Transcript non-covalent interactions

Introduction to Biophysics
Lecture 2
Molecular forces in Biological Structures
The Concept of Free Energy:
-“useful” energy of a system
- the part of total energy that can be harnessed to do “useful” work
F=E-TS
(total energy – randomness (or disorder))
If F<0 – process is spontaneous, T=constant
F can decrease if
E decreases (exmp. - heat loss)
S increases (disorder tents to increase)
Life doesn’t create order from nowhere. Life captures order,
ultimately from the Sun. Prosesses of free energy transduction then
transmit order through the biosphere.
Biological molecules are polymers :
The free energy associated with a covalent bond is ~ 100 – 150 kBT.
These bonds are therefore not disrupted by thermal fluctuations.
lipids
The Schrödinger equation is the theoretical basis for calculation of the
wave functions of electrons and the probability of their presence at a
particular point in space.
Quantum numbers: n, l, ml, ms
Pauli exclusion principle - It is impossible for two electrons with
identical quantum numbers to occur in the same atom.
Atomic orbitals - illustration of the statistical nature of the
electron distribution:
Note that spin quantum number does not influence either the
shape or the size of the orbitals.
How chemical bond is made?
What determines its length?
E = Ee,kin + Ee,e +Ee,n
Energy diagram for formation of the hydrogen molecule
Molecular orbitals / Molecular geometries
Carbon:
Peculiar property of carbon atom which enabled the emergences of life.
H2O
(H-O-H) = 104.5
CH4
Electrostatic
repulsion of
the valence
electrons
sp3
(H-O-H) = 90
sp2
sp-orbital
sp3-orbital (hybrid orbital)
- bond (-electrons) have rotational symmetry, can be subjected to thermal rotation
Name non-covalent interactions:
non-covalent interactions:
Electrostatic interaction (special case of ionic bond)
Charge – dipole interaction
Induced Dipoles
Dispersion forces
Hydrophobic forces
Hydration forces
Hydrogen bond
Steric repulsion
non-covalent interactions:
•govern how protein folds
•determine structure of nucleic acids and lipid bilayers
•drive association between macromolecule and ligand
They are generally well understood to the extent that good
approximate mathematical expressions are available.
Much is known about their relative strength under various
conditions.
Structure and dynamics of biological macromolecules are
determined by interplay of many forces.
Question biophysicists ask:
How are Genes Turned On and Off?
The discovery of the double helical
structure of the DNA was a breakthrough for
many branches of biology, because it explained
how the structure of the molecule allows it to
function as a template for copying
genetic information. However, it was not
clear how DNA works in three dimensions –
what sorts of three-dimensional
structures are superimposed on the double
helix and how these influence the interactions
of DNA with other molecules in its environment.
Binding of proteins to DNA determines when
and how genes are turned on and off and in
turn regulates both normal and abnormal
development.
Electrostatic interaction
Transport of ions across the biological membrane.
Some macromolecules are electrically charged (DNA)
Electrical charge on macromolecules (mostly negative) prevents
them from aggregation
Detailed pattern of the negatively and positively charged residues on
protein surface can be responsible for protein-protein or proteinsubstrate interaction and binding
Electrostatic interaction
Two charges q1 and q2, separated by a distance r.
The Coulomb force is given by
k=1/40, where 0= 8.85x10-12 C2/Nm2 is the permittivity of free space (vacuum).
(k = 9x109 Nm2/C2).
The potential energy U of two charges is defined as the work required to bring the two
charges to a distance r apart if they are initially infinitely far away:
The potential energy is negative when the force is attractive (q1 and q2 have opposite signs),
and positive when the force is repulsive.
The potential energy for the simple Coulomb interaction falls off rather gradually, as 1/r,
and hence it is also referred to as a long-range interaction.
Dielectric Constant
Dielectric constant () depends on how easy the molecules in the environment
are polarized.
In completely unresponsive medium (vacuum =1), U ~ 30 kBT for two charges
q1 = q2 = e- (1.6x10-19C) separated by r ~ 2nm.
In strongly responsive media (In water, =80) polarization of molecules
counteracts the electric field. The Coulomb interactions are reduced by a factor
which is equal to the .
Water molecules have a permanent dipole; they align in the direction of the
local electric field and effectively screen the charges. Therefore, in water, U ~
0.4 kBT for two ions carrying unit charges separated by ~ 2 nm.
Ion in water does a considerable amount of work
on the surrounding water molecules by forcing
them to rotate and orient their dipoles.
Dielectric Constant
In hydrocarbon, =2, this makes electrostatic interactions within proteins and
membranes very strong.
Complications: spatial variation in  inside biomolecules prevent simple use of Coulomb
potential. (solution – employ Poisson or Laplace equations with boundary conditions
given by geometry of system)
We will deal with simple planar, spherical or cylindrical systems.
Electrostatic self energy:
The energy of placing ion in a dielectric medium. Consider the work done to
bring a small increment of charge q’ to the surface of a sphere with radius r,
already carrying a charge, q’
This charging process can be integrated to get the total work done, starting with
charge = 0 and final charge = q.
Find a difference between the electrostatic self-energy for ion (Na+, r=0.95Å) in two
media (water and hydrocarbon(membrane)) and estimate the free energy of transfer of
Na+ ions between two media. Give an answer in Joule, kBT (at Room Temperature) and
kcal/mole.
Home work
1. Find a difference between the electrostatic self-energy for ion (Na+, r=0.95Å)
in two media (water and hydrocarbon(membrane)) and estimate the free
energy of transfer of Na+ ions between two media. Give an answer in Joule,
kBT (at Room Temperature) and kcal/mole.
Using G number you found estimate a partition coefficient of Na+ ion in water
versus hydrocarbon (model for membrane) media.
Partition coefficient is the ratio of concentrations of a compound in the two
phases of a mixture of two immiscible solvents at equilibrium.
2. Estimate the value of the bonding energy between the Na+ and Cl- in NaCl.
Consider interaction as pure ionic (Coulomb law).
3. Nelson page 31 problem 1.3 Metabolism
Suggested reading:
Chapter 2.1 (till 2.1.4) Roland Glaser “ Biophysics”