Conformation Induced Dynamical Heterogeneity of Water in

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Conformation Induced Dynamical Heterogeneity of Water in the Solvation Shell of Zwitterionic #-Aminobutyric Acid Bikramjit Sharma, and Amalendu Chandra J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.9b01771 • Publication Date (Web): 04 Sep 2019 Downloaded from pubs.acs.org on September 4, 2019

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The Journal of Physical Chemistry

Conformation Induced Dynamical Heterogeneity of Water in the Solvation Shell of Zwitterionic γ-Aminobutyric Acid

Bikramjit Sharma† and Amalendu Chandra∗

Department of Chemistry, Indian Institute of Technology Kanpur, India 208016

———————————————————— ∗ E-mail: [email protected] † Present address: Lehrstuhl Fuer Theoretische Chemie, Ruhr-Universitaet Bochum, 44780 Bochum, Germany.

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Abstract The structure and dynamics of water molecules around the carboxylate and amino groups of γ-aminobutyric acid (GABA), a primary neurotransmitter in mammals, are investigated by means of ab initio molecular dynamics simulation. Zwitterionic GABA has two major conformations in water, namely the open or the closed conformations. The angle-averaged one dimensional structures of water in the solvation shells around the carboxylate and amino groups are found to be quite similar for the closed and open conformations of the solute. The two dimensional structural correlations, which describe the solvation shell structure with better resolution, reveal some differences in the arrangement of water molecules around the solute for its open and closed conformations. It is found that the dynamics of solvation shells in the two conformations vary only slightly. However, the existence of trapped water between the oppositely charged carboxylate and amino groups of GABA in its closed form is found to give rise to very different dynamical behavior as compared to overall solvation shell in the same conformation as well as that in the open conformation. Thus, dynamical heterogeneity at local level is induced by change in the conformation of zwitterionic GABA. Such trapped water is not seen in the open form of the solute. Similar type of “connecting water” has also been observed for microsolvated β-alanine in a recent experimental and theoretical study (J. Phys. Chem. B, 2019, 123, 4392-4399). Thus, the current study shows the variation of binding properties of water with change of conformation of zwitterionic GABA, which in turn changes the dynamics of water at a local level. The conformation induced changes in the water dynamics constitute an example of dynamical heterogeneity of water which is normally observed in the presence of large biomolecules like proteins, DNA etc.


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1

Introduction

The hydration shell water is generally believed to play important roles in determining the structure and function of biomolecules in aqueous media 1–3 . In fact, the coupling between the dynamics of biomolecules and hydration layer water has been studied rather extensively 4,5 . It is believed that the activities of biomolecules in aqueous media arise both from the properties of biomolecules themselves and their interactions with associated water. Typically, biomolecules refer to very complex structures such as proteins, nucleic acids etc. However, the building blocks of these complex structures are smaller organic molecules. For example, the building blocks of proteins are amino acids and that of nucleic acids are nucleobases. Interactions of water with such biologically important smaller organic molecules can also lead to many interesting results 6–8 . The zwitterionic γaminobutyric acid (GABA) is one such small biomolecule which is of immense importance as a neurotransmitter. It regulates neuronal inhibition and thereby neuronal excitation in the brain 9 . GABA features in a number of neuronal disorder e.g. insomnia, epilepsy, anxiety, Alzheimer and Parkinson’s disease etc 10,11 . The structure of zwitterionic GABA has been investigated in microsolvated environment. For example, Jordan and co-workers 12 studied the GABA dihydrate (GABA.2H2 O) and GABA pentahydrate (GABA.5H2 O) with a dielectric continuum to model the long range solvation effects. This allows the investigation of short and long-range solvent effects and also possible structures of GABA in presence of explicit water. Nagy and co-workers 13 employed Hartree-Fock theory to optimize the structure of GABA dihydrate followed by single point energy calculation at MP2 level of theory. They also performed Monte-Carlo simulations using TIP4P potential for water and concluded that, although the dihydrated neutral form of GABA is prominent in the gas phase, inclusion of bulk effects tend to stabilize the zwitterionic form. There are also other quantum mechanical investigations 14–16 on GABA in presence of explicit water or continuum solvation model which explored energetics and conformational aspects. The solvation structure of GABA in water and trifluoroethanol has also been investigated by means of force field based molecular dynamics simulation 17 .

