Simulations in Biology and Biophysics

How to bring Physics to Life?

Péter Maróti

Department of Biophysics, University of Szeged, Hungary

Topics- (Young) physicists: face to biology (related problems)- (Bio)Molecules in motion: brief tutorial on molecular dynamics

(MD)- Applications

- K+ channel protein- aquaporin- titin- photosynthetic apparatus of bacteria

- harvesting the sun- temperature dependence of intraprotein

electron transfer- interquinone electron transfer coupled to

proton uptake

- protein and lipid control of energetics of QA

(effect of mutations)

Physics in Biology, Biological Physics, Biophysics

In 1944, the physicist Erwin Schrödinger, published a short book that changed the course of modern biology."What is Life?" he asked famously in his title. Could the events inside a living organism be explained solely by physics and chemistry? Yes, they could, Schrödinger answered. "The obvious inability of present-day physics and chemistry to account for such events is no reason at all for doubting that they can be accounted for by those sciences.„

At that time, there was a wide disconnect between physics and biology. No one knew

- the physical nature of a gene, - the molecular biology, and - many of the smartest scientists went into elementary particle

physics. No more today.

''Ask not what physics can do for biology,'‘said Hans Frauenfelder, one of the field's pioneers,

''Ask what biology can do for physics.'' .(Adaptation of famous phrase from J.F. Kennedy)

''Biology has provided physics with its new frontier,'‘said Robert Laughlin, who won the 1998 Nobel prize in physics (quantum Hall effect) and now devotes himself to theoretical problems in biology.

''The whole problem is that we are living in the 21st century with these 19th century guilds.''

said John Hopfield, a Princeton scientist, one of the first physicists to move into biology.

Molecules in Motion

Structural biologists have long determined the detailed three-dimensional structures of proteins and the cell's other macromolecules, pinpointing the position of the thousands of component atoms. Those structures offer clues about how proteins act as

• motors, • channels, • solar cells, or • genetic switches.

But the structure is just a starting point. To begin explaining how a protein functions, it's important to see how it moves. The need is large to make successful simulations of macromolecules at work: Molecular Dynamics (MD).

Experiments that show protein dynamicsHemoglobin

The oxygen would need seconds to diffuse through the protein matrix to the hem groups in rigid protein. However, the time scale of oxygen uptake is ms!

Hans Frauenfelder, PNAS 1979

O2

Bacterial Reaction Center

H+

The rate of proton uptake from the aqueous bulk phase is governed by the dynamics of exposure of the protonatable group of the protein.

P. Maróti and C.A: Wraight, Biophys. J. 1997

Use of Molecular Dynamics in Biophysics

Spe

ed u

p

A Brief Tutorial on MD SimulationsMD: The Verlet Method

Double V-shape

Obtaining files

Files can be downloaded through the Web

First, you need a PDB File

What you need to know to build a realistic atomistic model

of your system?

What you need to know to build a realistic atomistic model

of your system?

MD Simulations of the K+ Channel Protein

Temperature fluctuation

Water Transport in AquaporinsAquaporins are membrane water channels that play critical roles

in controlling the water contents of cells.

The Nobel Prize in Chemistry for 2003

Peter AgreJohns Hopkins University School of Medicine,

Baltimore, USA“for the discovery of water channels”

Fundamental molecular understanding of how the kidneys recover water from primary urine. Several diseases, such as congenital cataracts and nephrogenic diabetes insipidus, are connected to the impaired function of these channels. Aquaporins facilitate the transport of water and, in some cases, other small solutes across the membrane. However, the water pores are completely impermeable to charged species, such as protons, a remarkable property that is critical for the conservation of membrane's electrochemical potential, but paradoxical at the same time, since protons can usually be transferred readily through water molecules.

Water Transport in Aquaporins

Emad Tajkhorshid, Peter Nollert, Morten Ø. Jensen, Larry J. W. Miercke, Joseph O'Connell, Robert M. Stroud, and Klaus Schulten. Control of the selectivity of the aquaporin water channel family by global orientational tuning. Science, 296:525-530, 2002.

