Computational study of small molecule binding for both tethered and free conditions
CComputational study of small molecule binding for both tethered and free conditions
F. Marty Ytreberg ∗ Department of Physics, University of Idaho, Moscow, ID 83844-0903 (Dated: October 26, 2018)Using a calix[4]arene-benzene complex as a test system we compare the potential of mean forcefor when the calix[4]arene is tethered versus free. When the complex is in vacuum our results showthat the difference between tethered and free is primarily due to the entropic contribution to thepotential of mean force resulting in a binding free energy difference of 6.5 kJ/mol. By contrast,when the complex is in water our results suggest that the difference between tethered and free isdue to the enthalpic contribution resulting in a binding free energy difference of 1.6 kJ/mol. Thisstudy elucidates the roles of entropy and enthalpy for this small molecule system and emphasizes thepoint that tethering the receptor has the potential to dramatically impact the binding properties.These findings should be taken into consideration when using calixarene molecules in nanosensordesign.
I. INTRODUCTION
Calixarenes are macrocycles that are of interest dueto the fact that they can be easily synthesized and canbe functionalized to selectively bind neutral or ionic an-alytes; see review refs 1,2,3,4,5. One use for calixarenesthat is of specific interest to the current study is innanosensor design (e.g., refs 6,7,8,9). Calixarenes aretypically used in nanosensors by decorating the nanoma-terial with gold and then tethering the calixarenes to thegold surface. A reasonable question that is also the moti-vation for our study is: How does tethering calixarene toa surface affect the binding properties of the calixareneto analytes? This is an important question consideringthat typically a researcher may only have knowledge ofbinding properties for free (i.e., not tethered) conditions.For the current study we compare the effects of teth-ering a calix[4]arene on the binding properties for bothin vacuum and in water. Note that the “[4]” means thatthere are four aromatic rings in the structure. To ourknowledge there are no previous studies that have deter-mined the affects of such tethering on the binding prop-erties of calixarenes. Thus, we computed the potentialof mean force (PMF) for calix[4]arene-benzene bindingfor four cases: (i) in vacuum with the calix[4]arene teth-ered; (ii) in vacuum with the calix[4]arene free (i.e., nottethered); (iii) in water with the calix[4]arene tethered;and (iv) in water with the calix[4]arene free. Our resultsbelow show that when the complex is in vacuum the dif-ference between tethered and free is due primarily to theentropic contribution to the potential of mean force re-sulting in a binding free energy difference of 6.5 kJ/mol.By contrast, when the complex is in water our resultssuggest that the difference between tethered and free isdue entirely to the enthalpic contribution resulting in abinding free energy difference of 1.6 kJ/mol. ∗ [email protected] II. COMPUTATIONAL METHODS
The initial structure for the calix[4]arene-benzene com-plex was obtained from experimental X-ray crystallogra-phy (personal communication from Pam Shapiro’s lab atUniversity of Idaho). The necessary simulation topolo-gies for both the calix[4]arene and benzene were thengenerated by the PRODRG server . We then modifiedthe partial charges to be consistent with the GROMOS-96 43A1 forcefield , e.g., all CH3 groups were set tozero partial charge. The GROMACS simulation packageversion 3.3.3 was used for all molecular dynamics sim-ulations described below with the default GROMOS-9643A1 forcefield .For the vacuum simulations the calix[4]arene-benzenecomplex was first minimized using steepest decent for1000 steps. For subsequent production simulations allVan der Waals and electrostatic interactions were com-puted, i.e., no cutoffs were used. A timestep of 1.0 fs wasutilized with no constraints. The temperature was main-tained at a constant