Proteinigand Interactions Are Responsible for Signal ransduction ypes of Interactions: 1. ProteinProtein 2. ProteinDNA (RNA) 3. Proteinsmall molecule
Dynamic Proteinigand Interaction Dynamic interaction between Protein (, target) and igand () assumes equilibrium k on + koff he equilibrium binding constant is defined as: [] eq[] eq k he equilibrium dissociation constant is defined as: off Kd = = [ ] eq kon where [ ] eq, [] eq and [] eq are equilibrium concentrations of the complex, free protein and free ligand respectively. It is obvious that K b = K d 1 [ ] eq = = [] [] K b (K d ) can be found in equilibrium experiments by measuring somehow one of the following ratios: [] eq [] eq or [ ] [ ] eq at different [] 0 or [] 0 as we demonstrated with fluorescence anisotropy eq K b k k on eq eq off
Equilibrium Constant Measurements Methods for equilibrium constant measurements: 1. Fluorescence Fluorescence anisotropy (limitation small fluorophore) Fluorescence (absorbance) spectrum shift due to the change of microenvironment 2. Capillary Electrophoresis Capillary affinity electrophoresis (CAE) NonEquilibrium Capillary Electrophoresis of Equilibrium Mixtures (NECEEM) 3. Molecular Electrooptics 4. Surface plasmon resonance
OFF and ON Rate Constants: k off and k on o understand the DYNAMICS of interactions (how fast the complex forms and how fast it decays we need to know the rate constants of complex decay and formation (OFF and ONN constants): k off and k on. he OFF constant may be measured by: NECEEM Surface plasmon resonance he ON constant can be determined by 1. Stoppedflow spectroscopic measurements 2. Sweeping Capillary Electrophoresis (SweepCE)
Fluorescence (absorbance) spectrum shift due to the change of microenvironment Assume that changes its fluorescence spectrum upon binding to [ ] [] 0 eq [] 0 Fluorescence intensity at a fixed wavelength λ is an extensive (additive) function: [] [ ] I I I tot eq λ = λ + λ [] 0 [] 0 eq Absolute fluorescence intensities of pure and
Capillary affinity electrophoresis (CAE) Assume that: 1. igand is detected (by absorbance or fluorescence). 2. Free Protein () and igand () have different migration times 3. will have intermediate migration time Add protein to the run buffer at different concentrations Observe migration time shift as a function of [] 0. he following are the results of three different experiments: [] eq /[] 0 = 1 ([] 0 = 0) [ ] eq /[] 0 1/2 ([] 0 is intermediate) [ ] eq /[] 0 = 1 ([] 0 is high) Mobility is an additive function: Migration time [] eq [ ] eq v µ = µ + µ, µ = = [] [] E 0 0 1 1 [F] eq 1 [P F] = + t t [F] t [F] F 0 P F 0 Assignment: Derive formulas for ACEbased determination of K d using fluorescence anisotropy as a prototype eq te
Nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) Assume that Protein () and igand () have different migration times Incubate and to reach the equilibrium. he equilibrium mixture contains three components:,, and. EM = + + Separate them by electrophoresis.
