CHM695 Module 4Empirical Force-fields

(April 15)

Potential energy is driven by the complex electronic structural changes

Can I mimic these potential energy changes without doing quantum

mechanics?

QM

harmonic

Bonding Interactions: to describe bonds

H2 molecule

U(RN ) =?

Our model should be based on some experimental/

theoretical knowledge about the system

U(R1,R2) =1

2kr(RR0)2H1

H2

U(R1,R2) =1

2kr(RR0)2

parametersparametersR = |R1 R2|

reproduce experiments/theory =1

2

sk

k = 422 = 42c2v2 Expt/theory

U(R)

RR0

Harmonic

Actual

No dissociation for harmonic potential

H2O molecule OH bonds can be treated by harmonic bonds H-H as harmonic

OR

H-O-H angle as harmonic

O

H1 H2

U(R1,R2,R3) =1

2kOH

ROH1 R0OH

2+

1

2kOH

ROH2 R0OH

2+

1

2kHOH

H1OH2 0HOH

243

1 2DOF=3x3

H2O2 molecule

3 distances [2 types] 2 angles [1 type] 1 torsion [1 type]

O1

H1

H2

O2

=

U() =1

2k,I

2

U() =1

2kr,I h

2

OR

these describe out-of-plane motion

Potential for Torsions: Two kinds

Improper Torsion/Out-of Plane

(Proper) Torsion

U() =NXn=0

Vn2

[1 + cos(n )]

What value of N and gamma, and Vn are suitable to mimic ethane

potential energy surface?

U(R1,R2,R3,R4) =1

2kOH

RO1H1 R0OH

2+

1

2kOH

RO2H2 R0OH

2+

1

2kOO

RO1O2 R0OO

2+

1

2kHOO

H1O1O2 0HOO

21

2kHOO

H2O2O1 0HOO

2N 0Xn=0

VHOOH2

[1 + cos(nH1O1O2H2 H1O1O2H2)]

Some Other Examples:Bond Potentials

Bond R0 ()kr (kcal mol-1

-2)

Csp3-Csp3 1.523 317

Csp3-Csp2 1.497 317

Csp2=Csp2 1.337 690

Csp2=O 1.208 777

Csp3-Nsp3 1.438 367

C-N (amide) 1.345 719

Angle

Angle 0 (deg) k(kcal mol-1

deg-2)

Csp3-Csp3-Csp3 109.47 0.0099

Csp3-Csp3-H 109.47 0.0079

H-Csp3-H 109.47 0.007

Csp3-Csp2-Csp3 117.2 0.0099

Non bonding Interactions

Electrostatic Interactions

q+ q-

Point charges: due to electronic redistribution when a molecule is formed

Charges are only conceptual

Charges are not observables

Electronic density is an observable

U(R12) =1

40

q1q2R12

1 2

R12

Electrostatic Potential Derived Point Charges (ESP Charges)

Can we get point charges on atoms (i.e. atomic positions) such that we can reproduce the

electrostatic potential?

ESP charges Scheraga & his group,

Journal of Physical Chemistry, 1992, 96, 10276

Point charges are such that the electrostatic potential obtained from a quantum mechanical calculation is mimicked for the selected points

Fitting procedure is used hereR =

NpointsXi

wi0i calci

2I qI / |RI - r |

from quantum mechanics

developers to the present day. First, the effective charges of the more-buried atoms are often underdetermined, so that charges for atoms insimilar environments in different molecules might vary significantly. Ineffect, there are many combinations of atomic charges that will fit theelectrostatic potential almost equally well. There are a variety of ways toovercome this problem, often involving statistical techniques based onsingular-value decomposition, but Bayly et al. (Bayly et al., 1993; Cornellet al., 1993) chose to use a hyperbolic restraint term to limit the absolutemagnitude of charges on non-hydrogen atoms. This is called RESP (forrestrained electrostatic potential fit) and weakly favors solutions withsmaller charges for buried atoms, yielding fairly consistent charge sets withlittle degradation in the quality of the fit to the electrostatic potentialoutside the molecule. As an example, the left-hand side of Fig. 2 shows thecharges determined in this way for N-methylacetamide, modeling thepeptide bond; the right-hand side of this figure is for a more complexelectrostatic model, described below.A second and more fundamental problem with the RESP procedure is

that the resulting charges depend on molecular conformation, often insignificant ways. This is a manifestation of electronic polarizability, whichcan only be described in a very averaged way if fixed atomic charges are tobe used. Any real solution to this problem must involve a more complexmodel, such as those described in section III, below. The compromisechosen for the ff94 force field was to fit charges simultaneously to severalconformations, in the hopes of achieving optimal averaged behavior.Once the charges and the stiff internal parameters for bonds and

angles were available (the latter estimated in the same way as outlinedabove), the Lennard-Jones parameters could be established primarily by

Fig. 2. Charge models for the Amber potentials. (Left) HF-6-31G*RESP charges inthe style of Amber ff 94. (Right) polarizable, extra-point charge model in the style ofAmber ff02-EP with the atomic polarizabilities in A3 given in parentheses.