value using Langevin dynamics with a friction coefficient of 1.0 amu/ps.For the simulations in water the calix[4]arene-benzenecomplex was solvated in a cubic box of SPC water of ap-proximate initial size 4.5 nm a side. The system was thenminimized using steepest decent for 1000 steps. To allowfor some equilibration of the water the system was thensimulated for 100 ps with the positions of all heavy atomsin the complex harmonically restrained with a force con-stant of 1000 kJ/mol/nm . For this equilibration simu-lation the pressure was maintained at 1.0 atm using theBerendsen algorithm . Subsequent production simula-tions were carried out with the volume fixed at the finalvalue from the equilibration. For all water simulationsthe LINCS algorithm was used to constrain hydrogensto their ideal lengths allowing the use of a 2.0 fs timestep.The temperature was maintained at a constant value us-ing Langevin dynamics with a friction coefficient of 1.0amu/ps. Particle mesh Ewald was used for electro-statics with a real-space cutoff of 1.0 nm and a Fourierspacing of 0.1 nm. Van der Waals interactions used acutoff with a smoothing function such that the interac- a r X i v : . [ phy s i c s . b i o - ph ] D ec tions smoothly decayed to zero between 0.75 nm and 0.9nm. Dispersion corrections for the energy and pressurewere utilized .To perform the tethered simulations for both vacuumand in water we harmonically restrained the two sul-fur atoms shown in 1 using a force constant of 10,000kJ/mol/nm . The purpose is to mimic the effect of thecalix[4]arene binding to a gold surface. This harmonicrestraint on the sulfur atoms was not present for the freesimulations. A. Generating PMF estimates
We computed all PMFs using umbrella sampling andweighted histogram analysis (WHAM) . Our techniquefor estimating the PMF using WHAM is described inref 21. Briefly, the GROMACS 3.3.3 software package was modified to provide a harmonic biasing potential U r ( r ) = 0 . k r ( r − r ) which depends only on the centerof mass separation r between the calix[4]arene and thebenzene. For all PMF estimates we used a total of 33windows r = 0 . , . , . , . . . , . , .
00. For the vac-uum system each window was simulated for 32.0 ns; 16.0ns were discarded for equilibration and 16.0 ns were usedfor the WHAM analysis. For the water system each win-dow was simulated for 4.0 ns; 2.0 ns were discarded forequilibration and 2.0 ns were used for the analysis. Forall PMF estimates below the biasing potential U r used aforce constant k r = 3000 kJ/mol/nm and the estimatesinclude the 2 ln( r ) Jacobian correction .Note that for the simulations of the complex in wa-ter the system size prevents the long simulation timesnecessary to obtain converged PMFs without additionalrestraints. Thus, for the water simulations (but not forthe vacuum simulations) we utilized an axial restraintthat keeps the benzene on the binding axis relative tothe calix[4]arene as described in ref 21. Use of this re-straint means that it is not valid to directly comparethe vacuum and water PMFs. However, it is still valid tocompare the tethered and free conditions for water whichis the purpose of this study. B. Estimating entropic and enthalpic contributions
To estimate the entropic contribution to the PMF T ∆ S ( r ) we used the fact that the entropy is related tothe derivative of the PMF ∆ G ( r ) with respect to systemtemperature T (see also refs 23,24), T ∆ S ( r ) = − T (cid:18) ∂ ∆ G ( r, T ) ∂T (cid:19) . (1)This derivative was numerically estimated by computingthe PMF at three temperatures 270 K, 300 K and 330K and then using a three-point finite difference approx-imation. The enthalpic contribution ∆ H ( r ) was then estimated via ∆ H ( r ) = ∆ G ( r ) + T ∆ S ( r ) . (2) C. Uncertainty estimation
The uncertainty for ∆ G , T ∆ S and ∆ H were estimatedby computing the standard error over independent tri-als. For both the tethered and free conditions in vacuum10 independent estimates of the PMF were generated ateach of the three temperatures (i.e., 30 PMF estimatestethered and 30 free). For both the tethered and free con-ditions in water five independent estimates of the PMFwere generated at each of the three temperatures (i.e., 15PMF estimates tethered and 15 free). III. RESULTS AND DISCUSSION