12-nanosecond molecular dynamics simulations were carried out that define the spatial and temporal probability distribution and orientation of a single file of seven to nine water molecules inside the channel. Two conserved asparagines (Asn 68 and 203) force a central water molecule to serve strictly as a hydrogen bond donor to its neighboring water molecules. Assisted by the electrostatic potential generated by two half-membrane spanning loops, this dictates opposite orientations of water molecules in the two halves of the channel, and thus prevents the formation of a "proton wire," while permitting rapid water diffusion. Yellow ball: selected water molecule (or small salute).

Dozens of rounded red and white water molecules swarm around the much-larger channel like bees; a line of them squeeze single-file through a narrow hole in the channel’s center. Halfway through, each water molecule flips 180 degrees.

In the extreme sport of bungee jumping, a daring athlete leaps from a great height and free-falls while a tethered cord tightens and stretches to absorb the energy from the descent. The bungee cord protects the jumper from serious injury, because its elasticity allows it to extend and provide a cushioning force that opposes gravity during the fall. Amazingly, nature also uses elasticity to dampen biological forces at the molecular level, such as during extension of a muscle fiber under stress. The molecular bungee cord that serves this purpose in the human muscle fiber is the protein titin, which functions to protect muscle fibers from damage due to overstretching.

Molecular Bungee Cord

750 pN

Forced unfolding of titin Z1Z2

Photosynthetic Apparatus of Purple Bacteria.

Some problems for MD simulations

1. Harvesting the Sun

The light harvesting system displays a hierarchy of integral, functional units

How does the Light Harvesting System function with thermal disorder?

How does Q/QH2 pass through LH-I to/from RC within reasonable time (≈1 ms)?

2. Temperature-dependence of the rate of the initial electron transfer

The electron transfer is coupled to the thermal motion of the surrounding protein.

3. Interquinone Electron Transfer.Effects of Mutations

HisL190

HisL230

HisM219

M266His

M234Glu

Fe QA

QB

e-

0

1

0.5

0

0.5

0.25H

+/Q

A- p

roto

n up

take

H

+/Q

B- p

roto

n up

take

a

b

Extended network of strongly interacting protonatable groups

pH

WT

WT

M266HL

M266HA

■

O

□

Mutants

Mutants

WT

Delocalized proton uptake: the cytoplasmic part of the RC acts as proton sponge.

The high pH band of proton uptake reflects interaction among protonatable residues.

H. Cheap et al. Biochemistry (submitted)

4. Protein (M265ILE and M252TRP) and lipid (cardiolopin) control of QA/QA

- midpoint potential

László Rinyu et al. Biochim. Biophys. Acta 2004.

The free energy drop from P* to P+QA- in mutants

at residue M265 of the QA binding site. ΔGP*A was determined from the intensity of delayed fluorescence.

The effect of cardiolipin and M252WF mutation on the delayed fluorescence emission (DF) from RCs.

Trp→Phe mutant

Wild type

Thermodynamic box

RC-QA

RC-QA-

RC + QA

RC + QA-

AA QQ

boundG /

QQ

freeG/

AQ

ondissociatiG

AQondissociatiG

0G

Wild type Mutant M265IT

AQ

ondissociatiG

Linear Interaction Energy (LIE) methodfor determination of ligand binding free energies

J. Aqvist and J. Marelius, Combinatorial Chemistry and High Throughput Screening, 2001

Direct calculation of AQondissociatiGand

from MD model and determination of the change of the midpoint redox potential from the thermodynamic cycle.

AQ

ondissociatiG

This method is based on force field estimations of the receptor-ligand interactions and thermal conformational sampling. A notable feature is that the binding energetics can be predicted by considering only the intermolecular interactions between the ligand and receptor.

Acknowledgements.

Thanks to

• László Rinyu – Ph.D. student

• OTKA