Biomolecular Modelling

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Biomolecular Modelling

C

D

Carmen Domene

Physical & Theoretical Chemistry Laboratory University of Oxford UK

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THANKS …

Dr Joachim Hein Dr Iain Bethune

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• EPSRC Grant, ‘Simulations for Chemical Biology’ (£210,000), 2009, gy ( , ),

• EPSRC Grant, ‘Quantum simulations for Chemical Biology’ (£390,000), 2007-2008

~ 9 Million Aus (Open Access Initiative)

CODEs

(A) NAMD2 6 // 2 (IMD) d VMD

(A) NAMD2.6 // 2.7 (IMD) and VMD

NAMD2.6 ‘modified’ to include Metadynamics technique

http://www/ks uiuc edu/Reserach/namd http://www/ks.uiuc.edu/Reserach/namd

http://www.ks.uiuc.edu/Reserach/vmd/imd/tutorial (Visual Molecular Dynamics) 256 proc

256 proc.

Memory is not an issue. Data storage might be...g g

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Some Publications

• Atypical mechanism of conduction in potassium channels.

S. Furini, C. Domene, Proc. Natl. Acad. Sci. USA, 2009, 106 (38) 16074-16077.

• Dynamics, energetics and selectivity of the low-K+ _{KcsA channel} structure

structure.

C. Domene, S. Furini, J. Mol. Biol. 2009, 389, 637-45.

• Permeation of water through the KcsA K+ _channel.

S. Furini, O. Beckstein, C. Domene, Proteins, 2009, 74 (2), 437-448

• Conformational changes and gating at the selectivity filter of potassium channels

channels.

C. Domene, M. L. Klein, D. Branduardi, F. L. Gervasio, M. Parrinello, J.

Am. Chem. Soc. 2008, 130 (29) 9474-9480.

• Polarization effects and selectivity in K+ _channels.

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Membrane Proteins

•

Biological Membrane = Lipid

Bilayer + Membrane Proteins

B layer Membrane rote ns

• Selective Permeability due

to Channel & Transport

to hannel & ransport

Proteins

• Receptors & Recognition

Receptors & Recogn t on

• Membrane Bound Enzymes

Molecular Cell Biology, Fourth Edition W. H. FREEMAN, 2000

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Ion permeation in K

+

_-channels

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Permeation and Selectivity

S0 Sext S1 S2 S0 S2 S3 S4 S4 Cav

Zhou , Morais-Cabral, Kaufman,

Crystallographers assume in their

Cav

, , fm ,

MacKinnon Nature, 2001.

rysta ographers assume n the r refinements that if a site is not

occupied by an ion, the site is likely to be occupied by a water molecule

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Permeation and Selectivity

Berneche & Roux, Nature 2001 Aqvist & Luzhkov, Nature 2000

• The most favourable pathway for i t l ti i th i l li

• Largest free energy barrier ~ 2–3 kcal mol-1 • Each colour level =1 kcal mol-1

• Lowest energy pathway= Dotted line ion translocation is the simple cycling

between states 1010(1) and 0101(1) • Barrier for passage from 1010(1) to

0101(1) = 6 kcal mol-1 Lowest energy pathway= Dotted line • The position of the ions, Z₁, Z₂ and Z₃ 0101(1) = 6 kcal mol 1

• Among 3-ion states only 1101(1) has a non-prohibitive free energy

relative to the resting state which 9

relative to the resting state, which, in effect, excludes any mechanism involving the three-ion states

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(i) O f S4 d S2 i (i) Occupancy of S4 and S2 is

reduced

(ii) S1 and S3 unaltered

(iii) The mutation reduces the total occupancy of the filter and

complicated kinetic models were Site 4 is mutated _{compl cated k net c models were}

used to relate conduction and occupancy

‘but these calculations

have not given deeper insight into

the conduction mechanism’

KWK mechanism KWK mechanism X S2: Valid S1/S3: Valid X S2: Valid S1/S3: Valid

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Classical Mechanism of permeation

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Atypical Mechanism of Permeation??

