Question

Consider the thermodynamic data collected for two self-complementary RNA duplexes from optical melting experiments in the table below (JACS volume 109 page 3784). The buffer is 1 M NaCl, 10 mm Na2PO4, 0.5 mM Na EDTA, pH 7. An inosine base (1) differs from a guanine base (G) by one amino group. A. What is the difference in melting temperatures for the two duplexes at a concentration of 1 x 10-4 M? B. What is the free energy at 37 °C of a hydrogen bond in a guanine-cytosine Watson-Crick pair in these duplexes? sequence AH° AS (kcal/mol) (eu) AG°37 (kcal/mol) 5'CGGCC13 -53.0 -143.2 -8.55 3'ICCGGC5 5'CGGCCG3 3'GCCGGC5 -54.1 - 142.6 -9.90 Ho-cac-CEN C- Ng–c G ---- NEC N2- H o H22 C -- 62-N; Ci:

Answer 1

Ans: A) The formula for calculating melting temperature :

Where:

Tm = melting temperature in °C

ΔH = enthalpy change in kcal mol-1

A = constant of -0.0108 kcal K-1 ᐧ mol-1 (accounts for helix initiation during annealing / melting)

ΔS = entropy change in kcal K-1 ᐧ mol-1 (accounts for energy unable to do work, i.e. disorder)

R = gas constant of 0.00199 kcal K-1 ᐧ mol-1 (constant that scales energy to temperature)

C = oligonucleotide concentration in M or mol L-1

-273.15 = conversion factor to change the expected temperature in Kelvins to °C

[Na+] = sodium ion concentration in M or mol L-1

From the question we have to find the difference of melting temperature of these two sequences. Let's suppose that the melting temperature of 1 sequence is tm1 and 2 sequence is tm2. Taking the difference we get:

Tm1-Tm2= ΔH1/A+ΔS1+Rln(C/4)-ΔH2/A+ΔS2+Rln(C/4) (Since the concentration is equal for both sequnces)

Also the entropy is given in e.u and 1 e.u.= 0.001 kcal K-1 ᐧ mol-1. So ΔS1= -0.1432 and ΔS2= -0.1426

Putting the values we get :

(-53.0)/(-0.0108-0.1432+0.00199*ln(10-4/4) - (-54.1)/(-0.0108-0.1426+0.00199*ln(10-4/4)

Solving this equation we get: 302.85 Kelvin - 310.03 Kelvin.

So the difference between the melting temperature of these two sequences is equal to 7.18.
b) As given in the data that free energy for sequence 2 is -8.55 Kcal/mol and sequence 2 has all 6 pairs of GC so free energy for a single pair is -9.9/6= -1.65 and as per Watson and Crick there are three hydrogen bonds between a single pair of GC so for a single hydrogen bond the free energy is -1.65/3= -0.55 Kcal/mol.