Biophysics of macromolecules Department of Biophysics, University of Pécs

Macromolecules are HUGE molecules DNA double helix DNA 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 % other chemicals 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~ , But DNA: N~ BiopolymerSubunitBond ProteinAmino acidCovalent (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 Polymer quantity Covalent polymers: Enzyme-catalyzed process, from high-energy subunits Non-covalent polymers: Spontaneous, concentration-driven process Dynamic equilibrium

Shape of biopolymers The polymer chain is not rigid; due to its flexibility, it forms loose, random 3D network Basic flexibility mechanisms: 1. Rotation around C-C bonds, 2. Rigid segments connected with flexible (frictionless) joints (FJC), 3. Torsion of bonds (WLC) Linear 2. Branched 3. Circular

Polymer shape resembles random walk (Brownian motion) R r 1 r N r i = elementary vector R = ”end-to-end” distance = correlation length N = number of elementary vectors Nl = L = contour length “Square-root law”: N.B.: Diffusion! =2D  = mean squared displacement D = diffusion constant  = diffusion time (duration of observation)

Biopolymer mechanics Force (F) Correlation length End-to-end distance (R) Elasticity of the entropic chain Entropic elasticity The polymer chain exhibits thermally driven bending motions configurational entropy increases (orientation entropy of elementary vectors). F = force l = correlation length (persistence length, measure of bending rigidity) k B = Boltzmann’s constant T = absolute temperature L = contour length R/L = relative extension

Biopolymer elasticity L p >>L Rigid chain Lp~LLp~L Semiflexible chain L p <<L Flexible chain L p = persistence length (measure of bending rigidity) L = contour length Microtubule Actin filament Titin molecule

Mechanical investigation of biopolymers Grabbing single molecules with optical tweezers F F Microscope objective Laser Refractile microbead 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 filament manipulation Arai et al. Nature 399, 446, 1999.

Stretching a DNA molecule with force-measuring optical tweezers Laser trap Moveable micropipette Latex bead DNA molecule Laser focus Laser #1Laser #2 MCP CCD Fluor. CCD Fluor. Exc. Illumination Dual-beam optical tweezers setup