## Archive for July, 2009

### Computing protein stabilities from their chain lengths

Wednesday, July 29th, 2009

Ken Dill’s latest PNAS paper is one of his way of decomposing the protein stability. It is not very useful for the moment. Nonetheless, I found it very inspirational.

The folding energy of protein is ΔF = FN – FD, FN is the energy at native folded state, FD is the energy at denatured state. The total folding energy ΔF can be decomposed into to two parts:

ΔFtot = ΔFneural + ΔFelec(T, pH, cs)

ΔFneural is the part which there is no any charge effect in the folding process, while ΔFelec(T, pH, cs) is the electrostatic contribution to the energy as a function of pH, temperature(T), and salt contraction(cs).

ΔFneural = ΔH – T ΔS

ΔH = N[g0+m1cs]
ΔS = N k ln(z)

There are two temperatures at which the enthalpy and entropy vanish are called Th and Ts, respectively. So the temperature dependent parts of enthalpy and entropy can be expanded at the critical temperatures:

Enthalpy per amino acid:
$\Delta\,H(T)=\int_{T_{0}}^{T_{h}} \Delta\,c_P\,dT = \Delta\,c_P\,(T_{h}-T_{0}).$

Entropy per amino acid:
$\Delta\,S(T)=\int_{T_{0}}^{T_{s}} \frac{\Delta\,c_P}{T}\,dT = \Delta\,c_P\,ln(\frac{T_{s}}{T_{0}}).$

Put them back to the free energy, we have:

$\Delta\,F_{neutral}(T)= N [\Delta\,c_P\,(T_{h}-T_{0}) - T \Delta\,c_P\,ln(\frac{T_{s}}{T_{0}}) + g + m_{0}c + kTln(z)]$

The electrostatisis part is even simpler. A protein is considered a charged sphere with all charges on the surface. So the Born and Debye-Huckel treatment results the following energy for the eletrostatistics part:
$\frac{\Delta\,F_{elec}(T, pH, c_{s})}{kT} = \frac{Q_{n}^{2}l_{b}}{2R_{n}(1+\kappa\,R_{n})} -\frac{Q_{d}^{2}l_{b}}{2R_{d}(1+\kappa\,R_{d})}$
where Qn is the total charge on the native protein and Qd is the total charge on the denatured protein. lb is the Bjerrum length defined as
$l_{b} = \frac{Ce^{2}}{\epsilon\,kT}=\frac{1.39*10^{-4}J m mol^{-1}}{\epsilon\,RT}$ and its value at room temperature is given as 7.13 A.
The parameter $\kappa$ is defined as
$\kappa\,^{2}=2c_{s}l_{b}$

I’ll expand the Born and Debye-Huckel treatmentof electrostatistics later.

### A database annotating enzymes for proteins

Wednesday, July 29th, 2009

PDBsum has a function which annotate enzymes for protein structures. That is very usuful.

### Get GO terms for proteins with only pdbids

Wednesday, July 22nd, 2009

I found there is a way to get the GO terms for proteins with only pdbids. Though I hope there is a way to simply finish the mapping between GO terms and pdbids. Here is the procedure.