Simulating biomolecules

Steven O. Nielsen

Department of Chemistry

University of Texas at Dallas

Outline

• Concept of the energy landscape funnel for protein folding• Importance of low frequency normal modes of proteins• Hydrophobic effect and cold unfolding• Free energy

Stress the link between thermodynamics and biomolecular structure

Energy landscape theory: the protein

folding funnel

Jose Onuchic and Peter Wolynes (UCSD)

Protein folding should be complex. The classical view of protein folding is of a nearly sequential series of discrete intermediates.

In contrast, the energy landscape theory of folding considers folding as the progressive organization of an ensemble of partially folded structures through which the protein passes on its way to the natively folded structure. As a result of evolution, proteins have a ruggedfunnel-like landscape biased toward the native structure.

Energy landscape theory: the protein

folding funnel

This organization (the funnel) is not characteristic of all polymers with any sequence of amino acids, but is a result of evolution.

Evolution achieves robustness by selecting for sequences in which the interactions present in the functionally useful structure are not in conflict, as in a random heteropolymer, but instead are mutually supportive and cooperatively lead to a low-energy structure.

Jose Onuchic and Peter Wolynes (UCSD) Trade-off between entropy and enthalpy almost balance: why?

Energy landscape theory: the protein

folding funnel

Perfect funnel or Go models include only interactions that stabilize the native structure.

Very simple force field: only native contacts are favorable.

This theoretical construct has yielded enormous insight into protein folding, even though it is highly simplified.

THEORY / SIMULATION

Nobuhiro Go

Normal mode analysis: low-frequency modes important for

proteins

Normal mode analysis (NMA) is a powerful tool for predicting the possible movements of a given macromolecule. It has been shown recently that half of the known protein movements can be modelled by using at most two low-frequency normal modes. Applications of NMA cover wide areas of structural biology, such as the study of protein conformational changes upon ligand binding, membrane channel opening and closure, potential movements of the ribosome,and viral capsid maturation.

High frequency modes are usually localized – a bond stretch for example, and are not important. Low frequency modes are usually delocalized (eg. breathing modes)

apo (left) and holo (right) forms of lactoferrin

http://www.igs.cnrs-mrs.fr/elnemo/examples.html

Hydrophobic effectD. Chandler, Nature, 417, 491 (2002).

The separation of oil and water in ambient conditions is not due to repulsion between water and oil molecules, but to particularly favourable hydrogen bonding between water molecules.

Strong mutual attractions between water molecules induce segregation of oil from water and result in an effective oil–oil attraction called the hydrophobic interaction: primary source of protein stability.

ButBut: depends on length scale

Water–water interactions persist even in the presence of small oily species, (< 10 carbon alkane). In the close vicinity of the oily molecules, the possible configurations of hydrogen bonding may be restricted, but the overallamount of hydrogen bonding remains unchanged. Thus, the cost of hydrating a small, hydrophobic solute has more to do with the number of ways in which hydrogen bonds can form than with their strength. Thatis, the solvation free energy of the system is largely entropic and not enthalpic.

However, this geometric picture breaks down for an extended oily region, because not all hydrogen bonds can persist near to its surface. The nature of hydrophobicity therefore changes when the size of oily surfaces depletes the number of hydrogen bonds. This energetic effect — the loss of hydrogen bonding — drives the segregation of oil from water.

(VOLUME vs SURFACE AREA: crossover on the nanometer scale)

Hydrophobic effect

Hydrophobic effectD. Chandler, Nature, 417, 491 (2002).

The assembly of hydrophobic structures requires the removal of water from regions between these groups; this is the same as vaporization. Hence, the closer water is to the liquid–vapour phase transition, the stronger is the tendency for hydrophobic assembly. I [Chandler] believe this explains why proteins are denatured by cold.

Cold unfolding

These (experimental) results demonstrate the potential of cold denaturation as a means to dissect the cooperative substructures of proteins and to provide a rigorous framework for testing statistical thermodynamic treatments of protein stability, dynamics, and function. -- Babu, Hilser, Wand, Nature Struct. Mol. Biol. 11 352 (2002)

Usually have to go below the freezing temperature of water to see cold-unfolding, but there are experimental tricks to get as far down as -35oC and still have a liquid.

Cold unfolding : thermodynamics

temperature and pressure phase diagram

Cold unfolding : thermodynamics

Hawley theory: starts from the assumption that there are only two distinct states of the protein (native and denatured) and the transition between them is a two stateprocess. The Gibbs free energy difference between these states is defined as:

Upon integration of this equation from an arbitrarily chosen reference point T0,p0 to T,p we get:

where means the change of the corresponding parameter during denaturation (i.e. the value in the denatured state minus that in the native state).

Cold unfolding : thermodynamics

ilitycompressib

T

p

Vyexpansivitthermal

TP p

S

T

V

capacityheat

PP

P T

H

T

STC

The transition line, where the protein denatures (or refolds depending on the direction of the crossing), is defined by G=0.

VALVAL

ARG ARG

310K 278K

apo-myoglobin at 310K (left) and 278K (right). Water oxygens yellow.

Free energy is the fundamental measure of macromolecular stability. For example, the relative free energy (Gibbs, G, constant temperature and pressure conditions) between the native and unfolded states of a protein is what is measured experimentally.

Also might want to know the free energy barrier for a reaction (or in general for an event). This is one of the most important quantities to know in chemistry.

Free energy ( G = H – TS )

Will give an example for events in biological membranes

Biological membranes: packaging

In its fight for resources, bacterium Staphylococcus aureus secretes alpha-hemolysin monomers that bind to the outer membrane of susceptible cells. Upon binding, the monomers oligomerize to form a water-filled transmembrane channel that facilitates uncontrolled permeation of water, ions, and small organic molecules. Rapid discharge of vital molecules, such as ATP, dissipation of the membrane potential and ionic gradients, and irreversible osmotic swelling leading to the cell wall rupture (lysis), can cause death of the host cell. This pore-forming property has been identified as a major mechanism by which protein toxins can damage cells.

Experimentally, a free energy difference is determined either from the relative probabilityprobability of finding the system in a given state, or from the reversible work required to transform the system from one state to another.

QTkF B ln

Study energetics (free energy) of water going through the pore: big entropy change and also big change in hydrogen bonding

pattern, so both enthalpy and entropy must be considered

1

0

1

0

dU

dF

F

If an equilibrium simulation does not sample enough of the high free energy regions, a more powerful method is needed. One such method is the method of constraints, also called thermodynamic

integration.

Average force of constraint

Free Energy Profile of Membrane Meniscus against Hydrophobic Mismatch

2000 )(

2

1)( optuukuF

LKh 4/34/12/10 )2( k = 650 kJ/mol

Xibing He, S.O. Nielsen, et. al., manuscript in preparation: first time this effect has been quantified by computer simulation

Lipids do influence protein function—the hydrophobic matching hypothesis revisited (Biochimica et Biophysica Acta 2004, 1666, 205)

Synthetic antimicrobials a

Angew. Chem. Int. Ed., 43, 1158 (2004)

b

aryl amide oligomers

d

Shai-Matsuzaki-Huang