- nal, which should be found, τ is the relaxation time. In practice both the signal and the spectrum are discrete, thus G t A t fit i j i j j j N ( ) exp( / ,= ⋅ − ⋅ = ∑ τ ) τ∆ 1 (2) where N is the number of discrete spectral components used to approximate the real continuous spectrum. In order to find the weights of spectral components Aj one should minimize the deviation between the real signal and its approximation given by (2) in respect to Aj. This could be achieved by minimizing χ2 function: ( ) min ( ) min ( ) ( ) ( ) χ 2 2 1 A G t G t G t i fit i ii M = − = = ∑ = − ⋅ − ⋅∑      = = min ( ) exp( / ( ) , G t A t G t i j i j j j N ii M τ ) τ∆ 1 2 1 ∑ (3) where M is the number of experimental points in the signal. It is well known that such multidimensional optimi- zation problems are ill-posed [23, 25]. This means that there are many possible solutions, which provide the sa- me accuracy in terms of the mean square deviation from given experimental curve. We follow simplified formu- lation of MEM of Steinbach et al. [25], which allows solving such ill-posed problem. An auxiliary functio- nal Q is composed as Q = S(A) – Lχ2(A), (4) where S(A) is the Shannon-Jaynes entropy, L is un- known Lagrange multiplier. The S(A) reads S A A A A A A j j j j j j N ( ) ln ,= − −                = ∑ 0 0 1 (5) where A0 is the initial guess for A. It is possible to prove that maximization of the functional (5) produces a uni- que solution of initial optimization problem [23, 25]. According to (4) S is maximized under the constraint imposed by the χ2 of real signal G and its approxima tion Gfit. Such maximization ensures that the resulting set of values Aj possesses minimal information content among all sets, which are able to approximate the signal G with given accuracy. In the other words the solution is free from spurious correlations and the distribu tion of values in Aj is as smooth as possible [23, 25]. The following algorithm was used to maximize the functional (4): 1) uniform values are assigned to initial guess σ y 0 ; 2) initial value of L is chosen; 3) functional (4) is maximized using simple sequen- tial unconditional optimization until the difference in 488 YESYLEVSKYY S. O. the values of Q between two subsequent steps (toleran- ce) drops below given criterion; 4) L is increased; 5) go to step 3 until χ2 drops below given value. Custom MEMfit software (http://members.multima nia.co.uk.memfit/) was used to perform MEM compu- tations. Detailed information about this software is avai- lable by request. Fitting of the relaxation curve of pure water was performed using N = 200, while fitting of the curve of solvated protein was performing with N = 400. Results and discussion. Volume relaxation curves. The evolution of the periodic box volume after the pres- sure jump in MD simulations of solvated protein is shown in Fig. 2. The curve for pure water looks similar (data not shown). Apparently the curve shape is close to single exponential, which drops very fast in 0.01–0.1 ps. However, there are clear departures from a single expo- nential fit visualized in Fig. 2. It is clear, that this curve contains both very fast (~0.1 ps) and very slow (~50 ns) relaxation components. Relaxations of pure water. Fig. 3 shows the spectrum of exponential components obtained by MEM from the volume relaxation curve of the pure water system. There are three well defined components visible as sharp peaks. The first peak τ1 = 0.189 ± 0.12 ps is close to the relaxation time of the v-rescale thermostat used in our MD simulations (τt = 0.1 ps), while the second peak τ2 = = 0.592 ± 0.26 ps is close to the relaxation time of the Berendsen barostat (τp = 1 ps). These two peaks are li- kely to be methodological artifacts. The third peak τ3 = = 1.588 ± 0.33 ps is the only one, which could be attribu- ted to the relaxation of water molecules. It is of the sa- me order of magnitude as the time of dielectric relaxa- tion of SPC water τM, which varies from 3.5 to 4.1 ps de- pending