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Comparison of mechanisms of permeation

Conduction Conduction KirBac KcsA

Mechanism Direction [kcal/mol][ ] [kcal/mol][ ]

KWK Outward 2.81 ±0.56 2.40±0.48 Inward 2.72±0.30 3.05±0.67 KK Outward 2 10±0 78 2 53±0 20 KK Outward 2.10±0.78 2.53±0.20 Inward 2.60±0.20 2.24±0.40

• Both mechanisms display similar energy barriers

I b th t f i t d t i t th t t l i th • In both, movement of one ion tends to assist others to travel in the same direction

• The KK mechanism is in agreement with experimental observations, and explains some others that did not fit within the KWK model

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Comparison of mechanisms of permeation

1.45±0.33 kcal/mol in KcsA 0.82±0.77 kcal/mol in KirBac

ΔG solvation for a K+ ion in Cavity or y S_ext is in both mechanisms:

1 00±0 30 kcal/mol in KcsA 1.00±0.30 kcal/mol in KcsA 0.68±0.41 kcal/mol in KirBac

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KK mechanism Site 4 is mutated KWK mechanism KK mechanism X S2: Valid S1/S3: Valid X _X _X _X

Not valid N t lid S1 X S3:

X_X

S1/S2 or S2/S3

S2: Valid S1/S3: Valid _{Not valid} _{Not valid} _S1-X-S3: Valid S1/S2 or S2/S3

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Some Conclusions

Alt

ti th

t th KWK it

• Alternative pathways to the KWK exit

• Vacancies can be implicated in the conduction mechanism

• The KK mechanism described here is likely to be

just

one

example among the plethora of alternative configurations and

d ti

th

th t i

d

t

d t d i

conduction pathways that ions and water may adopt during

permeation

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Water flow through the empty bacterial

potassium channel KcsA

Peter Pohl, Proc. Natl. Acad. Sci. USA 2004, 101, 4805-4809

Ion channels may play a y p y

secondary role as water channels E.G. neurons lack channels

E.G. neurons lack channels

specialised in water transport, maybe K+_{-channels contribute to} water homeostasis

water homeostasis

Water flow occurs only when all i s i s d t f th filt ions are rinsed out of the filter Water move through KcsA 1000 times faster than K+

Hypothesis: all binding sites are yp g occupied by water

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Transport of water through KcsA

Osmotic permeability = 2.7 -2.3×10-13_cm3_/s

80 windows (2ns/window)

Furini S., Beckstein O., Domene C. Proteins, 74(2) 437-48, 2009. Fur n ., c t n ., D m n . r t n , 7 ( ) 7 , 9.

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Selectivity filter in the absence of ions

Pressure MD ΔP=200MPa

GROMOS/SPC CHARMM/TIP3P

ΔP=200MPa

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Some Conclusions

• Structural rearrangements of the SF take place in the absence of

K

+

_{ions that allow for rapid water permeation, as experimentally}

observed

• The SF collapses to an hour-glass shape , and the central pore is

blocked

• Water molecules can flow at high rates through KcsA by

alternative paths to the central pore, that is behind the SF instead

p

,

• Can the addition of K

+

_{ions ‘refold’ the SF to the four-fold}

symmetrical functional ion filter?

y

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Activated Events

ΔΔ

OPEN CLOSED

How to Explore this ‘Multidimensional’ Free Energy Surface?

E p

m

F

E

gy

f

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Metadynamics

y

Laio & Parrinello, PNAS 2002

•

Filling the wells adding “small” Gaussians: the forces are changed with a time-dependent term.

•

The dynamics brings us to the closest local minimum of E(s) plus the sum of all the Gaussians

( )

( ) ( )

2

V r

s r

∂

⎛

⎞

E(s)

_{( )}

_{( ) ( )}

' 2 '

exp

2

t i t t i i

V r

s r

F

w

r

<

δ

s

∂

−

=−

−

∂

⎛

⎞

⎜

⎟

⎝

⎠

∑

E(s)

Forces from the normal potential

Forces from Gaussians localized on configurations

already explored

s

_potential

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Permeation and Metadynamics

Is there a physical gate at the selectivity filter?

RMSD ≤ 0.6 Å

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K

+

permeation and Metadynamics

K permeation and Metadynamics

Crystal structure structure Val flip commonly observed in observed in MD S2 disappears

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The Path Collective Variable

“S” Collective Variable

• Path = a sequence of plausible intermediate configurations R(t) q p g between two states (Interpolation).

• Choose first frame, last frame and atoms involved.

• “S” measures progress along the pathS measures progress along the path

“Z” Collective Variable

• Measures distance from the tread

; B S=0 B S=0 B S=0 B A A B A A S=1

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Metadynamics with “S” and “Z”

y

Conformational Changes ) (Å 2 ) Backbone atoms of SF Position 1 K+ _ion B i 6 K l/ l Barrier = ~6 Kcal/mol