Dynamics of Protein Molecules: Modeling and Applications * 07/16/96 Dynamics of Protein Molecules: Modeling and Applications Huan-Xiang Zhou Physics/CSIT/IMB 11/27/2018 *

* 07/16/96 *

midvi/dt = Fi = -iU({ri}) * 07/16/96 Model I: General Each atom is modeled as a mass point, with mass mi, position ri, and velocity vi. The atoms interaction with each other, with a potential energy U({ri}). Motion of each atom is governed by Newton’s equation: midvi/dt = Fi = -iU({ri}) *

Model II: Harmonic Oscillator * 07/16/96 Model II: Harmonic Oscillator Molecule with two atoms, at r1 and r2. Interact with a potential U(r) = ½kr2, where r = |r1 - r2|. Only non-trivial motion is along r, mdv/dt = F = -kr *

* 07/16/96 r U t r r = Asin(wt) w2 = k/m *

Energy and Temperature * 07/16/96 Energy and Temperature Potential energy: U = ½kr2 = ½kA2sin2(wt). Kinetic energy: K = ½mv2 = ½mw2A2cos2(wt) = ½kA2cos2(wt). Total energy E = K + U = ½kA2. <K> = ¼kA2 = ½kBT, E = ½ kA2 = kBT. The amplitude of oscillation is determined by the temperature. *

Model III: Ethane Construct an energy function: Bonded terms: * 07/16/96 Model III: Ethane Construct an energy function: Bonded terms: ½∑kb(b- b0)2 + ½∑kq(q- q0)2 Torsion terms: ½∑Vf[1+cos(nf-d)] Nonbonded interactions: ∑(A/r12-B/r6) + ∑C/r f *

* 07/16/96 ½Vf[1+cos(3f)] *

* 07/16/96 Model III: Ethane Molecular dynamics: if position is x0 and velocity is v0 at time t, what will position and velocity be a short internal Dt later? Position at time t+dt can be expanded: x(t+Dt) = x0 + (dx/dt)Dt + ½(d2x/dt2)Dt2 = x0 + v0Dt + ½(F/m)Dt2 Solvent is an integral part of the system. *

Applications Functional dynamics – AchE Protein folding – Trp cage Zhou et al. (1998), Proc. Natl. Acad. Sci. USA 95, 9280-9283. Protein folding – Trp cage Simmerling et al. (2002), J. Am. Chem. Soc. 124, 11258-11259. Snow et al. (2002), J. Am. Chem. Soc. 124, 14548-14549. Chowdhury et al. (2003), J. Mol. Biol. 327, 711-717. Protein-protein interactions – Src kinases Young et al. (2001), Cell 105, 115-126.

Applications Functional dynamics – AchE Protein folding – Trp cage Zhou et al. (1998), Proc. Natl. Acad. Sci. USA 95, 9280-9283. Protein folding – Trp cage Simmerling et al. (2002), J. Am. Chem. Soc. 124, 11258-11259. Snow et al. (2002), J. Am. Chem. Soc. 124, 14548-14549. Chowdhury et al. (2003), J. Mol. Biol. 327, 711-717. Protein-protein interactions – Src kinases Young et al. (2001), Cell 105, 115-126.

Acetylcholinesterase breaks acetylcholine and allows for rapid transmission of neural signals

Transimission of Neural Signals Ach as a neural transmitter was first discovered by Otto Loewi, who won the Nobel Prize in 1936.

Neural Signals Rapid breakdown of Ach is essential! Burst of Ach

Apparent Poor Choice of Structure Active site is buried deeply in the center, with a ring of aromatic groups as a gate.

Fundamental Questions How could rapid breakdown be achieved? Is there any advantage in the gated channel?

Zhou et al., PNAS (1998)

Dynamic Gate o

Fraction of Open State 2.4% o

Gate Appears Open to Intended Substrate ~ ps ~ ns but is effectively closed for slightly larger ligand. Dynamic gate provides mechanism for enzyme specificity!

Implications Dynamics is essential for the proper functioning of AchE and many other proteins. Dynamics can be exploited to achieve selectivity.

Applications Functional dynamics – AchE Protein folding – Trp cage Zhou et al. (1998), Proc. Natl. Acad. Sci. USA 95, 9280-9283. Protein folding – Trp cage Simmerling et al. (2002), J. Am. Chem. Soc. 124, 11258-11259. Snow et al. (2002), J. Am. Chem. Soc. 124, 14548-14549. Chowdhury et al. (2003), J. Mol. Biol. 327, 711-717. Protein-protein interactions – Src kinases Young et al. (2001), Cell 105, 115-126.

Gellman & Woolfson, NSB (2002)

Experimental Study Hagen group, JACS (2002)

Simulation Studies Simmerling et al. (2002), J. Am. Chem. Soc. 124, 11258-11259. Snow et al. (2002), J. Am. Chem. Soc. 124, 14548-14549. Chowdhury et al. (2003), J. Mol. Biol. 327, 711-717.

Simulation Details: Common AMBER force field, with solvent implicitly treated by the Generalized Born model. MD simulations up to 100 ns.

Simulation Details: Specific Simmerling et al Simulations were carried out before NMR structure determination. Done at 325 K on a Linux/Intel PC cluster. Pande and co-workers Done through Folding@Home distributed computing Aggregated simulation time of 100 ms, consisting of 1000’s of simulations up to 1 ns and 100’s of simulations up to 80 ns. Duan and co-workers 100-ns simulation on a Pentium III PC.

Results: a Critique Simulations show RMSDs decrease with simulation time. However, little insight is gained on protein folding.

Contact Formation Model Folding occurs through accumulation of native contacts. Different segments of the protein chain come into contact through diffusion. Contact forms if both side chains are in the “correct” conformations. Zhou, JCP (2003)

Why Is Folding Fast? The fraction of time the two side chains are simultaneously in their respective “correct” conformations is small. However, inter-conversion between correct and incorrect occurs on a ps time scale, whereas chain diffusion occurs on a ns time scale. Rapid local dynamics contributes to fast folding.

Applications Functional dynamics – AchE Protein folding – Trp cage Zhou et al. (1998) Proc. Natl. Acad. Sci. USA 95, 9280-9283. Protein folding – Trp cage Simmerling et al. (2002) JACS 124, 11258-11259. Snow et al. (2002) JACS 124, 14548-14549. Chowdhury et al. (2003) JMB 327, 711-717. Protein-protein interactions – Src kinases Young et al. (2001) Cell 105, 115-126.

Critique Detailed simulations provide hints and insights to the type of motion required for kinase activation. However, quantitative link between simulation and experiment is not yet possible. Room for simpler models!

Balls Connected by Tether

Potassium Channel inactivation ball

Tether Is Essential Inactivation has to be rapid (~ 1 ms). Without tether, inactivation domain must be present at mM level. Dynamics of tether is fully exploited in channel opening and closing. Zhou JPC (2002)