Applications of relative free energy

calculationsRelative free energies are useful in two contexts:

1. Calculation of the free energy of binding of a ligand

relative to bulk. This is the most common application.

The simplest examples are binding of ions.

As the ligand gets more complex, it becomes less

accurate.

2. Calculation of the free energy change when a bound

ligand is mutated. This gives selectivity of a binding

site against different ligands. Again ion selectivity is

the simplest and most common example. Mutation of

amino acids is a powerful method but it has been

neglected.

1

1. Free energy calculations in potassium channels

The first crystal structure in 1998 (MacKinnon), followed by many

others.

Selectivity filter

S0

S1

S2

S3

S4

C

Permeation cycle

Waiting state: (S1-S3-C)

Trigger event:

(S1-S3-C) (S0-S2-S4)

K+ in S0 is ejected, leaving

two ions in the filter. Then

(S2-S4) (S1-S3)

Aqvist et al. (2000) did the

first FEP calculations where

they progressively loaded the

filter with K+ ions, confirming

the above picture.3

S0

S1

S2

S3

S4

Cavity

MD simulations of potassium channels

• Most of the simulations have been done for the KcsA channel,

which has two-transmembrane topology (similar to Kir

channels) and very stable structure. (See e.g. work of Roux

and Sansom)

• K/Na selectivity has been confirmed from FEP calculations

• Permeation involves recycling between 2 and 3 K ions in the

filter. Entry of a third ion makes the filter state semistable,

which results in ejection of the third ion in the direction of

applied electric field (confirmed by BD simulations).

• Voltage-gated potassium channels have six-transmembrane

topology (four of them function as voltage sensors) and are

less stable.

• Thus it is imperative to check that the results obtained in

KcsA are transferable to Kv channels.4

Comparison of the

filter structures:

Shaker Kv1.2 (top)

KcsA (bottom)

5

Basic dihedral configurations trans cis

Definition of the dihedral

angle for 4 atoms A-B-C-D

)cos(12 0 nV

U ndihedDihedral potential:

6

Effect of the dihedral energy correction terms (CMAP)

in selectivity of K+ channels

Without CMAP Shaker Kv1.2 With CMAP

7

Without CMAP KcsA With CMAP

8

Selectivity of S1 site

Selectivity free energy

G(K+ Na+)

=GS1(K+ Na+)

Gbulk(K+ Na+)G Calc. Exp.

Shaker -0.7 > 2.1

+ CMAP

5.2 > 2.1

KcsA 1.8 > 2.9

+ CMAP

8.4 > 2.9Units: kcal/mol 9

Transporters – the new frontier

Transporters have larger structures, which are partly outside the

membrane. Also they have no symmetries. Therefore they are

harder to crystallize compared to ion channels.

First complete transporter structure: ABC (ATP binding cassette) transporter, Locher et al. 2002.First glutamate (aspartate) transporter: GltPh from Pyrococcus horikoshii, Gouaux et al. 2004; 2007)First sodium-potassium pump structure: Nissen et al. Dec. 2007)

Two major families:

Primary active transporters use the energy from ATP (e.g., Na-K

pump)

Secondary active transporters harness the gradient of Na+ ions

(membrane potential) (e.g., Glu and Leu transporters)

2. Free energy calculations in glutamate transporters

Structure of sodium-potassium pump (Nissen et al. Dec. 2007)

ATP binding casette (ABC) transporters

ABC drug exporter (Sav1866)(Dawson and Locher, 2006)

Vitamin B12 importer(Locher et al. 2002)

Much interest because of multi-drug resistance in chemotherapy

Schematic picture of B12 import

Structure of GltPh from Pyrococcus horikoshii

Boudker et al. 2007

Binding sites for Asp and two Na ions

are revealed

Q: why is it called glut. transporter?

Closed and open states of Gltph

The crystal structure is in closed state. After the Na+ ions and Asp

are removed, the hairpin HP2 moves outward, exposing the binding

sites.

HP2

Opening of the extracellular gate HP2

Initial MD simulations of GltPh with 2 Na+ ions

In the crystal structure, Na1 is coordinated by the carbonyl oxygens

of Gly306, Asn310, Asn401and two carboxyl oxygens of Asp405

After (long) equilibration in MD simulations, Asp312 sidechain

swings 5 A and coordinates Na1. Also Gly306 moves out of the

coordination shell. This disagrees with the crystal structure.

Human Glu transporters use 3 Na+ ions in the transport. For the

GltPh structure to be useful in homology modeling, it must also have

3 binding sites for the Na+ ions.

It is possible that the third b.s. is not seen. Clue: what is holding

Asp312 sidechain in that location in the crystal structure?

