Enzyme Kinetics & Protein Folding 9/7/2004

Protein folding is “one of the great unsolved problems of science” Alan Fersht

protein folding can be seen as a connection between the genome (sequence) and what the proteins actually do (their function).

Protein folding problem • Prediction of three dimensional structure from its amino acid sequence • Translate “Linear” DNA Sequence data to spatial information

Why solve the folding problem?

• Acquisition of sequence data relatively quick • Acquisition of experimental structural information slow • Limited to proteins that crystallize or stable in solution for NMR

Protein folding dynamics

Electrostatics, hydrogen bonds and van der Waals forces hold a protein together.

Hydrophobic effects force global protein conformation.

Peptide chains can be cross-linked by disulfides, Zinc, heme or other liganding compounds. Zinc has a complete d orbital , one stable oxidation state and forms ligands with sulfur, nitrogen and oxygen. Proteins refold very rapidly and generally in only one stable conformation.

The sequence contains all the information to specify 3-D structure

Random search and the Levinthal paradox • The initial stages of folding must be nearly random, but if the entire process was a random search it would require too much time. Consider a 100 residue protein. If each residue is considered to have just 3 possible conformations the total number of conformations of the protein is 3 100 . Conformational changes occur on a time scale of 10 -13 seconds i.e. the time required to sample all possible conformations would be 3 100 x 10 -13 seconds which is about 10 27 years. Even if a significant proportion of these conformations are sterically disallowed the folding time would still be astronomical. Proteins are known to fold on a time scale of seconds to minutes and hence energy barriers probably cause the protein to fold along a definite pathway.

Energy profiles during Protein Folding

Physical nature of protein folding

• Denatured protein makes many interactions with the solvent water • During folding transition exchanges these non covalent interactions with others it makes with itself

What happens if proteins don't fold correctly?

• Diseases such as Alzheimer's disease, cystic fibrosis, Mad Cow disease, an inherited form of emphysema, and even many cancers are believed to result from protein misfolding

Protein folding is a balance of forces

• Proteins are only marginally stable • Free energies of unfolding ~5-15 kcal/mol • The protein fold depends on the summation of all interaction energies between any two individual atoms in the native state • Also depends on interactions that individual atoms make with water in the denatured state

Protein denaturation • Can be denatured depending on chemical environment – Heat – Chemical denaturant – pH – High pressure

Thermodynamics of unfolding • Denatured state has a high configurational entropy S = k ln W Where W is the number of accessible states K is the Boltzmann constant • Native state confirmationally restricted • Loss of entropy balanced by a gain in enthalpy

Entropy and enthaply of water must be added • The contribution of water has two important consequences – Entropy of release of water upon folding – The specific heat of unfolding (ΔC p ) • “icebergs” of solvent around exposed hydrophobics • Weakly structured regions in the denatured state

The hydrophobic effect

High ΔC p changes enthalpy significantly with temperature • For a two state reversible transition ΔH D-N(T2) = ΔH D-N(T1) + ΔC p (T 2 – T 1 ) • As ΔC p is positive the enthalpy becomes more positive • i.e. favors the native state

High ΔC p changes entropy with temperature • For a two state reversible transition ΔS D-N(T2) = ΔS D-N(T1) + ΔC p T 2 / T 1 • As ΔC p is positive the entropy becomes more positive • i.e. favors the denatured state

Free energy of unfolding • For ΔG D-N = ΔH D-N - TΔS D-N • Gives ΔG D-N(T2) = ΔH D-N(T1) + ΔC p (T 2 – T 1 )- T 2 (ΔS D-N(T1) + ΔC p T 2 / T 1 ) • As temperature increases TΔS D-N increases and causes the protein to unfold

Cold unfolding • Due to the high value of ΔC p • Lowering the temperature lowers the enthalpy decreases T c = T 2 m / (T m + 2( ΔH D-N / ΔC p ) i.e. T m ~ 2 ( ΔH D-N ) / ΔC p

Measuring thermal denaturation

Solvent denaturation • Guanidinium chloride (GdmCl) H 2 N + =C(NH 2 ) 2 .Cl

• Urea H 2 NCONH 2 • Solublize all constitutive parts of a protein • Free energy transfer from water to denaturant solutions is linearly dependent on the concentration of the denaturant • Thus free energy is given by ΔG D-N = ΔH D-N - TΔS D-N

Solvent denaturation continued • Thus free energy is given by ΔG D-N = ΔG H2O D-N - m D-N [denaturant]

Acid - Base denaturation • Most protein’s denature at extremes of pH • Primarily due to perturbed pK a ’s of buried groups • e.g. buried salt bridges

Two state transitions • Proteins have a folded (N) and unfolded (D) state • May have an intermediate state (I) • Many proteins undergo a simple two state transition

D <—> N

Folding of a 20-mer poly Ala

Unfolding of the DNA Binding Domain of HIV Integrase

Two state transitions in multi-state reactions

Rate determining steps