Polyvalency and Superselective Recognition Flashcards
Molecular Interactions
Rate Constants
- association rate constant, kon
- dissociation rate constant, koff
- both in units of inverse seconds
Molecular Interactions
Equilibrium Binding Constants
-association constant, Ka
-dissociation constant, Kd
Kd = koff/kon = 1/Ka
-with Kd in M units
Molecular Interactions
Binding Free Energy
ΔG / kbT = ln[Kd/ρo]
- where ΔG is the binding free energy
- the LHS is the binding free energy normalised by the thermal energy
- and Kd is the associatoin constant
- and ρo is the reference concentration equal to 1M
Molecular Interactions
Very Weak Reactions Biological Systems
Kd = 10^(-3) M ΔG = -6.9 kbT
Molecular Interactions
Weak Reactions Biological Systems
Kd = 10^(-6) M ΔG = -13.8 kbT
Molecular Interactions
Strong Reactions Biological Systems
Kd = 10^(-9) M ΔG = -20.7 kbT
Molecular Interactions
Very Strong Reactions Biological Systems
Kd = 10^(-12) M ΔG = -27.6 kbT
Multivalency
Definition
- interaction between multivalent binding partners
- multivalency is typically used for n>1 but less than 10
- polyvalency is typically used for n»1
Affinity
Definition
-strength of monovalent interaction
Kd,mono
ΔGmono
Avidity
Definition
-strength of multivalent interaction
Kd,multi
ΔGmulti
Multivalent Interactions in Biology
- multivalent interactions are ubiquitous in biology
- polyvalent interactions are important for cell-cell, cell-ECM and cell-pathogen recognition
- frequently either ligands or receptors are carbohydrates
Monovalent vs Multivalent Interactions
Strength
- individual ligand-recpetor interactions are typically weak (low affinity)
- multivalent interactions are typically very strong (high avidity from combining many low affinity interactions)
Monovalent vs Multivalent Interactions
Phenomena
- new phenomena also emerge in multivalent interactions which are not seen in simple monovalent interactions
- individual ligand-recpetor interactions can break and reform allowing e.g. cell to crawl across cell surface (dynamic)
- mechanically multivalent interactions are weak since each individual weak bond can just be broken separately, like ripping velcro
- multivalency enhances selectivity since not only ligand shape but also distance between ligands is important
Cooperativity Parameter
Definition
β = ΔGavg,multi / ΔGmono
-where ΔGavg,multi is the average free energy per bond for a multivalent interaction and ΔGmono is the free energy for a single interaction
Cooperativity Parameter
Values
β = 1 : additive interaction (no cooperation)
β < 1 : interfering interaction (negative cooperation)
β > 1 : synergestic interaction (positive interaction)
ΔG for Multivalent Interactions
ΔGn,multi = n * ΔGavg,multi
= β * n ΔGmono
Kd for Multivalent Interactions
Kd,n,multi = [Kd,avg,multi]^n
= [Kd,mono]^βn
Cooperativity Parameter
Biological Systems
- purely additive (β = 1) interactions are rare in biological systems
- positive cooperation is very rare in multivalent interactions
- negative cooperation is the norm in multivalent biological interactions
Factors Determining Avidity
- the multiplicity of the interaction is the main driver for avidity
- there are also scaffold interactions which
Positive Scaffold Effects
- multivalent ligands lose less translational and rotational entropy than several monovalent interactions
- combinatorial entropy favours multivalent interactions (many different ways for single probe to bind to target)
Negative Scaffold Effects
- strain on bonds decreases binding strength
- reduced scaffold conformational entropy favours multivalent interactions
Net Scaffold Effects
- as a whole scaffold interactions interfere with multivalent binding (β < 1) but the balance of effects varys significantly from one scaffold to another
- scaffold effects are interdependent
- e.g. if you try to reduce strain by increasing flexibility of scaffold you increase the decrease in conformational entropy and vice versa
- there is no universal rule to predict advidity from affinity
Selectivity
Definition
-ability to sharply discriminate surfaces by the type of their receptors
Superselectivity
Definition
-ability to sharply discriminate surfaces by density of receptors
Superselectivity Parameter
-parameter, α, is the measure of quality of superselectivity, superselective if α > 1
α = d ln(Γp) / d ln(Γr)
Boltzmann Law
S = kb ln[Ω]
-where S is entropy and Ω is the number of microstates
Combinatorial Entropy
Multivalent Polymer Bound to Multivalent Surface
- polymer size determines the volume of the unit cell
- assume an ideal gas of ligands in the unit cell so they can move freely within the cell
- the base of the cell is the receptor surface
Combinatorial Entropy
Single Bond Binding Free Energy
