Parameterization of OPLS–AA Force Field for the Conformational

Total Page:16

File Type:pdf, Size:1020Kb

Parameterization of OPLS–AA Force Field for the Conformational ParameterizationofOPLS–AAForceFieldforthe ConformationalAnalysisofMacrocyclicPolyketides KALJUKAHN,THOMASC.BRUICE DepartmentofChemistryandBiochemistry,UniversityofCalifornia,SantaBarbara, SantaBarbara,California93106 Received27February2001;Accepted16November2001 Publishedonline00Month2002inWileyInterScience(www.interscience.wiley.com).DOI10.1002/jcc.10051 Abstract:TheparametersfortheOPLS–AApotentialenergyfunctionhavebeenextendedtoincludesomefunctional groupsthatarepresentinmacrocyclicpolyketides.ExistingOPLS–AAtorsionalparametersforalkanes,alcohols, ethers,hemiacetals,esters,andketoamideswereimprovedbasedonMP2/aug-cc-pVTZandMP2/aug-cc-pVDZ calculations.Nonbondedparametersforthesp3 carbonandoxygenatomswererefinedusingMonteCarlosimulations ofbulkliquids.Theresultingforcefieldpredictsconformerenergiesandtorsionalbarriersofalkanes,alcohols,ethers, andhemiacetalswithanoverallRMSdeviationof0.40kcal/molascomparedtoreferencedata.Densitiesof19bulk liquidsarepredictedwithanaverageerrorof1.1%,andheatsofvaporizationarereproducedwithin2.4%of experimentalvalues.Theforcefieldwasusedtoperformconformationalanalysisofsmalleranalogsofthemacrocyclic polyketidedrugFK506.Structuresthatadoptedlow-energyconformationssimilartothatofboundFK506were identified.Theresultsshowthatalinkeroffourketideunitsconstitutestheshortesteffectordomainthatallowsbinding oftheketidedrugstoFKBPproteins.Itisproposedthattheexactchemicalmakeupoftheeffectordomainhaslittle influenceontheconformationalpreferenceoftetraketides. ©2002WileyPeriodicals,Inc. JComputChem23:977–996,2002 Keywords:forcefielddevelopment;conformationalanalysis;neuroregenerativepolyketides Introduction ofcalcineurin,leadstosuppressionoftheimmunesystem.10 Thisis thebasisforcurrentimmunosuppressivetherapyusingFK506(also Polyketidesformastructurallydiverseclassofnaturalproducts knownasTacrolitmus).However,long-termsuppressionoftheim- whosebiosynthesistakesplacethroughthesuccessivecondensa- munesystemisundesirablewhiletreatingnerveinjury. 1–3 tionofsimplecarboxylicacids. Despitetheirwidelyvarying Weareinterestedinfindingpolyketidestructuresthatshow sizeandstructure,polyketidescanbegroupedintotwosuperfami- highaffinitytowardsFKBP52butdonotinteractwithcalcineurin. 2 lies:thearomaticandthecomplexpolyketides. Someexamplesof BindingstudieswithanalogsofFK506andavailablecrystal aromaticpolyketidesinclude6-methylsalicylicacidandtetracy- structuresofFKBP12⅐FK506⅐calcineurincomplexesrevealthat clines,whileerythromycinsbelongtothesuperfamilyofcomplex polyketidescanbeconsideredasbuiltfromthe“bindingdomain” polyketides.Manypolyketidesarepharmacologicallyactiveor thatinteractswithFKBP12,the“effectordomain”thatinteracts possessusefulagriculturalproperties.Itisthoughtthatthebiolog- withcalcineurin(shownboxedinChart1),andthecyclohexylarm icalactivityofcomplexpolyketidesisdependentonconforma- thatinteractsweaklywithbothproteins.10,11 Thestructureofthe tionalpreorganization,whichdirectsfunctionalgroupsinspace binaryFK506⅐FKBP12complexrevealsthatthepipecolinylester andreducestheentropicpenaltyinvolvedinbinding.4 moietyandthe ␣-ketoamide portion of the binding domain make Somecomplexmacrocyclicpolyketides,suchasFK506(Chart 1)anditsanalogs,arepromisingneuroregenerativeagents.5,6 Theirmechanismofactioncurrentlyispoorlyunderstood,but strongevidencesuggeststhatinteractionofapolyketidedrugwith Correspondenceto:T.C.Bruice;e-mail:[email protected] thecellularproteinFKBP52isrequiredforaccelerationofnerve Contract/grantsponsor:ChristopherReeveParalysisFoundation;contract/ cellgrowth.7 Asignificantprobleminusingpolyketidedrugsfor grantnumber:BA1-9904-2 treatmentofnerveinjuryisthatothercellularproteinsalsointeract Contract/grantsponsor:UniversityofMissouri-Columbia(K.K.) withthesemolecules.Theinteractionofapolyketidewithother Thisarticleincludessupplementarymaterialavailablefromtheauthorupon proteinscouldleadtounwantedsideeffects.Onewell-character- requestorviatheInternetatftp.wiley.com/public/journals/jcc/suppmat/ 8,9 izedtargetforFK506anditsanalogsistheproteinFKBP12. 