It is to be noted that in the gas phase, GABA remains in the neutral form. The n → π ∗ interaction was shown 18 to govern the stability of the closed form of neutral GABA in the gas phase. However, an intramolecular proton transfer from the carboxyl 3 Environment ACS Paragon Plus


group to the amine group converts the neutral form to zwitterionic species in water. The interconversion of the neutral and zwitterionic GABA (in absence of water) in solid state and inert gas matrix at low temperatures has been studied earlier 19 . However, to the best of our knowledge, the energetics of intramolecular proton transfer in water for the conversion of the neutral form of GABA to the zwitterionic form has not been studied. The conformation of zwitterionic GABA in water can be divided into two major forms: The closed form and the open form 20 . In the closed form, an intramolecular hydrogen bond is formed between the negatively charged carboxylate oxygen and positively charged amino hydrogen of GABA (Fig.1a) while in the open form, the two ends of GABA remain separated (Fig.1b, 1c). The preferred conformation of zwitterionic GABA in water has been a matter of debate as some studies found the open conformation while some other studies found the closed form to be more preferred. In a recent study 21 , using ab-initio molecular dynamics in conjunction with metadynamics technique for enhanced sampling, it was shown that zwitterionic GABA can adopt one close form and six different open forms in water. Some of the open forms were found to be more stable while other open forms were found to be less stable than the closed conformation. Thus, the apparent anomaly in the findings of previous studies was resolved. However, the absolute energy difference between different conformations of zwitterionic GABA does not vary to a large extent 21 and they are found to be readily interconvertible 21 . The higher relative population of the open form of zwitterionic GABA in water was attributed to greater flexibility of the back bone as compared to that of the closed form 21 . Further insights into conformational preference of zwitterionic GABA in water was obtained based on calculations of dipole moment theoretically 21 and also experimentally 20 . The experimental study 20 assumed that since the closed form of GABA is structurally similar to proline, the dipole moment of the former should be closer to that of the later (∼15 D) whereas much higher dipole moment of GABA means the existence of the open conformation. The dipole moment of GABA was determined to be ∼27 D 20 and hence the open form was concluded to be prevailing in water. However, the experimental result is a weighted average of dipole moment values coming from different configurations and thus misses the microscopic picture. Subsequent theoretical study 21 explicitly determined the dipole moment of closed form of zwitterionic GABA to be ∼18 D and that of the open form to be ∼25 D. Conformational properties of microsolvated GABA has also been investigated earlier 13,15 . It was shown 13,15 that as the


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number of water molecules increases, the zwitterionic open form of GABA becomes the major conformation. Thus, solvation plays a significant role in determining the charged state and conformation of GABA.

Although, much attention has been paid to conformational properties of GABA in earlier studies, investigations of solvation structure and dynamics of this important biomolecule in bulk water is very rare. In this study, we have carried out Car-Parrinello molecular dynamics (CPMD) 22 simulations of zwitterionic GABA in water to investigate the solvation structure and dynamical properties. The CPMD method involves on-thefly calculations of interatomic forces based on quantum density functional theory (DFT) followed by dynamical propagation of the nuclei according to the calculated forces 22,23 . The dynamics of the associated electronic degrees of freedom are described by treating the electronic orbitals as dynamical variables by assigning a fictitious mass to each orbital. Subsequently, the equations of motion for the nuclei and electronic orbitals are solved based on forces derived from DFT 22,23 . Unlike force field based molecular dynamics methods, the CPMD method has the advantage of calculating the many-body potentials during the course of the simulation using DFT rather than depending upon pre-defined potential parameters. The CPMD method has been found to be very successful in exploring aqueous systems in many earlier studies 24–27 .

We have calculated the one dimensional and two dimensional radial distribution functions to investigate the average solvation structural properties for the closed and open conformations of zwitterionic GABA. The dynamics of water around the amino and carboxylate groups are investigated in terms of the mean square displacements (MSDs), residence dynamics, orientational relaxation and hydrogen bond dynamics. The water molecules in the overall solvation shells of the amino and carboxylate groups are found to show slight differences in their average dynamical behavior in both conformations of GABA. However, interesting features appear when a more detailed analysis is carried out on what is hidden behind the average solvation shell dynamics in the closed form of GABA. It is found that water can be trapped between the two oppositely charged amino and carboxylate groups of GABA in its closed form. Such trapped water is part of the overall solvation shell. However, the dynamics of such trapped water is very different from that of the overall solvation shell. Thus, there is a local heterogeneity in the dynamics of 5 Environment ACS Paragon Plus


water molecules around zwitterionic GABA in its closed form. In the open form of GABA, the two oppositely charged groups are well separated and are not in the right positions to trap water between them. Hence, locally heterogeneous dynamics is not observed in case of the open form. Thus, the current study reveals that although the dynamics of the overall solvation shells differ slightly for the two conformations of GABA, conformational changes induce very large difference in local dynamics. It may be noted that we have not differentiated between different open forms of the zwitterionic GABA 21 , i.e. different open forms are considered as belonging to one category of conformation in a broader sense in the present study. The conformational fluctuations induced changes in the hydration water dynamics have been reported for large biomolecules like proteins, DNA 1,28,29 etc. and it has been termed as dynamical heterogeneity of water. However, such dynamical heterogeneity is not a commonly observed phenomenon for small solutes. However, the current study shows that conformational fluctuations in small molecule also can also give rise to dynamical heterogeneity locally, if not globally.

The rest of the Paper is organized as follows: Sections 2 and 3 include the computational details and results on intramolecular proton transfer, solvation structure and dynamics of water in the solvation shells, respectively. A brief summary of the key results and our conclusions are included in Section 4.

