1. Stability-Activity Tradeoffs: Proximate vs. Ultimate Causes Jeffrey Endelman University of California, Santa Barbara

2. Causation in Biology Proximate (physicochemical) Ultimate (evolutionary) Mayr, E. (1997) This is Biology. Cambridge: Harvard Univ. Press.

3. Enzyme Activity Enzymes catalyze reactions, e.g. Active site is where reaction occurs LDH pyruvate + NADH + H +  lactate + NAD +

4. Enzyme Activity Enzymes catalyze reactions, e.g. Active site is where reaction occurs Activity measures rate of rxn –Use specific activity (per enzyme) –k cat = saturated specific activity LDH pyruvate + NADH + H +  lactate + NAD +

5. Enzyme Stability Enzymes denature (N  D) as T inc.  G u = G D -G N Lysozyme pH 2.5 CpCp T ( o C) Privalov, P.L. (1979) Adv. Prot. Chem. 33, 167-241.

6. Enzyme Stability Enzymes denature (N  D) as T inc.  G u = G D -G N T m :  G u (T m ) = 0 Lysozyme pH 2.5 CpCp T ( o C) TmTm Privalov, P.L. (1979) Adv. Prot. Chem. 33, 167-241.

7. Enzyme Stability Enzymes denature (N  D) as T inc.  G u = G D -G N T m :  G u (T m ) = 0  T ( o C) TmTm Creighton, T.E. (1983) Proteins. New York: Freeman.

8. Enzyme Stability Enzymes denature (N  D) as T inc.  G u = G D -G N T m :  G u (T m ) = 0 Residual activity (A r /A i )

9. Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225.

10. Stability-Activity Tradeoff IPMDH Svingor, A. et al. (2001) J. Biol. Chem. 276, 28121-28125. 20 o C 37 o C 75 o C

11. H1: Purely Proximate IPMDH natural homologs artificial? Tradeoff exists for all enzymes.

12. Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225. p-nitrobenzyl esterase (pNBE) Stability (A r /A i ) Activity at 25 o C (A i )

13. Stability Activity at 25 o C No enzyme’s land p-nitrobenzyl esterase (pNBE) Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225.

14. S/A Tradeoff Hypotheses 1.All enzymes have proximate tradeoff 2.Ultimate: Selection for high S&A Proximate: Highly optimized enzymes have S/A tradeoff

15. Proximate Tradeoff: Flexibility Enzymes achieve greater stability by reducing flexibility. Flexible motions are important for catalysis in many enzymes. Thus thermostability through reduced flexibility decreases activity. Somero, G.N. (1995) Annu. Rev. Physiol. 57, 43-68.

16. Flexibility & Activity Large motions (hinge bending, shear) –Pyruvate dehydrogenase –Triosephosphate isomerase –Lactate dehydrogenase –Hexokinase Small motions (vibrational, breathing, internal rotations) –No evidence, but not unlikely Fersht, A. (1999) Structure and Mechanism in Protein Science. New York: Freeman.

17. Proximate Tradeoff: Flexibility Enzymes achieve greater stability by reducing flexibility. Flexible motions are important for catalysis in many enzymes. Thus thermostability through reduced flexibility decreases activity. Somero, G.N. (1995) Annu. Rev. Physiol. 57, 43-68.

18. Stabilization involves all levels of protein structure Experiments typically probe small motions via amide hydrogen exchange Some thermophiles are more rigid than mesophile, others are not “... hypothesis [that] enhanced thermal stability … [is] the result of enhanced conformational ridigity…. has no general validity.” Jaenicke, R. (2000) PNAS 97, 2962-2964. Flexibility & Stability

19. Proximate Tradeoff: Flexibility Enzymes achieve greater stability by reducing flexibility. Flexible motions are important for catalysis in many enzymes. Thus thermostability through reduced flexibility decreases activity. Somero, G.N. (1995) Annu. Rev. Physiol. 57, 43-68.

20. Flexibility is Weak Link Protein flexibility is complex –Spans picoseconds to milliseconds –Varies spatially Only meaningful to discuss particular motions and how they affect stability and activity Stability and activity often involve different regions and different time scales Lazaridis, T., Lee, I. & Karplus, M. (1997) Prot. Sci. 6, 2589-2605.