FORCE FIELDS FOR PROTEIN SIMULATIONS 33

Dispersive Interactions

such interactions are due to instantaneous dipole-dipole interactions (dynamic electronic correlation)

HeHe

Can be generally mimicked by Lennard-Jones potential

attractive

repulsive

U(R) = 4

R

12 R

6

AB =p

AB

AB =A + B

2

BondAngle

TorsionNon-bonded

Overall potential form:

UMM(RN ) =

X 12k(x x0)2 +

X 12k( 0)2+X Vn

2(1 + cosn!)+X

IJ

(4IJ

"IJRIJ

12

ijRIJ

6#+qIqJRIJ

)

bonds angles

torsions

non-bonded pairs

2013

Martin Karplus Michael Levitt Arieh Warshel

for the development of multiscale models for complex chemical systems

2013 Nobel Prize Chemistry

Simulation ProtocolInitial

structure from X-ray(pdb.org)

Solvate protein

with water and ions

Equilibrate the system

Simulate till

adequate timescale

BUT what if we dont have the PDB structure?

approximate native

can MD predict the native structure?

Can MD tell us why nature chooses a specific folded structure of a protein and

how!?

Protein structure prediction

Simulation length will depends on the kinetic barrier going from the starting structure to the equilibrium/stable structure of the protein

Structure of the protein is mainly determined by the backbone structure

Rotational barriers of backbone atoms, and also side chains can determine the tertiary structure of the protein [Ramachandran Map]

limited torsional angles are only feasible due to

torsional barriers

H-bonds, solvent interaction, temperature etc. also affects the torsional values

Very large number of torsions difficult to

predict the preferred values of torsions

Rotational barriers can be several and high!

long timescale simulations required

native state

10-5 to 10 seconds =

Time Scale BottleneckMD time step: < 1 fs

Number of MD integration steps required for observing a protein folding is at least

I f one MD step costs 1 second computational time, total computing time would be 108 seconds = 3.2 years!!

To complete in one week, one step has to be comp l e t ed i n 6x1 0 -3 s e c o n d s (computational time)!

0.1s

1 fs= 108s

ligible role for these substances in the regu-lation of cystine stone formation.

Collectively, the AFM and bulk crystalliza-tion behavior for L-cystine suggest that L-CDMEis a viable therapeutic agent for the preventionof L-cystine kidney stones. This approach to stoneprevention uses a potentially benign crystal growthinhibitor at low concentrations rather than drugsthat rely on a chemical reaction with L-cystine(L-cystinebinding thiol drugs), increases in urinealkalinity (which are often accompanied by un-desirable side effects), or dramatic increases inurine volume (which can be unreliable owing topatient nonadherance). The reduction in massyield in the presence of inhibitors is a kinetic ef-fect that maintains a metastable supersaturatedL-cystine concentration, but from a pathologicalperspective this is a sufficient condition for pre-venting stone formation. L-cystine stone formerstypically have urinary L-cystine concentrationsranging from 250 to 1000 mg/liter (equivalentto 1 to 4 mM), which is comparable with theconcentrations we used for the AFM and bulkcrystallization studies. Therefore, L-CDME con-centrations near 2 mg/liter (

www.sciencemag.org SCIENCE VOL 330 15 OCTOBER 2010 309

NEWS OF THE WEEK

From the Science Policy Blog

A National Academies report on how U.S. universities have managed intellectual property in the wake of the 1980 Bayh-Dole Act has concluded that things are pretty much hunky-dory but that schools may be trying too hard to cash in on discoveries. Universities instead should aim to dissemi-nate technology for the public good, which may mean passing up a more lucrative licensing deal. http://bit.ly/bayh-dole-update

The U.S. Food and Drug Administration is pressing for a $25 million funding boost for research that can help it evaluate new treatments better and faster. Commissioner Margaret Hamburg says such regulatory sci-ence would allow the agency to help turn the nations sizable investment in basic biomedi-cal research into vital products for those who need them. http://bit.ly/fda-research

Israels minister of education, Gideon Saar, has fi red his chief scientist for comments that questioned the tenets of evolution and global warming. Gavriel Avitals trial appoint-ment last December had been controversial from the start. http://bit.ly/sacked-adviser