2

Details of Simulations

We have carried out Car-Parrinello molecular dynamics (CPMD) simulation of a GABA molecule dissolved in 107 water molecules in a cubic box of edge length 14.8 ˚ A at room temperature using the CPMD program 30 . The box was then periodically replicated in all three directions to remove any boundary effect. An important issue regarding the current study is whether the considered number of water molecules appropriately mimic bulk water or not for a fairly large solute like GABA. We have addressed this issue in the result and discussion sections.

The dispersion corrected BLYP-D2 31–34 functional

was used and the plane wave basis was truncated at a kinetic energy cut-off of 80 Ry. The Troullier-Martins 35 pseudopotentials were used to represent the core electrons. We assigned a fictitious mass of 800 au to the electronic orbitals and a time step of 5 au was used to integrate the equations of motion. In order to ensure that the nuclei and 6 Environment ACS Paragon Plus

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electronic orbitals remain adiabatically separated, the mass of a deuterium atom was used for all hydrogens. We started the simulation with the closed form of GABA and equilibrated for 10 ps. Then the production run was carried out for 260 ps. After ∼35 ps of the production run, the closed form was found to get converted to the open form. Subsequently, we identified parts of the trajectory corresponding to closed and open forms of GABA and performed analysis of the structure and dynamics of water around these two conformers.

3 3.1

Results and Discussions Intramolecular Proton Transfer of Neutral GABA in Water

GABA exists in neutral closed form in the gas phase and gets converted to the zwitterionic form in water via intramolecular proton transfer. It will be interesting to investigate the intramolecular proton transfer which would also shed light on the conversion of the neutral form to zwitterionic form. We have considered the neutral form of GABA in water and carried out CPMD in the NVT ensemble while keeping the GABA molecule fixed. All the simulation parameters are exactly same as mentioned in Section 2. The reason for starting the simulation with fixed geometry of GABA is that the initial surrounding water structure may affect the proton transfer. So, we have investigated the proton transfer with three different initial structures to account for this effect. If GABA is allowed to be flexible, then proton transfer may occur even before generating different initial structures. Thus, the initial structures are chosen from the NVT simulation trajectory of neutral GABA in water at times 4, 8 and 12 ps. The intramolecular proton transfer coordinates are shown in Fig.2a, the configurations capturing the proton transfer are shown in Fig.2b and the variations of the proton transfer coordinates are shown in Fig.2c. The proton transfer is found to occur spontaneously as shown in Fig.2. This suggests that the the proton transfer process is associated with a decrease of free energy.

In order to investigate the possible role of solvation on the proton transfer process, we have first looked at some of the average structural and electronic properties of neutral GABA molecule in water. For this purpose, we have considered the same three initial geometries as described above. Using these geometries, we have further performed 2.5



ps NVT simulations allowing the GABA molecule to be flexible, but restraining the O-H bond distance of the carboxyl group with a restraining potential of 20 kcal/mol. This approach allows us to have a equilibrated water structure around the neutral GABA molecule with its all degrees of freedom to be flexible except the O-H distance. Thus, we can investigate the water structure around the neutral GABA molecule which would not have been possible without restrain due to spontaneous proton transfer. We found the average number of water molecules to be ∼4.7 and ∼3.6 in the solvation shell of the carboxyl and amino groups of neutral GABA, respectively, which are less than that for the corresponding zwitterionic form (Table 1). This suggests that the zwitterionic species is solvated more effectively than the neutral form which is expected. The average dipole moment over the three simulation trajectories (with restrained O-H bond) is found to be ∼12.4 Debye which is much less than that of the zwitterionic closed conformation of GABA (∼18 Debye) 21 . Thus, the intramolecular proton transfer leads GABA to from a less polar to more polar form which is preferred in water. We have also investigated the proton transfer event starting from the geometries obtained after running 2.5 ps simulation with the O-H bond restrained. We removed the restraints from the O-H bond for this purpose and carried out further simulations. However, the proton transfer mechanism is found to be similar as obtained above. We note that since the proton transfer occurs so fast, the surrounding water structure does not change at this timescale. However, after the proton transfer, the enhanced electrostatic interactions between the charged groups and water molecules lead to enhanced solvation as can be seen by the comparison of average number of water molecules in the solvation shells of the neutral and zwitterionic forms of the solute.

3.2

Solvation Shell Structure of Zwitterionic GABA in Water

We have investigated the structure of solvation shells of the carboxylate and amino groups of GABA in its open and closed conformations. The radial distribution functions (RDFs) of water oxygen (OW) and hydrogen (HW) with respect to the carboxylate oxygen (O) and amino nitrogen (N) of the solute are shown in Fig.3. The RDFs suggest that the number of water molecules considered in the current study along with periodic boundary conditions is sufficient to reproduce bulk environment. When the bulk behavior is reached, the RDF goes to 1 in the asymptotic regime of distance. As the RDFs (Fig.3) for the distribution


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of water oxygen with respect to different solvation sites of GABA reach the value of 1 at large distances, it can be concluded that number of water molecules considered in this study is sufficient to mimic the solvation of GABA in bulk water.

The solvation shells are defined based on the first minimum of RDF for the distribution of water oxygen with respect to different sites of GABA. Thus, the amino solvation shell contains water molecules whose oxygen are within a distance of 3.5 ˚ A (first minimum of N-OW RDF in Fig.3) from the nitrogen atom of GABA. The carboxylate solvation shell encompasses water molecules whose oxygens are situated within a distance of 3.3 ˚ A (first minimum of O-OW RDF in Fig.3) from the carboxylate oxygen of GABA. It is clear from the RDFs that the distributions of OW and HW atoms with respect to O and N atoms of GABA vary only slightly for its open and closed conformations. However, the one dimensional RDF gives the angle-averaged one dimensional distribution for a particular type of atoms. The higher dimensional distribution functions can provide better insights into the solvation shell structures. We have calculated the two dimensional radial distribution function (2D-RDF), denoted as g(r1 , r2 ), which gives the distribution with respect to two chosen solvation sites of a solute. The variables r1 and r2 represent the distances of the atom of interest from the two solvation sites of the solute. We have employed the method of Engelsen 36 for calculation of the 2D-RDFs. Figs.4a and 4b show the distributions of water oxygen (OW) with respect to the two carboxylate oxygens of GABA in its two conformations. We have tagged the two carboxylate oxygens as OG1 and OG2 and the distances between OG1-OW (rOG1−OW ) and OG2-OW (rOG2−OW ) atoms are taken along the x and y axes of the 2D-RDFs (Fig.4). The densities parallel to the x and y axes represent the distribution of OW with respect to the OG2 and OG1 atoms, respectively. Clearly, the distributions of OW with respect to the two carboxylate oxygens are different in the closed form (Fig.4a) while the distributions are symmetrical in the open form (Fig.4b). We have calculated the power spectra for vibrations associated with water and the amino group by Fourier transformation of the velocity autocorrelation functions. The velocity of the deuterium atoms of water and amino group were chosen and the respective power spectra are shown in Figs.5a, 5b and 5c for solvation shell water and also for the amino group of GABA. The power spectra for vibrations associated with water in different regions i.e. amino and carboxylate hydration shells and bulk are



found to be very similar (Fig.5a and 5b). Since the hydrogen bond strength correlates well with the stretching frequencies of associated OD bonds, it can be inferred from the vibrational power spectra that the average strength of hydrogen bonds formed by water molecules in different regions is similar irrespective of the conformation of GABA. We have also compared the vibrational power spectra of the amino group with that of bulk water (Fig.5c). Expectedly, the stretch frequencies of the protonated amino group is found to be red shifted compared to that of the hydroxyl groups of bulk water (with all hydrogens carrying deuterium mass for both amino group and water). Again, the amino stretch frequencies are found to be very similar for the open and closed conformations of GABA.

3.3

Solvation Shell Dynamics of Zwitterionic GABA in Water We have also investigated the dynamics of water molecules around the carboxylate

and amino groups in the closed and open conformations of GABA. Fig.6 shows the mean square displacements (MSDs) of various types of water molecules solvating different sites of GABA in its closed and open conformations. The MSDs of overall solvation shells (black and red lines) is found to be somewhat different. Thus, the diffusion of solvation shell water molecules changes slightly in moving from open to the closed conformation of GABA. The diffusion coefficient values, which are obtained by using Eq.(1) of the Supporting Information (SI), are included in Table 2. In order to understand the origin of these trends in MSDs, we have investigated the effect of electric fields coming from the two oppositely charged polar groups, namely the carboxylate and amino groups, in the closed form of GABA. Because of the opposite electric fields, the water molecules in the solvation shells tend to reorient themselves in such a way that their oxygen atoms point towards the positively charged amino group and corresponding hydrogen atoms point towards negatively charged carboxylate group. Thus, the attractive electrostatic forces from both the ends tend to trap water molecules strongly in the closed form. It is found that, on an average, approximately 0.8 water molecules get trapped and remain strongly bound to GABA in its closed form. Fig.6 shows a representative snapshot of such a water molecule which appears in the solvation shells of amino as well as carboxylate groups. We note here that, although the favorable electrostatics have the tendency to trap more water molecules, spatial constraints forbid the same. A recent experimental and theoretical


