schematic diagram; EGF binding, dimerization, phosphorylation, Grb2 binding, etc.

Transcription

1 Lecture 1: Noncovalent Biomolecular Interactions Bioengineering and Modeling of biological processes -e.g. tissue engineering, cancer, autoimmune disease Example: RTK signaling, e.g. EGFR Growth responses are central in cell therapies, tissue engineering, and these are governed by growth factors and their receptors. schematic diagram; EGF binding, dimerization, phosphorylation, Grb2 binding, etc. These molecular processes of reversible binding and enzymatic reactions are at the heart of the overall response that we as engineers are interested in understanding and manipulating. How are engineering fundamentals related to biological problems? As bioengineers, the ability to measure, model, & manipulate at the molecular level is essential for understanding & designing biological systems. The overall goal of this course is to become proficient at the mathematical desription of biomolecular interactions as a tool to study & manipulate biological systems. Biological Mechanism Cartoon Schematic Mathematical Model Implementation (is interpretation consistent with assumptions?) The overall cellular behavior of interest is generally governed by a series of: protein/protein noncovalent binding - signaling

2 - structure formation - gene expression - immune recognition - enzyme/substrate covalent reactions - metabolism - signal transduction pathways - macromolecular synthesis Q: What are the major interactions in protein/ligand association? A: -hydrogen bonding solvent effects, water interacts with proteins in an illunderstood way -electrostatics (desolvation unfavorable vs. coulombic interactions favorable) -Van der Waals forces weak interactions of induced dipoles at close range -hydrophobic interactions complicated, structured water at interface is entropically unfavorable, and hydrophobic association liberates structured water Water is an active player in these processes water/protein and water/ligand interactions are traded for protein/ligand interactions, as opposed to P + L coming together in a vacuum. This tradeoff is often ~ even for electrostatic interactions ((Hendsch & Tidor,

3 Protein Sci. 3:211, 1994)). Ex: Why does NaCl dissociate into Na + & Cl - in water, if +/- charges interact in a net favorable way? -Hydrogen Bonds 1 Å 3 Å -D H :A D = Hydrogen Donor (often Nitrogen in protein interactions) A = Hydrogen Acceptor (often Oxygen or lone electron pair bearing atom) G H-bond = 2 kcal/mol in vacuo, but is less certain in water In water, each H2O participates in 4 HBs (2 as A, 2 as D). Van der Waals Electrostatics very weak attraction at close range induced dipole in nonpolar atoms tradefoff between two large counteracting terms, desolvation vs. coulombic net balance is usually not obvious a priori Hydrophobic interaction not a bond per se complicated phenomenon structured solvated hydrophobic solute surface gain entropy Thermodynamics when liberated by solute surface burial. P + L C P = protein, L = ligand, C = complex (k on = association rate constant, k off = dissociation rate constant)

4 Free Energy Change for complex formation G = G 0 + RTln{[C]/[P][L]} G 0 = defined at an arbitrary standard state (1M reactants and STP, often ph = 7.0 for biological systems) -if reaction is favored, G < 0 -reaction is in equilibrium when G = 0 G 0 = -RTln{[C]/[P][L]} -define equilibrium constant (units of molarity): K d = {[P][L]/[C]} equil = k off /k on Why can we take log form of a dimensional {[P][L]/[C]} term above? The unit of the {[P][L]/[C]} should be equal to the unit of concentration where standard free energy ( G 0 ) is defined (i.e. mol/l). Therefore, units must be mol/l. K d = exp( G 0 /RT) Typically, G 0 = 5 20 kcal/mol for biomolecular reactions -A G of -1 kcal/mol at room temperature results in a reduction in K d of 1/5 at room temperature, for a five-fold tighter binder. -the protein is half-complexed at a ligand concentration equal to K d. because K d = [P]/[C] x [L], so at [L]= K d, protein is half-complexed -Typical values of kinetic & equilibrium constants To a very rough approximation (i.e. ± 10x): k on = 10 5 M -1 s -1 for P-P interactions, k on = 10 6 M -1 s -1 for protein-small molecule interactions -By comparison to a maximum diffusion limited (to be discussed later) collision rate of k on = M -1 s -1

5 Affinity K d 1/k off (average complex persistence time) Type Non-specific mm milliseconds stickiness Low µm Seconds Multivalent cell surface interactions (adhesion, T-cell presentation) High nm minutes hours Antibodies, enzymes Very High pm Hours days Growth factors, receptors Ultra-high fm Days weeks Hydrolase inhibitors, biotin/steptavidin -Thermodynamic Relationships The components of free energy are enthalpy & entropy G = H T S - G measure by K d - H enthalpy, o bond making & breaking o vdw,hb,ionic o remember, P-W,P-L,L-W,W-W,P-P,L-L o can measure by isothermal titration calorimetry o <0 for most protein/protein interactions (except multimer assembly) - _S entropy, o freezing out side chain rotamers in complex o immobilizing flexible loops o 2 -> 1 molecule, changes degrees of freedom o hydrophobic effect

6 So what do these protein/protein interfaces look like? -Protein Association Active Sites (Chothin & Janin, J. Mol. Biol. 285:2177, 1999) -examined 75 protein/protein interactions (not multimer enzyme or virus capsid; many antibody/antigen and protease/inhibitor.) Q: What do you think interfaces look like? Hydrophobic? Charged? A: No different in general than the rest of a protein s surface! -Characteristics of Interfaces avg. surface for small globular proteins non polar 56% 57% neutral polar 29% 24% charged polar 15% 19% Note: interfaces are not more hydrophobic, are not more charged. -Average of 10 bridging hydrogen bonds -Between 3 and 50 (avg. 18) water molecules trapped in active site -Enriched aromatics (Tyr, Trp, Phe, His) 21% in active site vs. 8% elsewhere - Side chain is not the only interface in contact, main chain/backbone interaction is also important (19 %) - number of interfacial contacts >> number of energetically favored contacts - often, a small number of critical hot spot residues Alanine scanning is a method to identify hot spot residues. [Alanine scanning: Wells, Science 244, 1081 (1989)]