Biophysics of macromolecules
Department of Biophysics, University of Pécs
Macromolecules are HUGE molecules
DNA double helixDNA strand released from bacteriophage
Biological macromolecules are EXCITING molecules
Structural model of hemoglobin
Newly synthesized protein(silk fibroin)
Amount of macromolecules in the cell, by weight, is large
30 % otherchemicals
70 %Water
Bacterial cell
Ions, small molecules (4%)
Phospholipids (2%)DNA (1%)
RNA (6%)
Proteins 15%)
Polysaccharides (2%)
MACROMOLECULES
Biophysics of macromolecules
1. Biological macromolecules - polymers
2. Polymerization
3. Equilibrium shape of polymers
4. Polymer mechanics
5. Studying biopolymers
Biological macromolecules: biopolymers
Polymers:Chains constructed of similar building blocks (monomers, subunits)Number of monomers: N>>1; Typically, N~102-104, But DNA: N~109-1010
Biopolymer Subunit Bond
Protein Amino acid Covalent (peptide bond)
Nucleic acid(RNA, DNA)
Nucleotide (CTUGA)
Covalent (phosphodiesther)
Polysaccharide(e.g., glycogen)
Sugar(e.g., glucose)
Covalent(e.g., -glycosidic)
Protein polymer(e.g., microtubule)
Protein(e.g., tubulin)
Secondary
Formation of biopolymers: polymerization
Equilibrium
Lag
Growth(Log)
Time
Polymerquantity
Covalent polymers:Enzyme-catalyzed process, from high-energy subunits
Non-covalent polymers:Spontaneous, concentration-driven processDynamic equilibrium
Shape of biopolymers
The polymer chain is not rigid; due to its flexibility, it forms loose, random 3D networkBasic flexibility mechanisms: 1. Rotation around C-C bonds, 2. Rigid segments connected with flexible (frictionless) joints (FJC), 3. Torsion of bonds (WLC).
2 31
1. Linear
2. Branched
3. Circular
Polymer shape resembles random walk
(Brownian motion)
R
r1
rN
ri = elementary vectorR = ”end-to-end” distance
= correlation length
N = number of elementary vectorsNl = L = contour length
ri
l
R2 Nl2 Ll“Square-root law”:
N.B.: Diffusion!<x2>=2D
<x2> = mean squared displacementD = diffusion constant = diffusion time (duration of observation)
Biopolymer mechanics
Force (F)
Correlation length
End-to-end distance (R)
Elasticity of the entropic chainEntropic elasticity
The polymer chain exhibits thermallydriven bending motions
configurational entropy increases (orientation entropy of elementary vectors).
Fl
kBT~R
L
F = forcel = correlation length (persistence length, measure of bending rigidity)kB = Boltzmann’s constantT = absolute temperatureL = contour lengthR/L = relative extension
Biopolymer elasticity
Lp>>LRigid chain
Lp~L
Semiflexiblechain
Lp<<L
Flexiblechain
Lp = persistence length (measure of bending rigidity)L = contour length
Microtubule
Actin filament
Titin molecule
Mechanical investigation of biopolymersGrabbing single molecules with optical tweezers
F F
Microscope objective
Laser
Refractilemicrobead
Scattering force(light pressure)
Gradient force
EQUILIBRIUM
StarTrek Enterprise spaceship trapped by the tractor beam
Tying a knot on a single biopolymer!(without releasing its ends!)
Actin filamentmanipulation
Arai et al. Nature 399, 446, 1999.
Stretching a DNA molecule with force-measuring optical tweezers
Lasertrap
Moveablemicropipette
Latexbead
DNA molecule
Laserfocus
Laser #1
Laser #2
MCP CCDFluor.
CCD
Fluor.Exc.Illuminati
on
Dual-beam optical tweezers setup
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