23/977orhttp://www.interscience.wiley.com/jpages/0192-8651/suppmat/v23. TheinteractionofFK506withFKBP12,andthesubsequentbinding 977.html ©2002WileyPeriodicals,Inc. 978 Kahn and Bruice • Vol. 23, No. 10 • Journal of Computational Chemistry are similar and residues forming the binding pocket are highly conserved.18 The second approach consists of a design of mole- cules that would bind both FKBP52 and FKBP12 but have a modified effector domain rendering them unable to bind cal- cineurin. We assume, in the framework of this approach, that the binding modes of FK506 to the proteins FKBP12 and FKBP52 are similar. In this case, the problem reduces to finding polyketide structures that have low energy conformations with the binding domain maximally similar to the binding domain of the bound FK506. The viability of this approach has been demonstrated by evaluating the conformational energies of rapamycin analogs using the MM3 force field.19 In their work, Adalsteinsson and Bruice19 first performed a conformational search of three molecules (tem- plates) corresponding to the unsubstituted triketide, tetraketide, and pentaketide, respectively. Next, they calculated single point potential energies for a large number of substituted templates and Chart 1 identified structures that have low energy conformers similar to the conformation of the bound FK506. We now report an extension of this approach that allows a rapid conformational search with numerous favorable interactions with the FKBP12 protein.11,12 complete minimization of realistic polyketides as opposed to ide- The effector domain is not necessary for the polyketide to interact alized templates. with FKBP52, and various compounds lacking this linker region Computer modeling of biomolecular systems and large organic have been suggested as possible neuroregenerative drugs.13–15 One molecules is currently dominated by molecular mechanics calcu- shortcoming of drug candidates considered so far is that they can lations due to the advantage in speed. Several high quality force adopt a multitude of conformations, of which many are not com- fields, such as AMBER,20,21 CFF,22,23 CHARMM,24,25 COM- plementary with the binding site of FKBP52. In addition, many PASS,26 GROMOS,27 SPASIBA,28 MM3,29 MM4,30 OPLS– acyclic ligands bind to FKBP12 with a conformation that mini- AA,31 and MMFF9432,33 have been developed and are commonly mizes the amount of exposed hydrophobic surface area, a phenom- used for elucidating structures and properties of molecules in gas, enon called hydrophobic collapse.11 As a result, most acyclic liquid, and crystal phases. Currently, each force field has signifi- analogs show lower affinity towards FKBP12 than FK506 does.11 cant strength in the area where it was specifically parameterized, Also, the acyclic analogs of FK506 may require complicated that is, MMFF94 performs well for predicting the structures and organic synthesis. relative conformational energies of a wide range of organic mol- Studies with macrocyclic analogs of FK506 have shown that ecules while the OPLS–AA potential is well suited for describing many modifications in the effector domain abolish the interaction intermolecular interactions.32,34 Because we are also interested in with calcineurin while retaining a submicromolar affinity toward accurately predicting relative binding free energies of polyketides FKBP12. The comparison with FK506, which has a dissociation to target proteins via simulation methods, we chose the OPLS–AA constant of 0.4 nM from FKBP12,16 shows that further improve- force field for the conformational analysis. This force field has ment of the binding affinity should be possible. The macrocyclic been developed in the laboratory of William L. Jorgensen over the polyketides are especially promising candidates for neuroregen- course of several years and has been described in detail.31 In short, erative drugs because recent advances in identification and cloning the energy of a molecular system is derived as the sum of bond of polyketide synthase genes make it possible to produce such stretching, bond bending, torsional, and nonbonded terms. The polyketides via engineered biosynthesis.3 Such an approach prom- bond stretching and bending parameters come mostly from Wein- ises economic production of highly pure polyketides with the er’s 1986 AMBER force field,20 with the exception of alkane desired structure. In summary, the design goal for a neuroregen- parameters that have been adopted from CHARMM. The atomic erative drug is a compound that shows high affinity towards charges and Lennard–Jones parameters have been fitted to repro- FKBP52, does not interact with calcineurin, has a favorable solu- duce the densities, heats of vaporization, and free energies of bility profile, and can be synthesized economically via engineered hydration of a wide range of organic compounds.31,35–37 In some biosynthesis. instances, fitting to electrostatic potential has been used to assign In this article we have investigated which macrocyclic atomic charges.38 Also, ab initio calculations of intermolecular polyketide structures would bind strongly to FKBP52 but not energies of dimers or molecular hydrates in the gas phase have interact with calcineurin. In principle, at least two approaches are been used for determination of nonbonded parameters.35,38 Most possible for designing such compounds. In the first approach, one torsional parameters in the OPLS–AA force field were derived could try to design molecules that bind strongly to FKBP52 and do based on HF/6-31G* calculations