on simulation parameters [29]. Relaxations of solvated HSA. Fig. 4 shows the spect- rum of exponential components obtained from the vo- lume relaxation curve of solvated HSA protein. This spectrum is much more complex then for pure water and contains eight peaks. The first three peaks τ1 = 0.079 ± ± 0.046 ps, τ2 = 0.521 ± 0.27 ps and τ3 = 1.504 ± 0.66 ps are essentially the same as observed for pure water in Fig. 3. τ1 and τ2 originate from the thermostat and the barostat weak coupling algorithms respectively, while τ3 is probably caused by the fast relaxation of bulk wa- ter. Other five peaks are absent in pure water and cor- respond to much slower relaxations of the protein and its hydration shell. These peaks are τ4 = 7.53 ± 1.52 ps, τ5 = 86.5 ± 8.4 ps, τ6 = 545.9 ± 81 ps, τ7 = 3289.4 ± 317 ps and τ8 = 49787.6 ± 4803 ps. Comparison with experimental data. We compared our data with the results of the broadband acoustic spect- roscopy [8, 9] and optical spectroscopy of the HSA [10–13]. Four major components were detected in the acoustic spectra of HSA in various experimental condi- tions [9]. The shortest relaxation time of 200–600 ps may reflect the motions of small flexible segments on the globule surface. Our relaxation time τ6 falls into this region. The second experimental relaxation time is of order of 1–3 ns, which is close to our component τ7. The third experimental relaxation time is of order of 40 ns, which fits to our component τ8 nicely and is usually at- tributed to cooperative segmental motions of the pro- tein controlled by pH. The slowest experimental com- ponent lies in the microsecond region and can not be reached in our simulations. 489 CONFORMATIONAL RELAXATIONS OF HUMAN SERUM ALBUMIN STUDIED BY MD SIMULATIONS B o x vo lu m e, n m 3 640 680 720 760 800 820 1E-5 1E-4 1E-3 0.01 0.1 1 10 100 Time, ns 0.000 0.002 0.004 0.01 0.1 1 10 100 650 648 646 650 700 750 800 Fig. 2. Evolution of the periodic box volume in the course of production MD run. Curve 1 shows single exponential fit. The pressure jump occurs at time t = 0. Insets show the regions of small and large times separately W ei g h t, a rb it ra ry u n it s 0 5 10 15 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 τ, ps 0.592 0.189 1.588 20 Fig. 3. The spectrum of relaxation times obtained by MEM from the volu- me relaxation curve of pure water. Positions of the peak maxima are shown The data of the time-resolved fluorescent spectro- scopy of HSA revealed several relaxation components, which are attributed to either motions of the protein in the vicinity of chromophore or the dynamics of its hyd- ration shell. The phase-fluorimetry of dielectric relaxa- tions in HSA revealed two relaxation components in the regions of 0.4–2.0 ns and 4.9–8.1 ns [10], which cor- respond to our components τ6 and τ7. Time-resolved spectroscopy of the single tryptophan residue W214 in HSA revealed relaxation times of 25–100 ps [13]. Re- laxations of the surface hydration shell assisted by fluc- tuations of the protein is estimated to occur at the time scale of 100–150 ps in several proteins including HSA [12]. These relaxations correspond qualitatively to our component τ5. The component τ4 could be related to fast compo- nents of hydration dynamics, which occur at 3– 5 ps time scale [12]. Relaxation times of 5.6 ns and 41 ns were reported in other time-resolved fluorescence stu- dies of W214 in HSA [11], which agrees reasonably well with the components τ7 and τ8. Studies of the protein relaxations in MD simulations are usually limited to computing equilibrium fluctua- tions. This technique is not suitable for determining the whole spectrum of relaxations, which occur in the pro- tein globule after some global stress. In this case the di- rect observation of non-equilibrium relaxations is prefe- rable because it provides the whole spectrum of relaxa- tions present in the single MD trajectory. Such global overview of protein relaxations is useful for general understanding the