5.60 Thermodynamics & Kinetics Spring 2008

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1 MIT OpenCurseWare Thermdynamics & Kinetics Spring 2008 Fr infrmatin abut citing these materials r ur Terms f Use, visit:

2 5.60 Spring 2008 Lecture #17 page 1 Equilibrium: Applicatin t rug esign Based n Ratinal cytkine design fr increased lifetime and enhanced ptency using ph-activated histidine switching, Sarkar, Lwenhaupt, Hran, Bne, Tidr, and Lauffenburger, Nature Bitechnlgy 20, 908 (2002). The analysis fr uilibrium that we have used fr reactins invlving breaking and making cvalent bnds applies ually well t reactins such as thse invlved in ligand-receptr binding, where the ligand and receptr are prteins R + L = C where R is the receptr, L is the ligand, and C is the receptr-ligand cmplex. The interactins between these prteins typically invlve multiple nn-cvalent interactins, including hydrgen bnds, hydrphbic interactins, and electrstatic interactins. The uilibrium cnstant and Gibbs free energy change fr the reactin are related in the usual way G = RT lnk a where the uilibrium cnstant K a is called the assciatin cnstant K a = [ R][ L] The standard state needed t characterize G is defined at a set f specific reference cnditins (ph, salt cncentratin, etc.). By cnventin, the reverse prcess (the dissciatin) is used t characterize the strength f ligand binding thrugh the uilibrium cnstant K, als called the dissciatin cnstant

3 5.60 Spring 2008 Lecture #17 page 2 K = [ R][ L] The lwer the K, the better the ligand (the tighter the binding). In an experiment the ligand is typically labeled radiactively (e.g. with 125 I) and added t cells under cnditins that prevent the ligand frm being internalized (4 C).The ligand is usually in great excess cmpared t the number f receptrs, s that at uilibrium [L]=[L] 0 is a gd apprximatin (the ligand cncentratin is effectively unchanged during the prcess). If [R] T is the ttal cncentratin f receptrs, then [R] T =[R]+[C], s that at uilibrium, K = ([ R] )[ L] T [ ] r [ R ] T = L K K The value f K (and thus G 0 ) can be btained by measuring the cncentratin f cmplexes frmed at varius initial ligand cncentratins [L] 0 (thrugh the radiactive labeling) by pltting [ L] as a functin f (a Scatchard plt). The slpe gives 1 K. The fractin f receptrs ccupied is

4 5.60 Spring 2008 Lecture #17 page 3 [ R ] T 1 = K 1 + [ ] L [ L] Nte, when [L] <<K then [ R] K, T K when [L] >>K then 1 [ R] [ L] T Althugh free energies fr receptr-ligand binding reactins are generally determined experimentally (thrugh K ), it is pssible t cmputatinally estimate the changes in free energy that accmpany pint mutatins in ne f the amin acids in the ligand. This apprach can be used t design a new and better drug that binds with an affinity that imprves its prperties. An example f such a designed mutated ligand is an imprved versin f Granulcyte-Clny Stimulating Factr (GCSF). GCSF is a prtein drug that is used t treat chemtherapy patients and stimulates the grwth f white bld cells. It is desirable t have GCSF bind tightly t its receptr at the cell surface (at ph 7.4) as this signals the cell t prduce the desired prteins. But when the cmplex C is internalized in the cell in endsmal cmpartments (ph 5.5), it is desirable fr GCSF t fall ff its receptr t be recycled back t the slutin t be used again instead f being degraded within the endsme. Thus a design principle fr an imprved mutant GCSF is weaker binding at ph 5.5 (inside cell) than at ph 7.4 (cell surface), r in ther wrds K (ph5.5)> K (ph7.4).

5 5.60 Spring 2008 Lecture #17 page 4 Fr the wild type (WT) GCSF the data gives: K (ph 7.4), pm K (ph 5.5)/ K (ph 7.4) WT 270±90 1.7±0.5 Since G = RT lnk, we can get the difference f G s fr the dissciatin reactin at the different ph s G ( ph7.4) G ( ph5.5) / RT WT: 0.53±0.3 (measured frm K values) Calculatins were perfrmed n several mutants and tw shwed appreciable differences in free energies 110H: 113H: 8.3 (calculated) 17 (calculated) These mutant GCSF mlecules were synthesized and evaluated fr binding t the GCSF receptr with the fllwing results: K (ph 7.4), pm K (ph 5.5)/ K (ph 7.4) WT 270±90 1.7± H 370± ± H 320± ±2.4

6 5.60 Spring 2008 Lecture #17 page 5 The mutants d bind mre weakly than des the wild type at lw ph, and thus have the ptential t be better drugs (in fact, in animal trials the mutants have much lnger half-lives than the wild type). ifferences in free energies fr the mutants can be btained frm the experimental K s: G ( ph7.4) G ( ph5.5) / RT WT: 110H: 113H: 0.53±0.3 (measured frm K values) 1.5±0.2 (measured frm K values) 1.9±0.4 (measured frm K values)