Recommended publications
  • Development of an Advanced Force Field for Water Using Variational Energy Decomposition Analysis Arxiv:1905.07816V3 [Physics.Ch
    Development of an Advanced Force Field for Water using Variational Energy Decomposition Analysis Akshaya K. Das,y Lars Urban,y Itai Leven,y Matthias Loipersberger,y Abdulrahman Aldossary,y Martin Head-Gordon,y and Teresa Head-Gordon∗,z y Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley CA 94720 z Pitzer Center for Theoretical Chemistry, Departments of Chemistry, Bioengineering, Chemical and Biomolecular Engineering, University of California, Berkeley CA 94720 E-mail: [email protected] Abstract Given the piecewise approach to modeling intermolecular interactions for force fields, they can be difficult to parameterize since they are fit to data like total en- ergies that only indirectly connect to their separable functional forms. Furthermore, by neglecting certain types of molecular interactions such as charge penetration and charge transfer, most classical force fields must rely on, but do not always demon- arXiv:1905.07816v3 [physics.chem-ph] 27 Jul 2019 strate, how cancellation of errors occurs among the remaining molecular interactions accounted for such as exchange repulsion, electrostatics, and polarization. In this work we present the first generation of the (many-body) MB-UCB force field that explicitly accounts for the decomposed molecular interactions commensurate with a variational energy decomposition analysis, including charge transfer, with force field design choices 1 that reduce the computational expense of the MB-UCB potential while remaining accu- rate. We optimize parameters using only single water molecule and water cluster data up through pentamers, with no fitting to condensed phase data, and we demonstrate that high accuracy is maintained when the force field is subsequently validated against conformational energies of larger water cluster data sets, radial distribution functions of the liquid phase, and the temperature dependence of thermodynamic and transport water properties.
    [Show full text]
  • Simple Models for the Quick Estimation of Ground State Hydrogen Tunneling Splittings in Alcohols Cite This: Phys
    PCCP View Article Online PAPER View Journal | View Issue Simple models for the quick estimation of ground state hydrogen tunneling splittings in alcohols Cite this: Phys. Chem. Chem. Phys., 2021, 23, 17591 and other compounds† Robert Medel Models for the quick estimation of energy splittings caused by coherent tunneling of hydrogen atoms are evaluated with available experimental data for alcohols and improvements are proposed. The discussed models are mathematically simple and require only results from routine quantum chemical computations, i.e. hybrid DFT calculation of the equilibrium geometry and the transition state within the harmonic approximation. A benchmark of experimental splittings spanning four orders of magnitude for 27 alcohol species is captured by three evaluated models with a mean symmetric deviation factor of 1.7, 1.5 and 1.4, respectively, i.e. the calculated values deviate on average by this factor in either direction. Limitations of the models are explored with alcohols featuring uncommon Creative Commons Attribution 3.0 Unported Licence. properties, such as an inverted conformational energy sequence, a very light molecular frame, an elevated torsional frequency, or a coupling with a second internal degree of freedom. If the splitting of either the protiated or deuterated form of an alcohol is already experimentally determined, the one of the second isotopolog can be estimated by three additional models with a mean symmetric deviation factor of 1.14, 1.19 and 1.15, respectively. It is shown that this can be achieved with a novel approach without any quantum chemical calculation by directly correlating experimental splittings of isotopologs across related species.