protein dynamics and could be com- pared directly with experimental data. The necessary prerequisite for the direct observa- tion of relaxations in MD is robust and reliable techni- que of spectral decomposition of obtained decay curves. We utilized the Maximum Entropy Method, which se- lects the most plausible solution of decomposition prob- lem with minimal information content. Another prerequisite is a sufficient amount of data points for all time scales on the relaxation curves. We solved this problem by using variable sampling inter- vals increasing with an increase of time. Finally, the last prerequisite is an adequate initial stress, which triggers relaxations in the system. The jump of pressure is a good candidate for such stimulus be- cause it acts globally on all atoms in the system and ini- tiates the whole range of relaxations with very different time scales. Comparison of volume relaxations occurring in our MD simulations with the data of various experimental techniques is only possible on the semi-quantitative le- vel. We managed to attribute six relaxation components to either experimentally observed relaxations in HSA or to the relaxation of bulk water. The nature of all obser- ved relaxation components is summarized in Table. Components τ3 and τ4 are attributed to the motions with overlapping time scales, but there is no ambiguity because the component τ4 is not observed in pure water and thus clearly corresponds to hydration dynamics of the protein. Despite quite uncertain semi-quantitative nature of the acoustic data for HSA [8, 9] we managed to map three relaxation times τ6–τ8 to experimental re- laxation components in this technique. In general, it is remarkable that all relaxation components found in our 490 YESYLEVSKYY S. O. 0.0 W ei g h t, a rb it ra ry u n it s τ, ps 0.079 W ei g h t, a rb it ra ry u n it s 0.521 5 10 15 20 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.0 0.5 1.0 1.5 2.0 10 100 1000 10000 100000 1.504 7.53 86.5 545.9 3289.4 49787.6 Fig. 4. The spectrum of rela- xation times obtained by MEM from the volume rela- xation cur ve of solvated HSA shown in Fig. 2. Posi- tions of the peak maxima are shown. Log scale on X axis and different scale on Y axis are used after τ = 3 ps to show the peaks with large ti- mes and small weights simulations agree with the experimental data reasonab- ly well. To our knowledge the relaxation times of order ~50 ns were never detected before in MD studies. The sensitivity of our technique allows detecting even slower relaxations providing that MD trajectory is long enough. Conclusions. The protocol of MD simulations, which allows obtaining the spectrum of conformational rela- xations in the solvated protein at the time scales from ~0.1 ps to ~50 ns using a single simulation, is deve- loped. The method utilized an abrupt pressure jump to create non-equilibrium stress in the system and uses MEM fitting of the volume relaxation curve to extract in- dividual relaxation components. The structural relaxations of HSA, obtained by dif- ferent experimental techniques, are reproduced with go- od accuracy in our protocol. Acknowledgments. The author is grateful to T. O. Hu- shcha for inspiring MD studies of HSA and discus- sing the results. V. N. Kharkyanen and N. M. Berezets- kaya are acknowledged as developers and testers of the MEMfit software. С. О. Єси ле вський, Т. О. Гуща Виз на чен ня кон фор маційних ре лак сацій си ро ват ко во го аль буміну лю ди ни ме то дом мо ле ку ляр ної ди наміки зі стриб ка ми тис ку Ре зю ме Мета. Роз роб ка ме то ди ки, що доз во ляє от ри му ва ти спек три кон - фор маційних ре лак сацій со льва то ва но го білка ме то дом нерівно - важ ної мо ле ку ляр ної ди наміки. Ме то ди. Струк тур ну ре лак сацію білка ініціюва ли різкою зміною тис ку у про цесі роз ра хун ку в NPT- ан самблі. Про ве де но спек траль ну де ком по зицію кри вої зміни об’є- му білка після стриб ка тис ку ме то дом мак си маль ної ен тропії. Ре - зуль та ти. Одер