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study 37 on microsolvated β-alanine shows the existence of “connecting water”between the carboxylate and amino groups. The “connecting water”, which is similar to the trapped water in the current study, is found to enhance the stability of the zwitterionic β-alanine. However, one difference is that the microsolvated clusters represent a static picture and in the current study, the atoms evolve dynamically due to thermal effects. Thus, the “trapped water” in the current study keeps on breaking and reforming its hydrogen bonds with surrounding molecules. Nevertheless, the “trapped water” is in similar spirit as the “connecting water” in the recent experimental and theoretical findings 37 . Crittenden et. al. 15 also found molecular bridge of one or two water molecules for GABA.2H2 O and, for GABA.5H2 O. Thus, the results of the current study captures some of the features of existing studies 15,37 . We have resolved the dynamics of water by defining different subensembles as “trapped water” for water molecules common to the carboxylate and amino solvation shells in the closed form of GABA, “excluding trapped water” for the solvation shell water molecules excluding the trapped water, “overall amino solvation shell” and “overall carboxylate solvation shell” for water molecules which include both “trapped water” as well as “excluding trapped water” subensembles. The categorization of water into different subensembles is valid for the closed conformation as the carboxylate and amino groups of GABA in the open conformation are well separated. We have separately investigated the translational motion of the trapped water molecule. It is found that (Fig.6) the “trapped water” molecule has much slower translational diffusion. In fact, when the MSDs of solvation shell water in the closed form is resolved for water molecules for “excluding trapped water” ensemble, their translational diffusion is found to be very close to that of “overall solvation shell” water molecules of GABA in its open form (Fig.6). Thus, the translational dynamics differs locally for water molecules around the zwitterionic GABA in its closed conformation. Next, we have calculated the residence dynamics of water molecules around the carboxylate and amino moieties in the two chosen conformations of GABA. The decay of the residence correlation function (SR (t), defined by Eq.(2) of SI) of water molecules around the chosen solvation sites of GABA and of different subensembles of water shown in Fig.7. It is found that the escape dynamics of “trapped water” is faster as compared to other subensembles. This may be seen apparently contradictory as the translational dynamics of this subensemble is slower than that of the others. However, in the closed conforma-



tion, the trapped water remains in close proximity of the two polar groups in the closed form. There is overlap of the two solvation shells of the two polar groups which means the trapped water can enter one solvation shell from another rather quickly without really translationally moving away due to the favorable interaction with opposite electric fields. This quicker transition from one solvation shell to another makes the escape dynamics of “trapped water” faster in the closed conformation. In other words, the present results show that within the overall solvation shell, “trapped water” shows greater translational movement between the carboxylate and amino solvation shells of the GABA molecule in its closed form. The reorientational dynamics of water molecules in the solvation shells of the carboxylate and amino groups also shows interesting behavior for the two conformations of the solute. We have calculated the orientational dynamics of water OD bond vectors in the two solvation sites of GABA and the results are shown in Fig.8. The definition of orientational correlation function and orientational relaxation of the dipole vector of water are included in Eq. 3 and Fig.S1 of SI, respectively. The corresponding integrated orientational relaxation times are included in Table 3. Interestingly, the orientational dynamics of water molecules in the solvation shell of the carboxylate group is found to be faster for the open form of GABA as compared to that for the closed form. It is known that the rotational motion of water is intimately linked to the switching of hydrogen bonds. In the closed form of GABA, one of the oxygen atoms of the carboxylate group forms an intramolecular hydrogen bond with a hydrogen of the amino group while the other oxygen is fully available for forming hydrogen bonds with water. For the open conformation of GABA, on the other hand, there is no intramolecular hydrogen bond and both the oxygens of the carboxylate group are fully available for forming hydrogen bonds with water. The orientational dynamics of “trapped water” is found to be faster and slower than that of water molecules in the overall carboxylate and amino solvation shells, respectively. Thus, the “excluding trapped water” subensemble has even slower and faster dynamics (Fig.8) in the carboxylate and amino solvation shells, respectively, in the closed form of GABA. Thus, the slower orientational dynamics of water molecules in the carboxylate solvation shell in the closed form arises solely from the “excluding trapped water” ensemble as the orientation of “trapped water” is in fact faster. It was shown 39,40 that water reorientation occurs via large angular jumps and consequently hydrogen bond switching


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by a hydrogen bond donor from one hydrogen bond acceptor to other hydrogen bond acceptor takes place. This mechanism primarily influences the reorientational dynamics of hydrogen bonded systems in condensed phases. We have calculated the fraction of water molecules which switches hydrogen bonds from one carboxylate oxygen to another. Fig.9 shows this probability where the fraction of water molecules is seen to be much higher for the open form as compared to the closed form. Such switching of hydrogen bonds was shown to occur via large angular jumps 39,40 and the process depends on availability of hydrogen bond acceptors in the surrounding environment 41 . Thus, for the open conformation of GABA, a water molecule initially hydrogen bonded to one of the oxygens of the carboxylate group finds a partner (the other oxygen of the carboxylate group) for hydrogen bonding via angular jump. However, in the closed form, one of the carboxylate oxygens forms hydrogen bond with the amino group and less readily available to accept a hydrogen bond form a nearby water molecule. Thus, there is more rotational freedom to the water molecules hydrogen bonded to the carboxylate group of GABA in the open conformation than that in the closed conformation. This results in faster rotational kinetics of water in the solvation shell of the carboxylate group for the open form of the solute. For a given conformation, water molecules in the solvation shell of the amino group are found to rotate faster than those around the carboxylate group which can be attributed to different hydrogen bonding abilities of the two groups. While the carboxylate group binds to hydrogens of the water molecules by accepting hydrogen bonds through its two oxygens, the amino group (in its protonated form) has three hydrogens which link to the oxygen atoms of water by donating hydrogen bonds. Thus, for a given conformation of the solute, the carboxylate group restricts rotation of OH groups more effectively giving rise to slower reorientational relaxation of water in its solvation shell than the amino group.

