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