    [Show full text]
  • FORCE FIELDS for PROTEIN SIMULATIONS by JAY W. PONDER
    FORCE FIELDS FOR PROTEIN SIMULATIONS By JAY W. PONDER* AND DAVIDA. CASEt *Department of Biochemistry and Molecular Biophysics, Washington University School of Medicine, 51. Louis, Missouri 63110, and tDepartment of Molecular Biology, The Scripps Research Institute, La Jolla, California 92037 I. Introduction. ...... .... ... .. ... .... .. .. ........ .. .... .... ........ ........ ..... .... 27 II. Protein Force Fields, 1980 to the Present.............................................. 30 A. The Am.ber Force Fields.............................................................. 30 B. The CHARMM Force Fields ..., ......... 35 C. The OPLS Force Fields............................................................... 38 D. Other Protein Force Fields ....... 39 E. Comparisons Am.ong Protein Force Fields ,... 41 III. Beyond Fixed Atomic Point-Charge Electrostatics.................................... 45 A. Limitations of Fixed Atomic Point-Charges ........ 46 B. Flexible Models for Static Charge Distributions.................................. 48 C. Including Environmental Effects via Polarization................................ 50 D. Consistent Treatment of Electrostatics............................................. 52 E. Current Status of Polarizable Force Fields........................................ 57 IV. Modeling the Solvent Environment .... 62 A. Explicit Water Models ....... 62 B. Continuum Solvent Models.......................................................... 64 C. Molecular Dynamics Simulations with the Generalized Born Model........
    [Show full text]
  • Force Fields for MD Simulations
    Force Fields for MD simulations • Topology/parameter files • Where do the numbers an MD code uses come from? • How to make topology files for ligands, cofactors, special amino acids, … • How to obtain/develop missing parameters. • QM and QM/MM force fields/potential energy descriptions used for molecular simulations. The Potential Energy Function Ubond = oscillations about the equilibrium bond length Uangle = oscillations of 3 atoms about an equilibrium bond angle Udihedral = torsional rotation of 4 atoms about a central bond Unonbond = non-bonded energy terms (electrostatics and Lenard-Jones) Energy Terms Described in the CHARMm Force Field Bond Angle Dihedral Improper Classical Molecular Dynamics r(t +!t) = r(t) + v(t)!t v(t +!t) = v(t) + a(t)!t a(t) = F(t)/ m d F = ! U (r) dr Classical Molecular Dynamics 12 6 &, R ) , R ) # U (r) = . $* min,ij ' - 2* min,ij ' ! 1 qiq j ij * ' * ' U (r) = $ rij rij ! %+ ( + ( " 4!"0 rij Coulomb interaction van der Waals interaction Classical Molecular Dynamics Classical Molecular Dynamics Bond definitions, atom types, atom names, parameters, …. What is a Force Field? In molecular dynamics a molecule is described as a series of charged points (atoms) linked by springs (bonds). To describe the time evolution of bond lengths, bond angles and torsions, also the non-bonding van der Waals and elecrostatic interactions between atoms, one uses a force field. The force field is a collection of equations and associated constants designed to reproduce molecular geometry and selected properties of tested structures. Energy Functions Ubond = oscillations about the equilibrium bond length Uangle = oscillations of 3 atoms about an equilibrium bond angle Udihedral = torsional rotation of 4 atoms about a central bond Unonbond = non-bonded energy terms (electrostatics and Lenard-Jones) Parameter optimization of the CHARMM Force Field Based on the protocol established by Alexander D.