As the dipole moment of zwitterionic GABA is very high, it is likely that the orientational relaxation of water is affected beyond the first solvation shell. Thus, we have calculated the orientational relaxation of water molecules which are within a distance of 3.3 ˚ A to 5.0 ˚ A from the oxygen atoms of the carboxylate group and 3.5 ˚ A to 5.0 ˚ A from the nitrogen atom of the amino group. We found the orientational relaxation of the water molecules in these regions to be slightly slower as compared to bulk water molecules (Fig.S2 of SI). Thus, the orientational relaxation of water molecules is affected at longer



distances by the zwitterionic form of GABA.

Next, we have investigated the carboxylate-water and amino-water hydrogen bond dynamics for the closed and open conformations of GABA. We have used geometric criteria based on RDF (Fig.3) for defining hydrogen bonds. A water molecule is defined to be hydrogen bonded to a carboxylate or an amino group if rO−OW ≤ 3.3 ˚ A, rO−HW ≤ 2.4 ˚ A

or

rN −OW ≤ 3.5 ˚ A, rN H−OW ≤ 2.4 ˚ A where rO−OW represents the distance between the carboxylate oxygen and water oxygen, rO−HW is the distance between the carboxylate oxygen and water hydrogen, rN −OW is the distance between the amino nitrogen and water oxygen, and rN H−OW is the distance between the amino hydrogen and water oxygen. The hydrogen bond dynamics was investigated by calculating the continuous hydrogen bond correlation function(SHB (t)) 42–45 . The definition of SHB (t) is described by Eq.(4) of SI. The decay of SHB (t) for the amino-water and carboxylate-water hydrogen bonds are shown in Fig.10, and the corresponding integrated relaxation times are included in Table 3.

The dynamical behavior of the hydrogen bonds is found to be consistent

with the rotational dynamics of water in the solvation shells. This is expected since rotational motion is known to be the primary mechanism for hydrogen bond breaking. The carboxylate-water hydrogen bond lifetime is found to be shorter for the open form of GABA, in line with that found for the rotational relaxation. As discussed above, the open form of GABA allows hydrogen bond switching at enhanced rate due to availability of both the oxygens of the carboxylate group to form hydrogen bonds with water. The availability of both the carboxylate oxygens adds more cooperativity in the hydrogen bond rearrangement processes in the vicinity of the carboxylate group which, in turn, leads to faster breaking of hydrogen bonds. This cooperativity is reduced for the closed form as one oxygen is already occupied for an intramolecular hydrogen bond, hence the hydrogen bond relaxation also takes place at a relatively slower rate.

One issue with the calculations of above dynamical properties of water around the closed form of zwitterionic GABA is the long time behavior of the correlation functions. The simulations in the current study is started with the closed form of GABA which transforms into the open conformation after approximately 35 ps. Time required for the 14 Environment ACS Paragon Plus

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closed form to convert into open form in a particular simulation will depend on the initial structure. The ideal way to extract the timescale for closed form to open form transition is to run different simulations with a statistically meaningful number of initial configurations (with closed form of GABA) and then calculate the average time required for conversion to the open form. However, such an approach is computationally prohibited. Thus, in the current study, the long time behavior of mean square displacements and some of time correlation functions are unknown for the dynamics of water near the closed form of GABA. Some of the time correlation functions, e.g. hydrogen bond population correlation function, converge to the proper long time value even for the closed conformation of GABA. Such a problem does not arise in case of the solvation dynamics around the open conformation of GABA as this conformation is prevailed for the longer time in water. As mentioned in the Introduction, the prevalence of the open form is because of more backbone flexibility than the closed form. However, the current study deals with the existence of local heterogeneity due to the presence of trapped water in the solvation shell in the closed form of zwitterionic GABA. This is described in terms of large difference in the dynamics of trapped water as compared to the overall solvation shell of the zwitterionic GABA in its closed and open conformations. Thus, even if the long term behavior of the dynamics of water is not known for the closed form of GABA, the difference in the dynamics of trapped water and the existence of local dynamical heterogeneity is clearly evident. Nevertheless, we have shown some of the dynamical properties with long time behavior for the open form of GABA in the Supporting Information (Figs.S3, S4, and S5 of SI). We note that the reported timescales are extracted from bi or triexponential fits for the correlation functions while the diffusion coefficients are calculated from the slope of linear fit to MSD. We have also carried out block averaging analyis to determine the error bars in hydrogen bond lifetimes. For this purpose, we have divided the trajectory corresponding to the open conformation of GABA into 15 segments. The length of each segment is ∼12 ps. We note that the block averaging approach of such calculations generally gives a distribution of the timescales extracted from differnt segments of the trajectory. The standard deviation of such a distribution typically gives the error bar associated with the calculation of the timescales (property). Thus, it requires long trajectory which can be chopped into statistically meaningful number of pieces so that the calculated error bar becomes meaningful. We have shown the hydrogen bond