Electrophoretic zones in NECEEM Equilibrium fractions of and migrate as single zones Equilibrium fraction of decays and generates smears EM = + + EOF + EM Concentration Decay of Position in the capillary >>>
Concentration NECEEM Electropherograms No peak broadening Decay of Migration time Concentration Peak broadening Decay of Migration time
NECEEM Electropherograms Fluorescence Detection of One Component has a fluorescent tag does not have it Fluorescence Decay of Migration time
Determination of K d with NECEEM Case 1: Complex is stable enough (does not decay during the separation). hen two peeks will be observed in a single experiment. NECEEM is reduced to equilibrium separation A A Migration time Peak areas correspond to the equilibrium concentrations of and : A ~ [] eq, A P ~ [ ] eq, hus, K d [] (1 + R) [] [] A where R =, 0 1 (1+1/R) [ ] A 0 0 eq = = < R< eq
Determination of K d with NECEEM contd. Case 2: Complex is NO stable enough (does decay during the separation). hen the zone will be decaying during separation. he red area adjacent to peak is produced by decay of. A A Migration time Peak areas still correspond to the equilibrium concentrations of and : A ~ [] eq, A P ~ [ ] eq, However, A will now consist of two parts, the remnants of peak and signal produced by the decay of. It does not change, however, the formula for K d calculation: K d [] (1 + R) [] [] A where R =, 0 1 (1+1/R) [ ] A 0 0 eq = = < R< eq
Determination of k off constant by NECEEM Case 2: Complex is NO stable (it decays during the separation). he forward reaction does not proceed since free and are separated by electrophoresis. So that the only reaction going is: koff + Exponential decay, I = I 0 exp{k off a(tt 0 )}, where a = t /(t t ) is a constant needed to compensate for apparent change of the separation window from 0 t to t t t 0 A A 1 A 2 t t Migration time hus, k off can be found by fitting the exponential decay line. Alternatively: k off A + A = 1 2 ln / t A1
Molecular ElectroOptics Physical Bases: he method is based on a change of protein alignment in an electric filed upon binding to a ligand. he change can be registered optically, Implementation: Short pulses of electric field are applied to a solution of protein. Since all proteins are dipoles, the electric filed induces the alignment of electrical dipoles in the field. his molecular alignment is recorded by measurements of: Absorbance of polarized light by protein (electric dichroism) Anisotropy of the refractive index (electric birefringence) Fluorescence anisotropy ight scattering Etc. + + + + + + + + + + + + No electric filed Electric filed In the absence of an external filed the distribution of protein molecules is random In the presence of external filed protein molecules are partially oriented in the direction of the electric filed
Molecular ElectroOptics contd. When the field is turned off the molecules relax back to the random orientation. he rate of alignment and the rate of relaxation are equal to each other and depend on the size and shape of the molecule and the viscosity of the solution. his rate changes upon binding of the protein to the ligand
Surface Plasmon Resonance (SPR) SPR is an resonance between light and a cloud of free electrons in a thin layer of gold (electromagnetic filed of light penetrates inside the gold to small depth). Resonance results in dissipation of light energy and thus decreasing intensity of light reflected from the gold surface. here is a certain angle between incident light and surface at which the intensity of reflected light is minimum (energy absorbance or SPR is maximum) Resonance depends on the refractive index of the media on the back side of the gold mirror. Refractive index is sensitive to the change of surface chemistry. Incident light reflected light Refractive index of the media on this side of the mirror changes when surface bound ligand interacts with the protein. he change in the refractive index leads to the change in SPR.