    [Show full text]
  • Standard Methods for the Examination of Water and Wastewater
    Standard Methods for the Examination of Water and Wastewater Part 1000 INTRODUCTION 1010 INTRODUCTION 1010 A. Scope and Application of Methods The procedures described in these standards are intended for the examination of waters of a wide range of quality, including water suitable for domestic or industrial supplies, surface water, ground water, cooling or circulating water, boiler water, boiler feed water, treated and untreated municipal or industrial wastewater, and saline water. The unity of the fields of water supply, receiving water quality, and wastewater treatment and disposal is recognized by presenting methods of analysis for each constituent in a single section for all types of waters. An effort has been made to present methods that apply generally. Where alternative methods are necessary for samples of different composition, the basis for selecting the most appropriate method is presented as clearly as possible. However, samples with extreme concentrations or otherwise unusual compositions or characteristics may present difficulties that preclude the direct use of these methods. Hence, some modification of a procedure may be necessary in specific instances. Whenever a procedure is modified, the analyst should state plainly the nature of modification in the report of results. Certain procedures are intended for use with sludges and sediments. Here again, the effort has been to present methods of the widest possible application, but when chemical sludges or slurries or other samples of highly unusual composition are encountered, the methods of this manual may require modification or may be inappropriate. Most of the methods included here have been endorsed by regulatory agencies. Procedural modification without formal approval may be unacceptable to a regulatory body.
    [Show full text]
  • FORCE FIELDS and CRYSTAL STRUCTURE PREDICTION Contents
    FORCE FIELDS AND CRYSTAL STRUCTURE PREDICTION Bouke P. van Eijck ([email protected]) Utrecht University (Retired) Department of Crystal and Structural Chemistry Padualaan 8, 3584 CH Utrecht, The Netherlands Originally written in 2003 Update blind tests 2017 Contents 1 Introduction 2 2 Lattice Energy 2 2.1 Polarcrystals .............................. 4 2.2 ConvergenceAcceleration . 5 2.3 EnergyMinimization .......................... 6 3 Temperature effects 8 3.1 LatticeVibrations............................ 8 4 Prediction of Crystal Structures 9 4.1 Stage1:generationofpossiblestructures . .... 9 4.2 Stage2:selectionoftherightstructure(s) . ..... 11 4.3 Blindtests................................ 14 4.4 Beyondempiricalforcefields. 15 4.5 Conclusions............................... 17 4.6 Update2017............................... 17 1 1 Introduction Everybody who looks at a crystal structure marvels how Nature finds a way to pack complex molecules into space-filling patterns. The question arises: can we understand such packings without doing experiments? This is a great challenge to theoretical chemistry. Most work in this direction uses the concept of a force field. This is just the po- tential energy of a collection of atoms as a function of their coordinates. In principle, this energy can be calculated by quantumchemical methods for a free molecule; even for an entire crystal computations are beginning to be feasible. But for nearly all work a parameterized functional form for the energy is necessary. An ab initio force field is derived from the abovementioned calculations on small model systems, which can hopefully be generalized to other related substances. This is a relatively new devel- opment, and most force fields are empirical: they have been developed to reproduce observed properties as well as possible. There exists a number of more or less time- honored force fields: MM3, CHARMM, AMBER, GROMOS, OPLS, DREIDING..
    [Show full text]
  • Dynamics of Ions in a Water Drop Using the AMOEBA Polarizable Force Field Florian Thaunay, Gilles Ohanessian, Carine Clavaguera
    Dynamics of ions in a water drop using the AMOEBA polarizable force field Florian Thaunay, Gilles Ohanessian, Carine Clavaguera To cite this version: Florian Thaunay, Gilles Ohanessian, Carine Clavaguera. Dynamics of ions in a water drop using the AMOEBA polarizable force field. Chemical Physics Letters, Elsevier, 2017, 671, pp.131-137. 10.1016/j.cplett.2017.01.024. hal-01999944 HAL Id: hal-01999944 https://hal.archives-ouvertes.fr/hal-01999944 Submitted on 5 Feb 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Chemical Physics Letters 671 (2017) 131–137 Contents lists available at ScienceDirect Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett Research paper Dynamics of ions in a water drop using the AMOEBA polarizable force field ⇑ Florian Thaunay, Gilles Ohanessian, Carine Clavaguéra LCM, CNRS, Ecole Polytechnique, Université Paris Saclay, 91128 Palaiseau, France article info abstract Article history: Various ions carrying a charge from À2 to +3 were confined in a drop of 100 water molecules as a way to Received 13 October 2016 model coordination properties inside the cluster and at the interface. The behavior of the ions has been In final form 10 January 2017 followed by molecular dynamics with the AMOEBA polarizable force field.