lifetimes calculated from different segments of the trajectory in Figs.S6 and S7 of SI for carboxylate-water and amino-water hydrogen bonds, respectively, for the open conformation of GABA. The distribution of these data are then fitted to a Gaussian and the standard deviations are found to be ∼1.3 ps and ∼0.85 ps for the carboxylate-water and amino-water hydrogen bonds for the open conformation of GABA, respectively. However, due to limited availability of trajectory, such an analysis is not meaningful for the closed form of GABA. Fig.10 shows that the amino-water hydrogen bond population correlation fuction decays much faster (∼8 ps) than that of carboxylate-water (∼18 ps) when GABA is in closed form. Thus, we have also calculated the amino-water hydrogen bond lifetimes by dividing the trajectory corresponding to the closed form of GABA into three segments, each of length 12 ps. The amino-water hydrogen bond lifetimes for these three segments are given in Table S1 of SI. Although this is not a proper error analysis, still it gives some indication of the compactness of the data. We note that we have not done such analysis for the carboxylate-water hydrogen bonds in the closed form. This is because the hydrogen population correlation function corresponding to carboxylate-water hydrogen bonds in the closed form goes to 0 at around 18 ps (Fig.10) calculated for the entire trajectory i.e. ∼35 ps. Thus, in order to do block averaging analysis, we need trajectory segments of length greater than 18 ps and the total trajectory length at our disposal is not sufficient to do so for the carboxylate-water hydrogen bond dynamics in the closed form.

4

Conclusions In the current work, we have investigated the effects of conformation of the γ-

aminobutyric acid (GABA) molecule on the structure and dynamics of surrounding water molecules by using Car-Parrinello molecular dynamics simulation. We have used the dispersion corrected BLYP-D2 functional and the simulation was carried out at room temperature. We have divided the conformations of GABA into two major types: The closed and open forms. The properties of water molecules in the solvation shells of the carboxylate and amino groups of GABA are investigated. On the structural side, we have looked at the one and two dimensional radial distribution functions (RDFs). The one dimensional RDFs suggest that the average water structure does not vary to a significant extent around the selected solvation sites for different conformations of GABA. However, the two dimensional radial distribution functions reveal noticeably different distributions 16 Environment ACS Paragon Plus

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of water with respect to the two carboxylate oxygen atoms of the solute in different conformations. The vibrational power spectra of water reveals that the strength of waterwater hydrogen bonds in the two selected solvation sites is very similar to that of bulk water.

The dynamical properties of water molecules in the solvation shells of amino and carboxylate groups of zwitterionic GABA in its open and closed conformations are found to differ slightly. However, in the closed conformation, trapped water is found to exist between the oppositely charged carboxylate and amino groups. The trapped water forms part of the solvation shells of both the amino carboxylate groups in the closed conformation of GABA. In the open conformation of GABA, trapping of water is not possible as the carboxylate and amino groups are far apart. Thus, the existence of trapped water is a property of the closed conformation only. Dynamical behavior of the trapped water is found to differ significantly from that of the overall solvation shell of GABA. Thus, dynamical heterogeneity arises locally within the solvation shell due to the presence of trapped water. We note that the effect of trapped water on the dynamics of the overall solvation shell is not prominently observed in the calculations of different dynamical quantities. This is because the number of trapped water molecules is much less compared to the number of water molecules which are in the solvation shell but not trapped between the carboxylate and amino groups. The dynamical behavior of the overall solvation shells is largely governed by water molecules which are not trapped. Thus, the current study shows the existence of local dynamical heterogeneity around a small biomolecule induced by conformational changes.

The existing literature generally deals with the conforma-

tional fluctuation induced dynamical heterogeneity of water around large biomolecules such as proteins, DNA etc. However, conformation induced changes in water dynamics for small solutes are rarely investigated. The present work provides such a study of dynamical heterogeneity near a small biomolecular solute.

We note that in actual biological conditions, ions and other small organic molecules are also present.

In order to understand water structure and dynamics in the sol-

vation shell of zwitterionic-GABA in more complex environment e.g. in presence of salts and other small molecules dissolved in water, knowledge of simpler conditions e.g. biomolecules in pure water is necessary. Furthermore, water being the “biological sol17 Environment ACS Paragon Plus


vent”significantly governs the properties of biomolecules. The current study thus provides an understanding of the correlation between conformational fluctuations of an important biomolecule in water and its implications in solvation shell structure and dynamics. This study can be helpful in understanding the solvation shell structure and dynamics of GABA in more complex environments e.g. in the presence of ions and other biologically relevant molecules.

