• University of California, Berkeley

• MCELLBI 100B

MCELLBI 100B BIOCHEMISTRY: PATHWAYS, MECHANISMS

Units etc.
1L*atm=101.3J | RT≈2.5kJ/mol at 300K | VDW Radii O=1.5/N=1.6/C=1.7/H=1.2 | 1 cal = 4.184 J | 1N=1J/m |
Entropy units = J/K | RNA=kB | e=100.434 | Average AA Size = 110 Da (Leucine) | Typical Protein Domain is 10-30 kDa
| 3.7Angstrom = CAlpha/CAlpha bond | Leucine Radius ~3Angstrom | C-C Bond 1.45Angstrom | H bond separation
2.4-2.7Angstrom
Thermo
1st Law: Energy (U) of the system is conserved in the system + surroundings
 dUtotal=0
 UTotal=Usys+USurr=Constant
 dU
sys=-dUsurr i.e. energy changes in the system are balanced by the surroundings
2nd Law: Entropy, S, of the system + surroundings must increase for a spontaneous process
 dStotal=dSsys+dSsurr>0 for a spontaneous process
 dStotal=dSsys+dSsurr =0 at equilibrium
Enthalpy derivation under constant pressure:
 dqsys=dUsys-dWsys=dU-(-PextdV)=dU+PextdV
 H=U+PV=enthalpy of system
 dH
sys=dUsys+PsysdV+VdP=dUsys+PextdV because VdP=0 at constant pressure
 Change in enthalpy=heat transferred at constant pressure
 Most biological reactions occur under conditions of constant pressure
 If have constant pressure and volume (solution reactions not involving gases), ∆H ≈∆U
For an ideal monatomic gas, U=(3/2)nRT
Max value of heat capacity is when ½ protein molecule unfolded (melting temp)
Adiabatic expansion: dq=0
 Since dW is negative, dU is negative: expansion ‘fueled’ by KE of gas molecules
Isothermal expansion dU=0, expansion ‘fueled’ by heat/entropy
Boltzmann
Energy distribution with maximum multiplicity; with any large number, the Boltzmann distribution is the only
realistic distribution
Molecular Potential Energies
Negative F is attractive
Morse Potential: Energy required to break a bond: ri=infinity, rf=0 | When a=2Angstroms, have a double bond |
Energy has a high value when atoms are infinitely far apart because zero of energy scale is arbitrary | r0=optimum
bond length when repulsive and attractive forces cancel | Upot of system zero for large d and negative for closer
distances that correspond to covalent bond formation | U=0 when r=r0; U=D when r=infinity | D=amount by which
potential energy of atoms is reduced when covalent bond is formed (stabilization energy) | A=vibrational frequency of
A-B bond; measured experimentally
Hooke’s Law: approximates covalent bond energy when temperatures are low (thermal energy), so the covalent bonds
don’t break, since the function goes to infinity when r goes to infinity
VDW: Well depth E=1kJ/mol; stabilization energy or well depth that results from two nonbonded atoms moving from
infinity→rmin (optimal separation) | Rmin/2=VDWR
Electrostatic interaction approximation (Coulomb): Dielectric screening: energy is still calculated by Coulomb’s law
if all waters included, but difficult to do: instead, average out the effects of water and don’t explicitly include
Entropy
Most likely outcome is the outcome where W is maximal (max number of microstates): as number of events
increases, less likely events become more rare, and Nmax=M/2
For large M, the only observable outcome is the one with maximum multiplicity… which demonstrates the 2nd Law
of Thermodynamics; at equilibrium, entropy is at a maximum (kBlnW=S)
Energy Microstate: a specific configuration of specific molecules in energy levels
 All possible microstates must correspond to the same total energy distribution
Energy Distribution: how many molecules are in each level (don’t consider identity – distribution is sum of
microstates)
 Multiplicity of energy distribution determines likelihood of said energy distribution: highest multiplicity is the