жа ний спектр ре лак сацій містить один ком по - нент, що на ле жить до чис тої води, і п’ять ком по нентів, відне се- них до білка та його гідрат ної об олон ки. Кон фор мації всіх ком по- нентів відповіда ють струк ту рам, от ри ма ним ме то да ми оптич- ної і акус тич ної спек трос копії. Вис нов ки. Роз роблена ме то ди ка дозво ляє роз ра хо ву ва ти спек три струк тур ної ре лак сації сольва- това них білків у діапа зоні часів від ~0,1 пс до ~50 нс з однієї траєк- торії, одер жа ної ме то дом нерівно важ ної мо ле ку ляр ної ди наміки. Клю чові сло ва: ре лак сація білка, мо ле ку ляр на ди наміка, ме тод мак си маль ної ен тропії, стриб ки тис ку, си ро ват ко вий аль бумін лю ди ни. С. А. Еси лев ский, Т. О. Гуща Опре де ле ние кон фор ма ци он ных ре лак са ций сы во ро точ но го аль бу ми на че ло ве ка ме то дом мо ле ку ляр ной ди на ми ки со скач ка ми дав ле ния Ре зю ме Цель. Раз ра бот ка но вой ме то ди ки по лу че ния спек тра кон фор ма - ци он ных ре лак са ций со льва ти ро ван но го бел ка ме то дом не рав но - 491 CONFORMATIONAL RELAXATIONS OF HUMAN SERUM ALBUMIN STUDIED BY MD SIMULATIONS τ Relaxation component in MD Corresponding relaxation times in other techniques Description of relaxation 1 0.079 ± 0.046 ps 0.1 ps Coupling time of v-rescale thermostat in MD 2 0.521 ± 0.27 ps 1.0 ps Coupling time of Berendsen barostat in MD 3 1.504 ± 0.66 ps 3.5–4.1 ps Dielectric relaxation time τM of bulk SPC water in MD [29] 4 7.53 ± 1.52 ps 3–5 ps Fast vibrations and rotations of water molecules near the protein surface [12] 5 86.5 ± 8.4 ps 25–100 ps Slow hydration dynamics of the protein surface assisted by the fluctuations of protein [12, 13] 6 545.9 ± 81 ps 400 ps–-2.0 ns Dielectric relaxation revealed by time-resolved phase-fluorimetry [10] 200–600 ps Concentration-dependent relaxation in acoustic spectra. Probably motions of small flexible segments on the surface of the globule [9] 7 3.289 ± 0.317 ns 4.9–8.1 ns Dielectric relaxation revealed by time-resolved phase-fluorimetry [10] 1–3 ns Concentration-independent relaxation in acoustic spectra. Probably side- group rotations coupled to the changes of hydration water density [9] 5.6 ns Time-resolved fluorescence of W214 [11] 8 49.787 ± 4.8 ns 40 ns Observed in acoustic spectra. Cooperative segmental motions of the protein chain, controlled by pH [9] 41 ns Time-resolved fluorescence of W214 [11] The summary of observed relaxation components in solvated HSA simulations and their relation to experimental results вес ной мо ле ку ляр ной ди на ми ки. Ме то ды. Струк тур ную ре лак са- цию бел ка ини ци и ро ва ли рез ким из ме не ни ем дав ле ния в про цес се рас че та в NPT-ан сам бле. Про ве де на спек траль ная де ком по зи ция кри вой из ме не ния об ъ е ма бел ка по сле скач ка дав ле ния ме то дом мак си маль ной эн тро пии. В ка чес тве тес то во го об ъ ек та ис поль - зо ван сы во ро точ ный аль бу мин че ло ве ка. Ре зуль та ты. По лу чен - ный спектр ре лак са ций со дер жит один ком по нент, при над ле жа- щий чис той воде, и пять ком по нен тов, от но ся щих ся к бел ку и его гид рат ной об олоч ке. Кон фор ма ции всех ком по нен тов со от вет- ству ют та ко вым, по лу чен ным ме то да ми опти чес кой и акус ти - чес кой спек трос ко пии. Вы во ды. Раз ра бо тан ная ме то ди ка по зво- ляет рас счи ты вать спек тры кон фор ма ци он ных ре лак са ций соль- ва ти ро ван ных бел ков в ди а па зо не вре мен от ~0,1 пс до ~50 нс из еди нствен ной тра ек то рии, вычисленной ме то дом не рав но вес ной мо ле ку ляр ной ди на ми ки. Клю че вые сло ва: ре лак са ция бел ка, мо ле ку ляр ная ди на ми ка, ме тод мак си маль ной эн тро пии, скач ки дав ле ния, сы во ро точ ный аль бу мин че ло ве ка. REFERENCES 1. Brooks C. L. I., Karplus M., Pettitt B. M. 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Conformational relaxations of human serum albumin studied by molecular dynamics simulations with pressure jumps

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