proteins —polymer molecules
TRANSCRIPT
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Proteins —polymer molecules,folded in complex structures
Konstantin PopovDepartment of Biochemistry and
Biophysics
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Outline
• General aspects of polymer theory• Size and persistent length of ideal linear polymer chain• Volume interactions and Coil-Globule transition• Electrostatic and hydrophobic interactions
• Branched polymers as a next step towards proteins
• Proteins as extremely complicated and well designed polymers
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Model of ideal polymer chainIn 1920 Hermann Staudinger proposed existence of polymer chains — long chains of atoms covalently bounded one to another and called them macromolecules.
Examples:
poly(ethylene)
poly(vinyl chloride)
Polymers are long molecules, N>>1:
• Synthetic polymers N usually 102-104
• Biopolymers N up to 109
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Model of ideal polymer chainIdeal chain — model where monomer units do not directly interact if they are not neighbors
along the chain.
Simplest example:
Freely jointed chain. No interactions, no correlations.
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Flexibility of ideal polymer chainRectilinear conformation of a poly(ethylene) chain, shown on the picture, corresponds to the minimum of the potential energy. All monomer units are in trans-position. This conformation would be an equilibrium only at T = 0.
Energy
Thermal fluctuation will cause deviations from liner conformation. Probability to find particularconformation can be estimated according to Boltzmann law:
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Flexibility of ideal polymer chainPersistent length — roughly a maximum chain section remaining straight. At greater lengths,
bending fluctuations destroy the memory of the chain direction.
For many polymer chains it is shown that :
Internal rotational modelPersistent chain model
Where lp — persistent length of the polymer.
Correlations decay exponentially along the chain.
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Ideal polymer chain summary
• Monomers are connected into a chain, thus restricted in spatial movement. that makes polymer chains “poor” in entropy.
• Polymers are long chains: N>>1.
• Size of ideal polymer chain — polymer coil, is given by the universal expression that doesn’t depend on selected model:
Where a is monomers size and N is the number of monomer units.
• Ideal are flexible molecules. Flexibility is thermally driven. Directional correlation betweentwo segments decay exponentially with increasing the distance separating them.
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Model of real polymer chainConsider polymer chain with interacting monomers immersed into a solvent.
Interaction examples:
• Excluded volume interactions• Hydrophobic/hydrophilic interactions• Electrostatic interactions• Hydrogen bonds
These interactions significantly change conformational behavior of macromolecules.
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Solvent quality for real polymer chain
Typical potential between two monomersin the absence of solvent:
Presence of solvent can change the shapeof the potential:
Effective repulsion or attraction.
Solvent effect on polymer chain size:
• Effective repulsion will result in swelling of polymer coil
• Effective attraction will result in collapse of polymer coil
— good solvent
— bad solvent
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Solvent quality and temperatureThe free energy of polymer chain is a sum of energetic and entropic contribution:
At U = 0 we have ideal chain with
Taking into account low concentration of monomers in ideal coil we expand interaction energy in a power series of number of particles in a unit volume(virial expansion):
, where
describes pair interaction between monomers.
It can be seen:• At , B=0 and chain behaves as ideal
• At , B>0, repulsion dominate, chain swells
• At , B<0, attractions dominate, chain collapse
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Coil-Globule transitionSi
ze o
f pol
ymer
cha
in
Temperature, T
globule
coil
A globule-coil transition point lies around Theta point, and it is determined by the balancebetween entropy gain caused by chain extension and energy lose due to reducing attractions.
Bad solvent -solvent Good solvent
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Volume interactions summary
• Presence of solvent can introduce effective interaction between monomers
• Solvent quality is temperature dependent
• Size of the globule in the bad solvent is given by:
• Size of the ideal coil in the solvent is given by:
• Size of the swollen coil in the bad solvent is given by:
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Electrostatic interactions
Screened Coulomb repulsion.
• Presence of strong electrostatic interactions increase the size of the chain
• Conformation of charged macromolecule depends mostly on fraction of chargedmonomers and low molecular-weight salt concentration
++ +
+
+
+
–
––
–
–
Where rD is the screening (Debye) radius, which depends on temperature and low molecularsalt concentration.
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Hydrophobic interactions
Two non polar molecule immersed into a polar solvent (water).
Gibbs free energy:
— Can be either negative or positive, depending on the strength of dipole-dipole interactions
— Positive due to loss of the solvent structure
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Linear chain summary–
+
+
+
+
+ –
–
– –
–
––
• Connectivity into the chain• Hydrophobic core• Stretched electrostatic part• Swollen hydrophilic loops
All these leads to micro-phase separation phenomenon in polymer physics
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Outline
• General aspects of polymer theory• Size and persistent length of ideal linear polymer chain• Volume interactions and Coil-Globule transition• Electrostatic and hydrophobic interactions
• Branched polymers as a next step towards proteins
• Proteins as extremely complicated and well designed polymers
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Comb-like macromolecules
• Each side chain has properties of a single polymer chain, discussed above• Chains grafted on the backbone that make entropic effects very strong • Properties of of each grafted chain amplified on the scale of entire macromolecule
Description of such molecules is much more complicated compare to linear chains
Backbone Side chains
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Outline
• General aspects of polymer theory• Size and persistent length of ideal linear polymer chain• Volume interactions and Coil-Globule transition• Electrostatic and hydrophobic interactions
• Branched polymers as a next step towards proteins
• Proteins as extremely complicated and well designed polymers
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ProteinsImagine now of branched polymer which
• Has side chains of extremely complicated nature• Has to fold into preprogrammed structure for exact amount of time• Has to function in a very specific biological condition • Can not missfold• Has to interact with other molecule in extremely crowded environment
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Proteins fold into specific structures
Taken from wiki
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Proteins fold into specific structures
Simple homo-polymer like protein. Side chains glycine.
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Proteins fold into specific structuresSide chains are random amino acids:
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Proteins fold into specific structuresReal protein:
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Proteins fold into specific structures
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Thank you.