F = kb T ln[Kd,mono Na a³]
-where a is the length of the unit cell
Combinatorial Entropy
Activity of Polymers in Solution
z = ρ Na a³
-where ρ is the molar concentration and a is the width of the unit cell
Combinatorial Entropy
Generalised Langmuir Isotherm
-average number of bound polymers per cell is given by:
θ = zq / [1 + zq]
Superselective Binding
- combinatorial entropy is the main driver of superselective binding
- universal effect as long as interactions are ‘disordered’ such that bonds can form in many combinations
Simple Scaling
-in the limit of weak binding: nr exp(-F/kbT) < < 1 => e^x = 1 + x -simple scaling with: χ = nr nl Kd^(-1) -this enables rational design of superselective probes by simple tuning of the threshold density
Superselectivity Examples
Hyaluronan
- extracellular HA polymers recognise cells superselectivity
- CD44 is the best known HA receptor e.g. on immune anc cancer cells
- LYVE-1 is a receptor on the surface of lymphatic cells crucial to the immune response
Superselectivity Examples
Viruses
- express many copies of the same ligand to bind to the host
- likely that selection of a suitable host is influenced by superselective binding
- the outer shell of the virus is solid so ligands can’t move relative to each other, in this case superselectivity comes from the flexibility of the target cell membrane and the movement of the receptors within that membrane
Superselectivity Examples
Protein Annexin A5
- forms 2D crystals on cel membranes to stabilise damaged membranes and aid repair
- it requires high Ca2+ as a co-factor for binding
- usually there is a low concentration of Ca2+ inside the cell and a high concentration ouside, anx A5 is produced in the cell but remains in solution in the cytoplasm
- when the cell membrane is damaged, Ca2+ can move in and concentration inside the cell gets high causing the Anx A5 to move out of solution and binds to binding lipids on the inside surface of the membrane to stabilise it
Host-Guest Model
- chemistry enables surface and probe design
- planar support surface, a self-assembled monolayer
- the guest ‘receptor’ molecules are attached to the support surface
- the HA polymer is modelled as a chain with host molecules on it which are complimentary to the guest molecules
Techniques to Quantify How Much Polymer Binds to Surface
- usually need to use a whole set of techniques:
- -quartz crystal microbalance
- -spectroscopic ellipsometry
- -contact angle geometry
- -electrochemistry
- to find:
- -how many guest there are on the surface
- -how mant host on the polymer
- -how much polymer binds
Ideal Gas Model
Evidence
-experimental data confirms the simple ideal gas model focussing on the universal effect of combinatorial entropy can make quanitative predictions about superselective binding
-plotting ln(probe density) against ln(receptor/guest density) gives:
α ~ 3 > 1
=> superselectivity
Ideal Gas Model
Cons
-neglects any correlations of ligands as imposed by the polymer backbone
Soft Blob Model
- computer simulations aid understanding
- the soft blob model explicitly considers polymeric properties of the scaffold
- it shows that:
- -connectivity of polymer does not effect fundamental behaviour of probe
- -but does enhnce quality of superselectivity moderately
- predicts α even higher than 3 not seen experimentally most likely because in experiment you have a large distribution of polymer sizes
Insights into Tuning Biological Interactions
Overview
- HA receptor interactions works as on/off switches (small changes -> big effects)
- biology has many biochemical knobs to turn to switch between binding and non-binding
- essentially have different flavours of both HA and cell surface receptors
- changes in the properties / flavour of either HA or the cell surface recpetors can move the response above and below the threshold density
Insights into Tuning Biological Interactions
HA ‘flavour’ in ECM
- HA size
- HA cross-linking and occupancy with proteoglycan
- debris of degraded HA competes with HA polymers
Insights into Tuning Biological Interactions
Cell Surface Receptor ‘flavour’
- receptor density and local clustering
- modification of affinity (e.g. by receptor glycosylation)
Practical Applications of Superselectivity
- the universal nature of combinatorial entropy effects provides opportunities ofr development and rational design of superselective nanoprobes to target biological surfaces (membranes) or 3D matrices (tissues)
- -enhanced imagin contrast (e.g. to aid cancer surgery)
- -cell isolation / purification
- targeted drug delivery
Rational Design
- individual interactions should be weak (low affinity)
- multivalency is key (nl > > 1)
- simple scaling facilitates rational design (χ ∝ Γr nl Kd^(-1) )