Simulation system for GltPh

It is important to obtain a minimal system to save from computation

time Original system Minimized system (150,00 atoms) (87,000 atoms)

Movement of the D312 sidechain in MD simulations

Initially, D312 - O is > 7 A from Na1. After about 35 ns, it swings to

the coordination shell of Na1, pushing away G306 – O and also one

of the D405 – O.

Hunt for the Na3 site after the experiments revealed

its existence

Reject those sites that do not involve D312 in the

coordination of Na3 (Noskov et al, Kavanaugh et al.)

Two prospective Na3 sites are found that involve D312 as well

as T92 and N310 sidechains

1. In MD simulations that use the closed structure, the 5th

ligand is water. (Tajkhorshid, 2010)

2. In the open (TBOA bound) structure N310 sidechain is

flipped around, which shifts the Na3 site, making the Y89

carbonyl as the 5th ligand.

(Question: Why isn’t the Na3 site seen in the crystal structure?)

Position of the Na3 binding site

Na3’ coordination shell from the

closed structure:

T92, N310, D312 (2), H2O

Na3’ coordination shell from the

open structure:

T92, S93, N310, D312 (1), Y89 (bb)

Both remain stable in long MD

simulations.

Which one is correct?

open

closed

Tests for the Na3 site

We need to find out which configuration of N310 is more likely.

1. In 5 ns MD simulations without the Na3 ion, the N310 sidechain

remains stable in the open structure but flips after 0.2 ns. in the

closed.

2. After MD simulations

with the Na3 ion, N310

sidechain moves 2 A away

from the crystal structure

in the closed case, but not

in the open.

3.Free energy of binding for the Na3 site are 23.3 kcal/mol (open)

and 19.3 kcal/mol (closed). Compare with Na1: 16.2

kcal/mol.

openclosed

MD

crystal

Binding free energies for Na+ ions and Asp in GltPh

The crystal structure provides a snapshot of the ion and Asp bound

configuration of the transporter protein but it does not tell us

anything about the binding order and energies. We can answer

these question by performing free energy calculations. The specific

questions are:

1.We expect a Na+ ion to bind first - does it occupy Na1 or Na3 site?

2.Does a second Na+ ion bind before Asp?

3.Are the binding energies consistent with experimental affinities?

4.Are the ion binding sites selective for Na+ ions?

5.Can we explain the observed selectivity for Asp over Glu (there is

no such selectivity in human Glu transporters)

Once we answer these questions successfully in GltPh, we can

construct a

homology model for human Glu transporters and ask the same

there.

TI calculation for binding of a Na+ ion to Na3 site

Total simulation time is 1.4 ns; equilibration, 0.4 ns; production, 1

ns.

Open structure with only one Na+ ion at Na3 site is used in the

calcul.

TI calculation for binding of Asp

Calculation is performed in the presence of Na+ ions at Na1 and

Na3.

Asp is replaced by 5 water molecules in the binding site.

Na+ binding free energies

Energies are obtained for binding of Na+ ions to the empty

transporter (i.e. Asp and ions are removed and the gate is

open)

Single Na binding energies (kcal/mol):

Na3(open) : 19.3 Na3(closed) : 23.3

Na1 : 16.2

Na3 binds first and Y89 coordination is preferred to that of

water.

As Na2 binds last, we next calculate Na1 binding energy in

the presence of Na3 : 11.9

Asp binding free energies (gate open)

Asp is replaced with 5 water molecules.

Asp binding energies (kcal/mol):

With Na3 present : 4.3

With Na3 and Na1 present : 12.3

Na1 binds after Na3.

Asp binds after Na3 and Na1.

The order of binding:

Na3 Na1 Asp Gate closes Na2

23.3 11.9 12.3 4.1

Binding energies (gate closed)

All three Na ions and Asp are present

Na3 : 14.6 kcal/mol

Na1 : 28.7

Asp: 2.6

Na2 : 4.1

Asp becomes unstable after closing of the gate!

This may be useful for quick release of Asp to the cell interior.

What about the Asp/Glu selectivity?

Free energy difference for Asp/Glu binding : ~2 kcal/mol

Experiments indicate ~4 kcal/mol (1000-fold reduction in bind.

const.)

Lessons from the free energy simulations

Correct reading of the crystal structure is essential:

Respect the long and medium distance structure but be

careful with the short distance.

Free energy simulations can help to resolve structural issues

as well as providing an overall picture for binding processes.

Computational program for protein-ligand interactions

1. Find the initial configuration for the bound complex using a

docking algorithm (e.g. AutoDock, ZDOCK, HADDOCK, etc. )

2. Refine the initial complex via molecular dynamics (MD)

simulations

3. Calculate the potential of mean force for binding of the

ligand along a reaction coordinate → binding constants and

free energies

4. Determine the key residues involved in the binding

5. Consider mutations of the key residues on the ligand and

calculate their binding energies (relative to the wild type)

from free energy perturbation in MD simulations

6. Those with higher affinity are candidates for new drug leads