    [Show full text]
  • Electronic Supplementary Information CHARMM All Atom Force Field
    Electronic Supplementary Information CHARMM all atom force field employs a Lennard-Jones (6-12) function to describe Van der Waals interactions. This potential is a combination of attractive and repulsive contributions. The repulsive term describes internuclear electrostatic repulsion and short-range repulsive forces (or exchange forces) between electrons with the same spin. The attractive term is due to dispersion forces, which in turn are due to instantaneous dipoles arising during the fluctuations in the electron clouds. The form of the potential energy function of two interacting atoms is: 12 6 éæs ö æs ö ù VvdW = 4e êç ÷ - ç ÷ ú ëêè r ø è r ø ûú Where r is the distance between the two atoms, s is the collision diameter (the distance at the zero energy) and e is the Lennard-Jones well depth. For a q atom and a c atom, these empirical parameters are expressed from the Lorentz-Berthelot mixing rules: 1 s = (s +s ) qc 2 qq cc e qc = e qqe cc Van der Waals interactions are also important to well describe the interaction between QM and MM regions in hybrid QM/MM enzyme simulation. The Van der Waals parameters relative to the QM atoms of the FAAH-oleamide complex, applied in all the simulations performed, are reported in the table below. These are consistent to those reported in the combined parameter file (CHARMM22 for protein, CHARMM27 for lipid) par_all27_prot_lipid.prm. For further details see www.charmm.org PRIVILEGED DOCUMENT FOR REVIEW PURPOSES ONLY ATOM NAME ATOM TYPE e (kcal mole-1) s (Å) Notes O1 O -0.120000 1.700000 Oleamide
    [Show full text]
  • Surface Science 652 (2016) 26 –32
    Surface Science 652 (2016) 26 –32 Contents lists available at ScienceDirect Surface Science journal homepage: www.elsevier.com/locate/susc The role of low-energy ( ≤20 eV) electrons in astrochemistry Michael C. Boyer a,NathalieRivas b,AudreyA.Tran b, Clarissa A. Verish b, Christopher R. Arumainayagam b,⁎ aDepartment of Physics, Clark University, Worcester, MA 01610, United States bDepartment of Chemistry, Wellesley College, Wellesley, MA 02481, United States article info abstract Article history: UV photon-driven condensed phase cosmic ice reactions have been the main focus in understanding the extra- Received 7 January 2016 terrestrial synthesis of complex organic molecules. Low-energy ( ≤20 eV) electron-induced reactions, on the Received in revised form 2 March 2016 other hand, have been largely ignored. In this article, we review studies employing surface science techniques Accepted 8 March 2016 to study low-energy electron-induced condensed phase reactions relevant to astrochemistry. In particular, we Available online 12 March 2016 show that low-energy electron irradiation of methanol ices leads to the synthesis of many of the same complex Keywords: molecules formed through UV irradiation. Moreover, our results are qualitatively consistent with the hypothesis Astrochemistry that high-energy condensed phase radiolysis is mediated by low-energy electron-induced reactions. In addition, Low-energy electrons due to the numbers of available low-energy secondary electrons resulting from the interaction of high-energy Temperature programmed desorption radiation with matter as well as differences between electron- and photon-induced processes, low-energy Infrared re flection absorption spectroscopy electron-induced reactions are perhaps as, or even more, effective than photon-induced reactions in initiating Cosmic ices condensed-phase chemical reactions in the interstellar medium.
    [Show full text]
  • Computation of Free Energy
    Helvetica Chimica Acta ± Vol. 85 (2002) 3113 Computation of Free Energy by Wilfred F. van Gunsteren*a), Xavier Daurab), and Alan E. Markc) a) Laboratory of Physical Chemistry, Swiss Federal Institute of Technology Zurich, ETH-Hˆnggerberg, CH-8093 Zurich (e-mail: [email protected]) b) Institucio¬ Catalana de Recerca i Estudis AvanÁats (ICREA) and Institut of Biotechnologia i de Biomedicina, Universitat Auto¡noma de Barcelona, E-08193 Bellaterra c) Department of Biophysical Chemistry, University of Groningen, NL-9747 AG Groningen Dedicated to Professor Dieter Seebach on the occasion of his 65th birthday Many quantities that are standardly used to characterize a chemical system are related to free-energy differences between particular states of the system. By statistical mechanics, free-energy differences may be expressed in terms of averages over ensembles of atomic configurations for the molecular system of interest. Here, we review the most useful formulae to calculate free-energy differences from ensembles generated by molecular simulation, illustrate a number of recent developments, and highlight practical aspects of such calculations with examples selected from the literature. 1. Introduction. ± The probability of finding a molecular system in one state or the other is determined by the difference in free energy between those two states. As a consequence, free-energy differences may be directly related to a wide range of fundamental chemical quantities such as binding constants, solubilities, partition coefficients, and adsorption coefficients. By means of statistical mechanics, free-energy differences may also be expressed in terms of averages over ensembles of atomic configurations for the molecular system of interest.