Results for both vacuum and water simulations areshown in 2. The binding free energy differences be-tween tethered and free conditions ∆∆ G bind for vacuumand water were obtained by numerically integrating the∆ G ( r ) curves from r = 0 . r = 1 . r > . r ≈ . r ≈ . r ≈ . G bind = − . FIG. 1: The calix[4]arene-benzene model system used for the current study. The calix[4]arene molecule has a basket shapedbinding pocket and can be functionalized to bind both neutral and ionic analytes. The two sulfur atoms are shown in a largersize and allow the calix[4]arene to be tethered to a gold surface. The difference between the tethered and free simulations in thecurrent study is that these sulfur atoms were harmonically restrained to the position shown in the figure during the tetheredsimulations but were not restrained for the free simulations. This image was generated using VMD .FIG. 2: The calix[4]arene-benzene potential of mean force (black) showing the enthalpic (red) and entropic (green) contribu-tions. Both tethered (dashed line) and free (solid line) conditions are shown. The error bars are the standard error obtainedfrom performing multiple independent simulations. (a) Simulation results in vacuum. Due primarily to the entropic contribu-tion there is a free energy difference of 6.5 kJ/mol between tethered and free conditions. (b) Simulation results in water. Dueprimarily to the enthalpic contribution there is a free energy difference of 1.6 kJ/mol between tethered and free conditions. Results for the calix[4]arene-benzene complex in waterare shown in 2b. The only appreciable difference betweentethered and free conditions is the enthalpic contribu-tion when the PMF plateaus ( r > . r > . r ≈ . r ≈ . G bind = − . IV. CONCLUSION
We have studied the effects of tethering on smallmolecule binding properties using a calix[4]arene-benzenecomplex as a test system. Simulations of the complex invacuum and in water were performed and the potential ofmean force (PMF) curves were computed and comparedfor tethered and free conditions.Our results for the calix[4]arene-benzene complex invacuum show that the primary difference between freeand tethered conditions is the entropic contribution tothe PMF. Thus, in vacuum the free energy of bindingunder tethered conditions is more favorable than freeby ∆∆ G bind = − . G bind = − . Acknowledgements
The author thanks Pam Shapiro and Steven Hungfor providing the experimental structure for thecalix[4]arene-benzene complex, and Conrad Shyu forhelpful discussion. The project described was supportedby Award Numbers P20RR016448 and R21GM083827from the National Institutes of Health. The content issoley the responsibility of the authors and does not nec-essarily represent the official views of the National In-stitutes of Health. The research was also supported byIdaho NSF-EPSCoR, and by IBEST and BANTech atUniversity of Idaho. A. de Namor, R. Cleverley, and M. Zapata-Ormachea,Chem. Rev , 2495 (1998). J. Schatz, Collect. Czech. Chem. C. , 1169 (2004). R. Ludwig, Microchim. Acta , 1 (2005). J. Princy and M. Shobana, Bioinorg. Chem. Appl. ,65815 (2007). S. Sameni, C. Jeunesse, D. Matt, and J. Harrowfield,Chem. Soc. Rev. , 2117 (2009). D. Filenko, T. Gotszalk, Z. Kazantseva, O. Rabinovych,I. Koshets, Y. Shirshov, V. Kalchenko, and I. Rangelow,Sensor. Actuat. B-Chem. , 264 (2005). I. Koshets, Z. Kazantseva, Y. Shirshov, S. Cherenok, andV. Kalchenko, Sensor. Actuat. B-Chem. , 177 (2005). L. Chen, X. He, X. Hu, and H. Xu, Analyst , 1787(1999). F. Dickert and O. Schuster, Microchim. Acta , 55(1995). A. W. Sch¨uttelkopf and D. M. F. van Aalten, Acta Cryst.D , 1355 (2004). W. F. van Gunsteren, S. R. Billeter, A. A. Eising, P. H.H¨unenberger, P. Kr¨uger, A. E. Mark, W. R. P. Scott, andI. G. Tironi,
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