- 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

Modelling Proteins Flashcards by Sophie Wilkinson

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

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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

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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

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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

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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

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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

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Mechanical Stability of Alpha Helices

alpha helices tend to be mechanically weaker

- this is because helices can unfold in a step-wise sequential manner

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Force Unisotropy

-the direction of applied force relative to the topology of the secondary structure determines the mechanical strength of the protein

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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

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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

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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

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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

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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)

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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

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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

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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