Practical Aspects of SPR What is detected in SPR? he change in the angle at which the intensity of reflected light is minimum (SPR is maximum) he ligand is immobilized on the gold surface he protein solution flows over the surface When the protein binds to the ligand the angle of minimum reflected light changes. he change is proportional to the mass of protein bound to the surface. Figure. P 256, ProteinProtein interactions
igand Immobilization in SPR igand immobilization without disruption of its activity is the most challenging part of experimentation in SPR. Direct immobilization of ligand to the surface has a number of drawbacks: Provides only heterogeneous immobilization due to multiple reactive groups on ligands (proteins) Often disrupts binding to the protein Require pure ligand since the impurities will bind to the surface as well Indirect immobilization of ligand to the surface through another molecule: igand is seldom inactivated he ligand does not have to be pure; it can be captured from a crude sample (e.g. by using antibodies) Immobilized molecules can have homogeneous orientation
Sensogram in SPR Figure. P 260, ProteinProtein interactions
StoppedFlow Spectroscopy Is based on spectral changes of one of the components (e.g. ) upon binding to another one 1. Reacting components are mixed fast: 2. In the initial stages the reverse reaction is negligible k on + 3. Rate of reaction is: Rate = k on [][] 4. he simplest approach to find k on is based on the assumption of the pseudofirst order reaction. For this, the invisible component (e.g. ) is taken in excess to the visible component (e.g. ). It is assumed that does not change during the reaction: [] [] 0. herefore, rate of reaction (k on [] 0 ) []. he apparent rate constant, k app (= k on [] 0 ), is found from fitting the exponential line. he rate constant is then calculated as k on = k app /[] 0
Finite mixing time leads to the phenomenon of dead time Dead time Dead time
imitation of Stopped flow spectroscopy he spectral change may be insignificant o detect the small change large concentrations of and must be used Reaction rates become very fast at large concentrations so that the reaction reaches equilibrium during the mixing period As a result large k on cannot be often measured
Sweeping Capillary Electrophoresis (SweepCE) SweepCE is the only nonstopped flow technique for measuring k on of fast reactions Is based on sweeping of a slowlymoving component by a fastmoving component t 0 + Slowly moving component t 1 Fast moving component + Slowly moving component t 2 + Fast moving comp. Slowly moving component Sweeping zone
Fluorescence intensity (a.u.) 3 2 1 0 SweepCE Electropherogram Slowmoving component is fluorescent Sweeping in the presence of the fast component No fast component No sweeping 0 50 100 150 200 Migration time to the end of the capillary (s)
Mass transfer equations to describe SweepCE Reaction: + tx (, ) tx (, ) + v = kon(, t x) (, t x) t x tx (, ) tx (, ) + v = kon(, t x) (, t x) t x i (, t x) i (, t x) + v i = kon(, t x) (, t x) t x
Analytical solution for SweepCE on 0 0 on 0 on 0 on 0 0 on 0 exp ( ) (, ) exp 1 ( ) exp 1 ( ) 1 exp ( ) (, ) exp x v t k x v t v v tx x v t k x v t v v x v t k x v t v v x v t k x v t v v tx k θ θ θ θ + = + + + + = on 0 on 0 1 ( ) exp 1 ( ) 1 (, ) (, ) (, ) t x v t x v t v v x v t k x v t v v t x k t x v t x v d θ θ τ τ τ τ τ + + + + = i i i
Sum concentration of DNA and the proteindna complex (nm) Finding k on by fitting experimental 25 20 15 10 5 0 30 70 80 90 100 110 120 130 20 10 SweepCE electropherograms 0 70 80 90 100 110 120 130 Migration time to the end of the capillary (s) [] = 40 nm [] = 5 nm k on = 3.9 10 6 M 1 s 1 [] = 40 nm [] = 10 nm k on = 3.7 10 6 M 1 s 1
Accuracy of SweepCE A: [] = 40 nm [] = 1 nm B: [] = 40 nm [] = 5 nm C: [] = 40 nm [] = 10 nm Sum concentration of DNA and the proteindna complex (nm) 8 7 6 5 4 3 2 1 0 30 25 20 15 10 5 0 30 20 10 A B C Experiment Model: best fit, k on = 2.7 10 6 M 1 s 1 Model: k on = 10 6 M 1 s 1 Model: k on = 10 7 M 1 s 1 Experiment Model: best fit, k on = 3.9 10 6 M 1 s 1 Model: k on = 10 6 M 1 s 1 Model: k on = 10 7 M 1 s 1 Experiment Model: best fit, k on = 3.7 10 6 M 1 s 1 Model: k on = 10 6 M 1 s 1 Model: k on = 10 7 M 1 s 1 0 70 90 110 130 150 170 Migration time to the end of the capillary (s)
Advantages of SweepCE over Stoppedflow Spectroscopy Does not require spectral changes Can employ low concentration of a visible component Can be used for measuring very high k on Can also be used for measuring k off if numerical modeling is used to fit the experimental data (under development)