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UI ECE 591 - Free Energy Calculation in Biophysics

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Introduction to free energy calculationwhat is free energy?molecular simulationFree energy methodologywhy develop new methods?non-equilibrium unbinding studyApplications for free energy calculationprotein evolutionnanosensor designNMR ensemblesIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationMethods and applications for free energycalculation in biophysicsF. Marty YtrebergUniversity of IdahoDepartment of PhysicsF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhat is free energy?molecular simulationFree energy introductionDefinition of free energy G = H − T SH is enthalpy, S is entropyQ: In which well will the particle spend most of the time?A: The well with lowest free energy G.F. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhat is free energy?molecular simulationFree energy introductionDefinition of free energy G = H − T SH is enthalpy, S is entropyQ: In which well will the particle spend most of the time?A: The well with lowest free energy G.F. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhat is free energy?molecular simulationFree energy introductionI∆G gives most likely stateIBetter yet gives relative probability e−β∆GA→B= PB/PA1-D systemProtein systemA BF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhat is free energy?molecular simulationMolecular simulation exampleAtoms are treated classicallyIThis small protein-ligand system with water contains ≈15,000 atomsIAbout 1 ns/day on a single year-old processorF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhat is free energy?molecular simulationMolecular dynamics1. Compute acceleration for each atom viaP~F = m~a2. Determine new positions ~x and velocities ~v consistent with ~a3. Increment time by a small amount; repeat from step 1F. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhat is free energy?molecular simulationYtreberg computer clusterI23 compute nodes, 1 head nodeIDual quad-core Xeon processorsI8 GB memoryI2 TB storage RAID 6IInfiniband interconnectsIRocks/CentOSF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhy develop new methods?non-equilibrium unbinding studyReason for developing new free energy approachesDifficulties:IAccurate binding affinity ∆Gbindcalculation is difficultIErrors in forcefields and implementationIInsufficient samplingICurrent methods are too slow for applications such as drug designF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhy develop new methods?non-equilibrium unbinding studyReason for developing new free energy approachesDifficulties:IAccurate binding affinity ∆Gbindcalculation is difficultIErrors in forcefields and implementationIInsufficient samplingICurrent methods are too slow for applications such as drug designF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhy develop new methods?non-equilibrium unbinding studyNon-equilibrium unbinding simulationsIJoin center of mass of protein and ligand by a springIExtend spring at constant speed to force ligand out of pocketIKeep ligand restrained to binding axis relative to protein†(mustcorrect for this restraint)†Woo H-J, Roux B, Proc Natl Acad Sci USA 102:6825 (2005)F. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhy develop new methods?non-equilibrium unbinding studyMathematical formulation for ∆Gbindestimation“The power of multiplying by 1”e−β∆Gbind=1V0Rbdd~x e−βURfrd~x δ(~r − ~r∗) e−βU=1V0Rbdd~x e−βURfrd~x δ(~r − ~r∗) e−βU×Rbdd~x e−β(U+Ua)Rbdd~x e−β(U+Ua)×Rfrd~x δ(~r − ~r∗) e−β(U+Ua)Rfrd~x δ(~r − ~r∗) e−β(U+Ua)=Rbdd~x e−βURbdd~x e−β(U+Ua)×1V0Rbdd~x e−β(U+Ua)Rfrd~x δ(~r − ~r∗) e−β(U+Ua)×Rfrd~x δ(~r − ~r∗) e−β(U+Ua)Rfrd~x δ(~r − ~r∗) e−βU≡ I1× I2× I3I1: restrain ligand with axial restraint when in the binding pocketI2: pull ligand out of pocket with restraint presentI3: release ligand from restraint when far away from proteinF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationwhy develop new methods?non-equilibrium unbinding studyFKBP-DMSO: Non-equilibrium unbinding results†Experiment: -9.7‡Speed (nm/ps) N pulls ∆Gbind1.0e-4 25 -12.2 ± 1.32.0e-4 50 -10.9 ± 3.63.0e-4 100 -8.8 ± 3.44.0e-4 200 -11.0 ± 0.9(All energy units are kJ/mol)‡Burkhard P, Taylor P, Walkinshaw MD, J Mol Biol 295:953 (2000)†FMY, J Chem Phys 130:164906 (2009)F. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free energy calculationFree energy methodologyApplications for free energy calculationprotein evolutionnanosensor designNMR ensemblesProtein evolution in virusesIViruses have high mutation rates allowing them to quickly adapt tonew host and develop vaccine resistanceIUnderstanding viral evolution is important to predicting, preventingand responding to epidemicsILittle is known about underlying biophysical mechanisms for proteinevolution in virusesF. Marty Ytreberg Methods and applications for free energy calculation in biophysicsIntroduction to free


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UI ECE 591 - Free Energy Calculation in Biophysics

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