Polymerization of Cytoskeletal Filaments Rami Amro Instructor: Dr.Alexander Neiman
properties Actin filaments range in length: ~35 nm in Cortex of erythrocytes and other cells 10-100 nm in the stereocilia of hair cells, the sensory receptors of the vertebrate inner ear. Microtubules: 1um in mitotic spindle of the yeast. :100um in axons of rat neurons :>1mm in insect sperm Intermediate filaments are in micron range. ** cytoskeletal filaments span the scale from molecular to cellular.
Einstein Polymer: single-stranded filament(hill,1987) Average polymer is few subunits long. Subunit:: is the building block It takes two forms monomeric or polymeric Actin building block is 45 KDa actin monomer Tubulin it is dimer of alpha and beta tubulin subunits.
Cont. Properties Cytoskeletal filaments contain tens tens of thousands of protein subunits; proteins that form these filamens are few to few tens of nanometer long. Such long filaments needs special structural adaptation. Filaments must be multistranded, since single stranded filaments are easy to break in the middle.
The shrinkage and elongation of these filaments happens by adding or subtracting of subunits at both ends of the filaments. for the sake of simple polymerization process, the dissociation constant is defined interms of the concentration of the subunits: A + A A n [ An ].[ A1 ] [ A ] n+ 1 kon 1 k n+ 1 off Koff = K = ; n 1 K on
Disscociation constant DC.. K = Dissociation Association rate constant(k ) off rate constant(k ) on The equilibrium concentration of n-mer doesn t depend doesn t depend on the individual rates. Einstein Model is not accurate, since the assumption that all reactions have the same D.C. is not accurate.
Einstein Polymer K = ΔG exp( T k B ) moles/liter where ΔG is the free energy change under standard conditions (1M), it is also the sum of potential energy(bond formation), and entropic energy (loss of rotational and translational entropy)
Dissociation constant is smaller for dimers than polymers by one order of magnitude. The entropic effect influencing the nucleation not the growth. Single-Stranded filaments are short the length of the polymers at equilibrium is given by the exponential distribution [ A ] = Kexp( n/ n ) n [ At ] navg, where [ At ] is the total concentration of the subunits. K shortcoming:: if [ A] = 100 K, then n = 10 subunits!!! t Ex: for actin [ A] = 200 μm, K 0.1 μm still short length!!! t avg
Multistranded filaments are long.
and so there are two different nuclei A, and A, and three different D.Cs K,K, 1 2 1 2 * ** 2 2 K1 [ At ] navg ;[ At ] K K K Ex: K 1 μm, and K K 0.1 M,[ A] 10μM n 1000 2.75μM avg K t
Multistranded Filametns Grow and shrink at their ends The rate of elongation by subunits is given by: dn = Kon[ A1] Koff where [ A1] is monomer Conc. dt ; One Capped end. * annealing reaction: dn = kon[ A1 ] 2 kon,2[ A2 ] +... + mkon, m[ Am ] +... dt 1 monomer, 2 dimer,m m-mers length dn if k = k = k m[ A ] = k [ A] on, m on on m on t dt m= 1 since, in general [ A] > [ A], then elongation is not necessarly an end propety. t 1
Notes: when m is large, the translational and rotational diffusion becomes very slow, which clearly shown by the Diffusion coefficient: D ln(m)/m ; Translational. D 1/m; axial rotation. 3 D ln(m)/m ;perpendicular rotation << k M s 6 1 1 kon, annealing on, monomer 10. ; for large m. [A ] k anealing [A ] K n 5 and since 10 has very limitid 1 1 role in the growth reaction
Binding Energies and loss of Entropy the standard free energy asscociated with the individual bond is: Δ G =Δ G +ΔG (i=1,2) i i i s ΔG the intrinsic binding energy (-ve) ΔG s the entropic energy(+ve). since part of the entropic energy loss is compensated by the vibrational entropy when the subunit attached to two sites(two-stranded); then an interction entropic term( ΔG ) should apear, and so; Δ G =Δ G +Δ G +Δ G +Δ G =Δ G +ΔG Δ G +ΔG 1 2 s 12 1 2 s 12 and so the D. C. is calculated as: ΔG Δ G + ΔG Δ G + ΔGs K=exp( )=K K exp( ); K exp( ) k T k T k T s 12 i 1 2 i = B B B 12
The entropy interaction term ( ΔG ΔG ) "in many texts usually ignored" s B 12 Quantum Mechanically 40k T. Experimentally 10k B B T. " based on polymerization of tubulin,actin" 10k T is more likely true ; it gives the the right length of filaments in mico-range. why 10k T? B Consider : if ( ΔG Δ G ) = 0; for K 1μM, K = K 1mM length 100 < 1000 s 12 1 2 ΔG Δ G =Δ G = T = length too 6 6 if ( s 12) s 40k B ; then K1 K2 10 M 3 10 long ( ΔG Δ G ) 9k T; then K 1μM, K = K 0.1 M,[ A] = 10K length 1000 s 12 B 1 2 1 c
Conclusions: Multistranded filaments are much longer than single-stranded filaments. Single stranded filaments change length by annealing and breaking subunits. Monomers are the most contributor too the growth and breakage.