    [Show full text]
  • Behavior of Gas Reveals the Existence of Antigravity Gaseous Nature More Precisely Described by Gravity-Antigravity Forces
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 29 January 2020 Article Behavior of gas reveals the existence of antigravity Gaseous nature more precisely described by gravity-antigravity forces Chithra K. G. Piyadasa* Electrical and Computer engineering, University of Manitoba, 75, Chancellors Circle, Winnipeg, MB, R3T 5V6, Canada. * Correspondence: [email protected]; Tel.: +1 204 583 1156 Abstract: The Author’s research series has revealed the existence in nature, of gravitational repulsion force, i,e., antigravity, which is proportional to the content of thermal energy of the particle. Such existence is in addition to the gravitational attraction force, accepted for several hundred years as proportional to mass. Notwithstanding such long acceptance, gravitational attraction acting on matter has totally been neglected in thermodynamic calculations in derivation of the ideal gas law. Both the antigravity force and the gravitational force have to be accommodated in an authentic elucidation of ideal gas behavior. Based on microscopic behavior of air molecules under varying temperature, this paper presents: firstly, the derivation of the mathematical model of gravitational repulsive force in matter; secondly, mathematical remodeling of the gravitational attractive force in matter. Keywords: gravitational attraction, gravitational repulsion, antigravity, intermolecular forces, specific heat, thermal energy, adiabatic and isothermal expansion. 1. Introduction As any new scientific revelation has a bearing on the accepted existing knowledge, some analysis of the ideal gas law becomes expedient. The introduction discusses the most fundamental concepts relating to the ideal gas law and they are recalled in this introduction with fine detail to show how they contradict the observations made in this discussion.
    [Show full text]
  • Characterizing and Predicting the Antimicrobial Properties of Lignin Derivatives
    University of Kentucky UKnowledge Theses and Dissertations--Biosystems and Agricultural Engineering Biosystems and Agricultural Engineering 2020 CHARACTERIZING AND PREDICTING THE ANTIMICROBIAL PROPERTIES OF LIGNIN DERIVATIVES Ryan Kalinoski University of Kentucky, [email protected] Author ORCID Identifier: https://orcid.org/0000-0001-8774-275X Digital Object Identifier: https://doi.org/10.13023/etd.2020.455 Right click to open a feedback form in a new tab to let us know how this document benefits ou.y Recommended Citation Kalinoski, Ryan, "CHARACTERIZING AND PREDICTING THE ANTIMICROBIAL PROPERTIES OF LIGNIN DERIVATIVES" (2020). Theses and Dissertations--Biosystems and Agricultural Engineering. 76. https://uknowledge.uky.edu/bae_etds/76 This Doctoral Dissertation is brought to you for free and open access by the Biosystems and Agricultural Engineering at UKnowledge. It has been accepted for inclusion in Theses and Dissertations--Biosystems and Agricultural Engineering by an authorized administrator of UKnowledge. For more information, please contact [email protected]. STUDENT AGREEMENT: I represent that my thesis or dissertation and abstract are my original work. Proper attribution has been given to all outside sources. I understand that I am solely responsible for obtaining any needed copyright permissions. I have obtained needed written permission statement(s) from the owner(s) of each third-party copyrighted matter to be included in my work, allowing electronic distribution (if such use is not permitted by the fair use doctrine) which will be submitted to UKnowledge as Additional File. I hereby grant to The University of Kentucky and its agents the irrevocable, non-exclusive, and royalty-free license to archive and make accessible my work in whole or in part in all forms of media, now or hereafter known.
    [Show full text]