It is worth mentioning that the behavior of actual atoms are quantum mechanical and quantum effects are more pronounced for lighter atoms like hydrogen and at temperatures much lower than room temperature. In the current study, replacement of hydrogen mass by that of deuterium and setting the temperature at room temperature are expected to significantly reduce the quantum effects. In order to investigate the effects of quantum nature of the motion of nuclei, in principle, the method of ab initio path integral molecular dynamics could be employed. However, such calculations involve huge computational cost. We note that the quantum effects can be crucial in certain properties specially at low temperatures. However, the bulk water properties at room temperature have been found to be close in AIMD with and without nuclear quantum effects 46 . For example, Markland and coworkers 46 found strong similarity in bulk water structure in AIMD simulation with and without nuclear quantum effects. Furthermore, the diffusion coefficient of bulk water was found be 2.22×10−9 m2 s−1 with GGA functional in absence of quantum effects as compared to 2.29×10−9 m2 s−1 with hybrid functional in presence of quantum effects. Thus, GGA functionals without quantum effect is reasonably good for aqueous systems at room temperature. Considering all these factors of deuterium mass, room temperature, reasonable results for bulk water without quantum effects and computational cost associated with the treatment of nuclear quantum effects, the methodology used in the current study sounds reasonable even without treating all the quantum effects. Furthermore, the current study can provide a good basis for future studies involving more accurate methodologies including nuclear quantum effects of solute and water molecules.

Acknowledgment Financial support through a J.C. Bose Fellowship to A.C. from the Science and Engi-


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neering Research Board, a statutory body of the Department of Science and Technology, and Council of Scientific and Industrial Research (through a Junior/Senior Research Fellowship to B.S.), Government of India, is gratefully acknowledged. We Also thank Mr. Banshi Das and Dr. Ravi Tripathi for their help. Part of the calculations was done at the High Performance Computing Facility at Computer Center, IIT Kanpur.

Supporting Information The statistical mechanical definitions of different dynamical quantities are included in the Supporting Information. Furthermore, figures corresponding to the orientational relaxations of water in the first and second solvation shells, long time behavior of different dynamical properties of water, and block averaged hydrogen bond lifetimes are included in the Supporting Information.



TABLE 1. Average number of water molecules in the amino and carboxylate solvation shells in the closed and open forms of GABA

Conformation Amino solvation shell Carboxylate solvation shell Closed 4.15 5.3 Open 4.45 5.5

TABLE 2. Diffusion coefficients (D) of water molecules in different solvation shells. The solvation shells for the closed conformation below refers to ”overall amino or carboxylate solvation shells” as mentioned in the text.

Conformation Property Closed D (10−5 cm2 s−1 ) Open D (10−5 cm2 s−1 )

Amino solvation shell Carboxylate solvation shell 0.18 0.21 0.48 0.29

TABLE 3. Average orientational relaxation lifetimes of OD bond vector (τOD ), water dipole vector (τµ ) and water-water hydrogen bond lifetimes (τHB ). The solvation shells for the closed conformation below refers to ”overall amino or carboxylate solvation shells” as mentioned in the text.

Conformation Property Amino solvation shell Carboxylate solvation shell Closed τOD (ps) 5.63 15.75 Open τOD (ps) 8.18 13.62 Closed τµ (ps) 3.80 8.25 Open τµ (ps) 6.50 6.92 Closed τHB (ps) 1.74 5.34 Open τHB (ps) 1.79 2.97


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Figure 1: (a) Representative closed form of GABA, (b) and (c) Representative open forms of GABA. The negative charge on the carboxylate group is found to be delocalized and is shown by the dashed lines near this group.

+

Figure 2: (a) Proton transfer coordinates, (b) Proton transfer reaction, and (c) Variation of proton transfer coordinates averaged over the trajectories with three different initial structures,


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Figure 3: Radial distribution functions for water oxygen (OW) and hydrogen (HW) atoms with respect to different solvation sites of GABA.

(a)

(b)

Figure 4: Two dimensional radial distribution functions for water oxygen (OW) with respect to the two carboxylate oxygens (OG1 and OG2) of GABA in (a) closed, (b) open forms.



Figure 5: Vibrational power spectra of water in the (a) carboxylate, (b)amino solvation shells of GABA and (c) Vibrational power spectra of the amino group of GABA.

Figure 6: Schematic representation of trapped water and mean square displacements of different subensembles of water.


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Figure 7: Continuous residence time correlation functions of water in the amino and carboxylate solvation shells of GABA in its closed and open conformations.

Figure 8: Orientational relaxation of different subensembles of water.



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(a)

(b) Figure 9: (a) Schematic presentation of hydrogen bond switching and (b) Fraction of water molecules per time step performing jump from one carboxylate oxygen to the other in the closed and open conformations.

Figure 10: Decay of the continuous hydrogen bond population correlation functions of different hydrogen bonds for the two conformations of GABA.


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Conformation Induced Dynamical Heterogeneity of Water in

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