21. S/A Tradeoff Hypotheses 1.All enzymes have proximate tradeoff 2.Ultimate: Selection for high S&A Proximate: Highly optimized enzymes have S/A tradeoff –No known generic mechanism, e.g. flexibility –Experiments do not support notion

22. p-nitrobenzyl esterase (pNBE) Stability Activity at 25 o C No enzyme’s land

23. Stability Activity at 25 o C Most mutations are deleterious or nearly neutral.

24. Stability Activity at 25 o C Mutations that improve either property are rare. p = O(  ) p = O( 

25. Stability Activity at 25 o C Mutations that improve both properties are very rare p = O(   )

26. Stability Activity at 25 o C Consistent with p(S, A) = p(S) p(A) p(S>WT) = p(A>WT) = O(  << 1 p = O(  ) p = O(   )p = O( 

27. Proteins in nature are well-adapted: S&A are far above average S/A WT frequency

28. Buffering/Evolvability More mutations are nearly neutral than might be expected for random tinkering of complex system Compartmentalization –protein domains Redundancy –Hydrophobicity –Steric requirements Gerhart, J. & Kirschner, M. (1997) Cells, Embryos, & Evolution. Malden: Blackwell Science.

29. Stability Activity at 25 o C Consistent with p(S, A) = p(S) p(A) p(S>WT) = p(A>WT) = O(  << 1 p = O(  ) p = O(   )p = O( 

30. Giver, L. et al. (1998) PNAS 95, 12809-12813. Directed Evolution: Improved S&A Activity (mmol/min/mg) Melting T ( o C) pNBE 5 12 2 1

31. S/A Tradeoff Hypotheses 1.All enzymes have proximate tradeoff 2.Ultimate: Selection for high S&A Proximate: Highly optimized enzymes have S/A tradeoff 3.Proximate: Most mutations are deleterious or nearly neutral Ultimate: Selection for threshold S&A Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225.

32. Stability Activity at 25 o C Viable Lethal H3: Mutation-Selection

33. Threshold Selection  G u (T h ) =  kT h –K D/N = e -  –Proteins typically have  > 7 –No reason (or evidence) to believe higher S has selective advantage

34. Threshold Selection  G u (T h ) =  kT h –K D/N = e -  –Proteins typically have  > 5 –No reason (or evidence) to believe higher S has selective advantage A(T h ) =  –With low flux control coefficient, higher A may offer no advantage –When important for control, higher A may be disadvantageous

35. Stability Activity at 25 o C Viable Lethal H3: Mutation-Selection

36. Stability Activity at 25 o C Viable Lethal Mutation brings S&A to thresholds

37.   A(T h ) 20 o C 37 o C 75 o C S/A for H3 (Mutation-Selection)  G u (T h ) kT h

38. IPMDH Svingor, A. et al. (2001) J. Biol. Chem. 276, 28121-28125. 20 o C 37 o C 75 o C S/A in Nature = A(T o )

39. A T ThTh  Arrhenius melting

40.  A 20 o C 37 o C 75 o C T ThTh

41.  20 o C 37 o C 75 o C T ToTo A

42.  20 o C 37 o C 75 o C  A(T o )  G u (T h ) kT h S/A for H3 (Mutation-Selection)

43.  G u /kT TThTh 0 TmTm  20 o C 37 o C 75 o C

44. 0 T 20 o C 37 o C 75 o C  G u /kT 

45. 0 TmTm TmTm TmTm 20 o C 37 o C 75 o C

46. S/A for H3 (Mutation-Selection) 20 o C 37 o C 75 o C  A(T o ) TmTm

47. IPMDH Svingor, A. et al. (2001) J. Biol. Chem. 276, 28121-28125. 20 o C 37 o C 75 o C S/A in Nature

48. Conclusions Because biological phenotypes are well-adapted, most mutations are deleterious This mutational pressure pushes phenotypes to the thresholds of selection Selection that requires homologs to have comparable S&A at physiological temperatures creates the appearance of S/A tradeoffs at a reference temperature The proximate causes for S&A among homologs are unlikely to be universal

49. Performance Tradeoffs Pervasive in biological thinking Resource allocation (time, energy, mass) Design tradeoffs Biochemistry: Stability/Activity Behavior: Foraging, Fight/Flight Physiology: Respiration, Biomechanics