## Archive for March, 2010

### Reading: evolution of protein modularity

Monday, March 15th, 2010

This is a review paper from Edward Trifonov and Zakharia Frenkel. The starting points of the review are basically two points. Evolution is a pretty gradual procedure, and the other is the (biological) systems start with a simpler version then evolves to a more complex one. So based on knowledge and experience, Brenner proposed essentially three steps for evolution:

1. Peptides (~ 10aa)
2. domains (~100aa)
3. multidomain proteins.

The author themselves suggested a slightly modified version:

1. Peptides (~7aa)
2. (a) Closed loops(25~30aa)
3. (b)folds (100~150aa)
4. Multifold proteins

### Briefs of two experiments: Differential Scanning Calorimetry and Pressure Perturbation Calorimetry

Tuesday, March 2nd, 2010

I happened to read a paper on the measurement of $\frac{\Delta V_{pr}} {V_{pr}}$. And the heat capacity measurement was used, so I dig into it and found how it is done.

Two pans are connected to a single heater to make sure the heating rate is exactly same. One pan with sample molecule plus solvent, the other pan is reference pan, so just with same amount of the solvent in the sample pan. Then heat up both pans simultaneously and at exact same speed. Suppose we have T1 and T2 for increased temperatures in the sample and reference pans, respectively. And the total amount of heat for each one is $\Delta Q$. Then we have the heat capacity of the molecule determined by:

$C_{p}=\frac{\Delta Q}{T_{1}}(1-\frac{T_{1}}{T_{2}})$

This is essentially what “Differential Scanning Calorimetry” experiment is doing. A good reference that I used is here.

Regarding the Pressure Perturbation Calorimetry experiment. We need start with the thermodynamics laws.

We have $\Delta Q_{reversible} = T \Delta S$, therefore $(\frac{dQ_{rev}}{dP})_{T} = T(\frac{dS}{dP})_{T}$.

Maxwell relation tells us that

$(\frac{dS}{dP})_{T}=-(\frac{dV}{dT})_{P}$ (1).

So we have:

$(\frac{dQ_{rev}}{dP})_{T} = -T (\frac{dV}{dT})_{P}$ or $(\frac{dQ_{rev}}{dP})_{T} = - TV\alpha$ (2), where,

$\alpha = \frac{1}{V}(\frac{V}{T})_{P}$.

Integrate Eq. 2, we have:

$Q_{rev} = - T V \alpha \Delta P$.

The Pressure Perturbation Calorimetry measures the thermal expansion coefficient $\alpha$. Same as in DSC, there two pans, one is for the sample and the other is for the reference. Suppose the heat flow into two pans are $Q_{sample}$, $Q_{reference}$. The total volume of the sample pan is $V_{total} = g_{0}V_{0} + g_{s} V_{s}$, and $g_{0}$ is the mass of solvent and $V_{0}$ is its volume, $g_{s}$ is the mass of the sample. So the PPC measures $Q_{sample} = -T(g_{0}V_{0} \alpha_{0} + g_{s} V_{s} \alpha_{s})\Delta P$, and $Q_{reference}=-T(g_{0}V_{0} \alpha_{0} + g_{s} V_{s} \alpha_{0})\Delta P$. Simplify both equations we have:

$\alpha_{s}=\alpha_{0}-\frac{\Delta Q}{Tg_{s}V_{s}}, \Delta Q = Q_{sample}-Q_{reference}$.

That is how PPC measures the thermal expansion coefficient. A good reference that I used is here.