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Utilize Brownian Dynamics simulations to analyze diffusional rates and predict relative rates for protein-protein interactions. The method involves starting trajectories from a b-surface, monitoring reactions, and calculating electrostatic interaction energies between proteins. Additionally, explore the impact of buried area terms on simulation outcomes, allowing for more realistic interaction energies.
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SDA development • Description of sda-4.23 • Description of sda-5a • - Sda for docking
Brownian dynamics simulations Give the diffusional rate k1 (upper estimate for catalytic rate) k1 k-1 k2 k-2 E + S E:S ES E + P Best predictions are for relative rates when post-diffusional step (2) is the same/similar
Brownian Dynamics simulations • start a number of trajectories from b-surface • monitor reaction • - fraction of reactive trajectories • rigid proteins • atomic level description • no overlaps • electrostatic forces • steps ~ 0.5 Å, ~1 ps A B b-surface B c-surface
Brownian dynamics simulation forcefield 110-130 150 1000 300 exclusion check
Boltzmann factor calculations (sdabf) • one protein is fixed • the other - placed on the grid points and rotated randomly • electrostatic interaction energy between the proteins computed • positions with low energy stored • stored conformations clustered
Electrostatic interaction energies Where qki – effective (fit to reproduce its electrostatic potential) charges of protein k, ri=(xi,yi,zi) charge coordinates, - electrostatic potential of protein l computed by solving Poisson-Boltzmann equation numerically
Electrostatic desolvation energies Where qi – charges, xi– charge coordinates, - electrostatic potential computed by solving Poisson-Boltzmann equation numerically
Electrostatic desolvation energy computations 12 charges 1=0 2
Electrostatic desolvation energy computations 2 treatments of the surface of proteins in electrostatics: nmap -molecular surface – interior is inside analytically computed molecular surface, obtained by rolling solvent probe vdw - van der Waals surface – interior is inside Van der Waals surfaces of atoms Solvent probe, any point which can be inside it is a solvent Ds grid factor 1.7 Ds grid factor 4.2
Protein-protein simulation results • Mutation and ionic strength dependence of rates are reproduced by simulations better than the rate differences for different proteins • Association in the case “3hfm” (HyHEL-10:HEL) is far from diffusional control • Formation of 2 contacts at 6 A separation should be required in order to association to occur
Buried area Elcock & McCammon, Biophys.J. (2001) 80, 613 ~ 25 cal/mole/Å2
Buried area/sda5 • Using buried area term makes BD simulations: • better • more realistic interaction energy description • worse • because flexibility should now to be taken into account, but it is not • longer : • Plastocyanin-cytf case – factor of 100, when typical sda4 encounter times are ~ 10 ns, sda5 encounter times are ~ 1000 ns ~ experimental complex lifetime • Longer living complexes will be even more longer to simulate (barnase-barstar with =13 cal/mole/Å2 ~ 1 min per run, estimated for =25 cal/mole/Å2 ~ 1 min *106 per run)
Buried area/sda5 • Using buried area term makes BF sampling: • better • more realistic interaction energy description • worse • because flexibility should now to be taken into account, but it is not • longer : • not significantly, but BF samplings are long anyway
Buried area/sda5 • Some expectations (?) • If electrostatic desolvation is used, then buried area = hydrophobic desolvation should be used too • Using buried area term in docking will give realistic energy values, but not good docked complexes • Using buried area term in BD simulations should give more realistic encounter times, but worse quantitative estimates for rate constants
E12= Ecoul + Edes + Ehyd E12= Ecoul + Edes E12= Ecoul
Docking using restraints • SDABFCW - previous version of sampling program SDABF which compute energies only when restraints are satisfied and writes sorted low-energy complexes • SDA5DOCK - new version of SDABF, which computes buried area as a sum of accessible areas of atoms of the protein 2 which lay on the skin of the protein 1 . The main results here are that applying restraints (constraints) is very efficient in reducing sampling time.
Docking using restraints • SDAW - Brownian dynamics simulations with the possibility of writing low-energy complexes, which satisfy pre-defined restraints. (There are no forces resulted from restraints, restraints are only used in deciding if the complex should be stored.) • This method can be much faster than systematic search of low energy complexes, when comparable sampling accuracy is achieved. For example, in case of www-domain/peptide case: systematic sampling with 1.5 A sampling grid spacing takes ~ 4 hours, while sdaw simulations (giving even lower energy complexes) ~ 20 min. Sampling accuracy of BD is also much better - sqrt(6Dt)~0.3 A. However, docking by sdaw has obviously different meaning than systematic sampling. • Apparent drawback is that many complexes are stored which are very similar. Realistic is to write out 1000 complexes for further analysis, but the number of low-energy conformations found during BD is much larger. Therefore, it might be necessary to add some clustering during BD simulations in order to not write similar complexes. • Restraints can be applied in atom-based fashion. One test was done with ww-domain/peptide docking case, when CG_TRP_38 was restricted to be within 5A to any heavy atom of the peptide. This requires 540 reaction pairs to be checked. The same simulation was done when CB_TRP_38 was restricted to be within 8 A to any CB of the peptide, which requires 7 pairs to be checked. The simulations with 540 pairs (77 times more than 7) took only 6 times more computing time.
Docking using restraints • SDAWB - Brownian dynamics simulations with the possibility of biasing dynamics by pre-defined restraints and writing low-energy complexes, satisfying pre-defined restraints. The difference here is that the dynamics is biased by applying Metropolis procedure favourng the motions resulting in better satisfaction of restraints. Biasing is done along the 1-contact (any one of defined pairs) distance restraint with piecewise linear function constant at large and small contact distances and changing linearly inbetween. • The performance of the algorithm is not very well tested. It should have some advantages compared to SDAW, but its performance probably depends on the parameters of the biasing function.