The National Ignition Facility, the highest energy laser in the world, has fi red its fi rst shot in what offi cials at Lawrence Livermore National Laboratory hope will be a suc-cessful campaign to achieve ignitiona self-sustaining fusion burn that produces more energy than was pumped in to make it happen. http://bit.ly/fi rst-blast

The National Institutes of Health has launched a $60 million program that will allow a few talented young scientists to become independent investigators shortly after earning their Ph.D.provided they can get jobs with institutions willing to nominate them for the award. http://bit.ly/early-independence

The European Union has unveiled a new plan to foster innovation. Offi cials hope its emphasis on making it easier for companies to actually use the fruits of science will bridge a valley of death that slows commer-cialization. http://bit.ly/innovation-union

For more science policy news, visit http://news.sciencemag.org/scienceinsider.

mine-tagged benzene as well as one from the olefi n, bringing them close enough to pair up. When they do so, they form styrene, the building block of polystyrene plastics. The reacting molecules kick the bromine out into solution and send the palladium on its way to orchestrate another hookup. In the late 1970s, Japanese-born Negishi, who spent the bulk of his career at Purdue University in West Lafayette, Indiana, and Suzuki, of Hok-kaido University in Sapporo, Japan, modi-fi ed the approach, adding different tagging atoms as well as metals to tailor the reaction to make other organic compounds.

Today, the three approaches are col-lectively known in chemistry parlance as palladium-catalyzed cross-coupling reac-tions, and they continue to grow more popu-lar. Of all methodologies developed over the past 50 years, it is safe to say that palladium-catalyzed cross-coupling methodologies have had the biggest impact on how organic compounds are made, says Eric Jacobsen, an organic chemist at Harvard University. Cross-coupling methods are now used in all facets of organic synthesis, but nowhere more so than in the pharmaceutical industry, where they are used on a daily basis by nearly every practicing medicinal chemist.

As a result, Jacobsen and other chemists say they were not surprised by the award. It was just a matter of time for this chemistry to be recognized, says Joseph Francisco, a chemist at Purdue University and the pres-ident of the American Chemical Society. Jacobsen says the Nobel Committee could have also chosen any of a few other cross-coupling pioneers, such as Barry Trost of Stanford University. But Nobel rules limit the committee to picking no more than three recipients. I think they got it right, says Jeremy Berg, who heads the National Institute of General Medical Sciences in Bethesda, Maryland.

For Negishi in particular, the prize is a dream come true. After immigrating to the United States from Japan, Negishi says he had the opportunity to interact with several Nobel Laureates while studying at the Uni-versity of Pennsylvania. I began dreaming about this prize half a century ago, Negishi says. At a press conference televised in Japan, Suzuki said he hopes his work will have a sim-ilar effect on the next generation. Japan has no natural resources. Knowledge is all weve got, Suzuki says.

ROBERT F. SERVICE

With reporting by Dennis Normile in Tokyo.

relatively simple calculations involved in determining how neighboring atoms in a protein interact. By speeding computa-tions, Shaw says, Anton has run all-atom simulations 100 times longer than general purpose supercomputers can. In the current study, for example, Shaw and his colleagues were able to track 13,564 atoms, compris-ing a relatively small protein and surround-ing water molecules, long enough to see the protein fold and unfold repeatedly.

Like all supercomputers, the Anton used in the current study still has its limits and cant run such lengthy simulations of very large

proteins. But Shaw says he and his colleagues are already making progress on that. In addition to build-ing 11 supercomputers incorporating 512 custom-designed computer chip cores, or nodesShaw

donated one to the National Resource for Biomedical Supercomputing in Pittsburgh, PennsylvaniaShaws team has built a 1024-node machine and one with 2048 nodes. The larger machines, he notes, are more effi cient tracking the motions of larger proteins. More-over, Shaw says his team is already building successors to Anton, using the next genera-tion of chip technology to burn through cal-culations signifi cantly faster. And Shaw says hes happy to be back in the thick of a knotty intellectual challenge: I love this. Its just the most fun Ive ever had. Its very satisfying.

ROBERT F. SERVICE

Custom job. By speeding cal-culations, this Anton super-computer can run all-atom simulations (inset) 100 times longer than can general pur-pose supercomputers.

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Published by AAAS

Addressing the grand challenge as we speak...

D. E. Shaw & his Anton Machinehttp://www.youtube.com/watch?v=PGqCeSjNuTY

1000x faster

Anton Vs others

Machine computational time for 1 MD step (s)

Intel Xeon chips ~104

Anton ~20

Anton has a speed up of ~1000

How Anton Does it?

Chips are designed for fast computation and look-up of pairwise interactions

Communications between the chips are extremely fast

http://www.cs.utah.edu/hpca08/papers/6A_1_Larson.pdfFor those who want to read more about it, see: