Modelling Proteins Flashcards
What type of polymer are proteins?
- linear, random heteropolymers composed of amino acids
- rather than being a random coil, many proteins have a well defined structure
- complex interplay between polymer rigidity, chain entropy, monomer-monomer interactions and monomer-solvent interactions
Single Molecule Force Spectroscopy of Proteins
Intramolecular Forces
- polyprotein chain attached to gold substrate at on end and pointed end of cantilever at the other
- laser bounced off of cantilever to measure the force exerted
- cantilever pulls on the polyprotein chain causing the domains to unravel one by one
- in a chain of different domains, the weakest always break first
Single Molecule Force Spectroscopy of Proteins
Intermolecular Forces
- one molecule attached to the substrate
- other molecule attached to the cantilever
- lower the cantilever towards the other molecule and measure the force on the cantilever
Other SMFS Techniques
Optical Tweezers
- molecules tethered to a planar surface and beads held by an optical trap
- distance changes are obtained from the motion of the bead
- forces obtained from the displacement of the bead from the centre of the trap
Other SMFS Techniques
Magnetic Tweezers
- molecules tethered to a planar surface and magnetic bead held by magnetic trap
- distance changes obtained from the motion of the bead
- forces set by the strength of the magnetic field
Mechanical Stability of Beta Sheets
- beta sheet proteins tend to be mechanically strong
- this is because shearing apart of two beta sheets requires simultaneous rupture of the non-covalent interactions along the length of the sheet
Mechanical Stability of Alpha Helices
- alpha helices tend to be mechanically weaker
- this is because helices can unfold in a step-wise sequential manner
Force Unisotropy
-the direction of applied force relative to the topology of the secondary structure determines the mechanical strength of the protein
Mechanical Clamp
- some beta sheet proteins have mechanical clamps
- a series of hydrogen bonds along the shearing interface
- it is the breakage of these bonds that is the rate limiting step in protein unfolding
Freely Jointed Chain Model
Define Parameters
-polymer is a chain of N perfectly rigid segments of length b, the Kuhn length
-no restriction on the angles between adjacent segments, no energy is required to change the angles
-no interactions between segments (except the end-to-end connectivity)
-contour length:
Lc = bN
-where N is the number of segments
Freely Jointed Chain Model
Forces
-tensile force tends to align the segments in the direction of the force
-opposing the stretching is the tendency of the chain to maximise its entropy
-extension corresponds to the equilibrium point between the external force and the entropic elastic force of the chain
-at low forces the force-extension relationship is give by:
F = 3kbT/b * x/Lc
-the FJC describes a Hookian spring relationship with a spring constant kb*T/b between the unfolding force and the extension of a polymer at low force
-the spring constant is proportional to the temperature reflecting the entropic origin of chain elasticity
Freely Jointed Chain Model
Limitations
- the FJC model is good at low and high forces but not in between
- this is because the FJC model simplifies the description of the polymer molecule:
- each Kuhn segment has a fixed length, is unstretchable and completely straight
- -no thermal fluctuations away from the straight line are allowed
Worm-Like Chain Model
Description
-the WLC model describes the behaviour of semi-flexible polymers
-the entropic elasticity of the polymer involves small deviations of the molecular axis due to thermal fluctuations
-the direction of the chain is correlated over a distance, the persistence length Lp
-the persistence length Lp quantifies the stiffness of the chain:
cos(β) = e^(-L/Lp)
Worm-Like Chain Model
Forces
- an interpolation formula has been numerically determined to describe the relationship between the applied tensile force, F, and the extension x of the polymer
- for small forces (and small extensions) the WLC model behaves like a Hookian spring with a linear relationship between force and extension
What can we learn using single molecule force spectroscopy?
- a protein’s mechanical stability is determined by intramolecular interactions and the direction of the applied force
- we can use polymer models to examine force-extension behaviour
What can we learn using single molecule force spectroscopy?
- a protein’s mechanical stability is determined by intramolecular interactions
- a protein’s mechanical stability is determined by the direction of the applied force
- we can use polymer models to examine force-extension behaviour
Unfolding and Unbinding
Definitions
- unfolding: disrupting intra-molecular bonds
- unbinding: disrupting inter-molecular bonds
Protein Unfolding/Unbinding
Description
-protein mechanical unfolding/unbinding are stochastic processes described by a lifetime
Effect of Force on Bond Lifetime
- force acts as a denaturant by diminishing activation barriers to unfolding/unbinding
- an external force tilts the energy landscape by F(x-x0)
Single Bond Lifetime Without Force Present
Arrhenius Expression
τo = 1/vo * e^(ΔG/kb*T)
-where vo is the characteristic vibrational frequency
Unbinding Mechanics of Multiple Bonds
Unfolding
- disrupting intra-molecular bonds
- two beta sheets hydrogen bonded together
- force being applied parallel to the clamp in opposite directions at opposite ends of the sheet on each chain
- bonds in parallel
Unbinding Mechanics of Multiple Bonds
Unbinding
- disrupting inter-molecular bonds
- two beta sheets hydrogen bonded together
- force applied perpendicular to the sheets at the same end
- zipper arrangement
Unbinding Mechanics of Multiple Bonds
Zipper Arrangement
-bonds break in sequence at random times from first to last
-assuming individual bonds break independently, the total lifetime is the sum of the individual bond lifetimes
-for N identical bonds:
τ1 = τo * e^(-FΔxu/kb*T)
-so
τN,zipper = τ1 * N
Unbinding Mechanics of Multiple Bonds
Bonds in Parallel
-bonds break one by one in random order and the external force is shared amongst the remaining bonds
-give the first bond to break index N and the last bond to break index 1
then, for the ith bond to break, the force is F/I and the lifetime needs to be scaled by 1/I:
τ1 = τo/i * e^(-FΔxu/ikbT)
-so:
τn,parallel =
τo * Σ[ 1/i e^(-FΔxu/kbT)]
= Σ[ 1/i * τ1^(1/I)]
-where the sum is taken from i=1 to i=N
Catch Bonds
Definition
- a type of non-covalent bond whose dissociation lifetime increases with the tensile force applied
- conceptually similar to a chinease finger trap
- the opposite of what we would normally expect, usually increasing tensile force would decrease bond lifetime
Catch Bonds
One-State Two-Path Model
- an alternative dissociation pathway is introduced along which the system can dissociate against low external forces resulting in a tightened bond for larger forces
- as a certain critical force the system reaches maximum stability and switches to the slip dissociation path
Catch Bonds
Two-State Two-Path Model
- two distinct bound states, B1 and B2
- both states individually obey slip bond characteristic and dissociation can occur from either of the two state depending on the external force
- the relative occupancy of the two bound states is force dependent
- at low force the system dissociates directly from state B1
- at high force the system crosses to B2 and then dissociates
- this can be achieved through spatially separated bound states or through a force-induced switch in protein molecular conformation from B1 to B2
What are three examples of where catch bonds are found?
- cell adhesive molecules
- intracellular bonds exposed to force
- bacterial adhesive molecules
Protein Folding
Levinthal’s Paradox
-Levinthal pointed out that since each amino acid has three accessible conformations, even for a short polypeptide chain of 100 amino acids the protein would have to sample 3^100 conformations in its search for a single native conformation
-since it takes 10^(-13)s for a chemical bond to to rotate it would take 10^27 years to do this
-in reality polypeptide chains fold into their unique 3D structures in a matter of seconds by a random search of the available conformation space
=>
-there must be defined pathways for a protein to old
What are the three conceptual models of protein folding?
- framework model
- nucleation and growth model
- hydrophobic collapse model
Conceptual Models of Protein Folding
Framework Model
- sequential formation of native-like micro domains (alpha helice, beta sheets etc.)
- these small secondary structural units are formed locally during the initial stage of protein folding and come together by random diffusion and collision
Conceptual Models of Protein Folding
Nucleation and Growth Model
- a few key residues of the polypeptide chain form a local nucleus of secondary structure in the rate-limiting step of folding
- around this nucleus, the whole native structure develops as in a crystallisation growth process
Conceptual Models of Protein Folding
Hydrophobic Collapse Model
- folding begins by an initial clustering of hydrophobic residue chains which prefer to be excluded from an aqueous environment
- the clustering of hydrophobic residues is expected to be non-specific and happen rapidly
- the formation of an ensemble of collapsed structures would rapidly reduce the available conformational search-space
Which is currently the best model for protein folding?
-hydrophobic collapse model
Energy Landscape Theory
- statistical mechanics based models postulate that protein molecules traverse a funnel-shaped energy landscape during folding
- and the protein folding pathways more closely resemble funnels than random diffusion in the configuration space
- a folding funnel is a plot of the free energy against configurational entropy
- an individual folding trajectory is envisaged for each polypeptide chain traversing down the folding funnel
Protein Folding and Force
-protein folding can be impeded by force
Force on Bonds in a Linear Chain of Protein Domains
- in a chain of N proteins, the force on each bond is still F
- only one bond has to break for the entire chain to break
- there are N possible breaking points each with the same breaking probability as a single bond
- the probability of breakage is therefore N times greater than a single bond
