Stability-Activity Tradeoffs: Proximate vs. Ultimate Causes Jeffrey Endelman University of California, Santa Barbara
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Stability-Activity Tradeoffs: Proximate vs. Ultimate Causes
Jeffrey Endelman
University of California, Santa Barbara
Causation in Biology
• Proximate (physicochemical)
• Ultimate (evolutionary)
Mayr, E. (1997) This is Biology. Cambridge: Harvard Univ. Press.
Enzyme Activity
• Enzymes catalyze reactions, e.g.
• Active site is where reaction occurs
LDHpyruvate + NADH + H+ lactate + NAD+
Enzyme Activity
• Enzymes catalyze reactions, e.g.
• Active site is where reaction occurs• Activity measures rate of rxn
– Use specific activity (per enzyme)
– kcat = saturated specific activity
LDHpyruvate + NADH + H+ lactate + NAD+
Enzyme Stability
• Enzymes denature (ND) as T inc.
• Gu = GD-GN
Lysozyme pH 2.5
Cp
T (oC)
Privalov, P.L. (1979) Adv. Prot. Chem. 33, 167-241.
Enzyme Stability
• Enzymes denature (ND) as T inc.
• Gu = GD-GN
• Tm: Gu(Tm) = 0 Lysozyme pH 2.5
Cp
T (oC)Tm
Privalov, P.L. (1979) Adv. Prot. Chem. 33, 167-241.
Enzyme Stability
• Enzymes denature (ND) as T inc.
• Gu = GD-GN
• Tm: Gu(Tm) = 0
T (oC)Tm
Creighton, T.E. (1983) Proteins. New York: Freeman.
Enzyme Stability
• Enzymes denature (ND) as T inc.
• Gu = GD-GN
• Tm: Gu(Tm) = 0
• Residual activity (Ar /Ai)
Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225.
50
55
60
65
70
75
80
85
90
0 2 4 6 8 10 12
kcat (s-1) at 20oC
mel
ting
T (
o C)
Stability-Activity Tradeoff
IPMDH
Svingor, A. et al. (2001) J. Biol. Chem. 276, 28121-28125.
20oC
37oC
75oC
50
55
60
65
70
75
80
85
90
0 2 4 6 8 10 12
kcat (s-1) at 20oC
mel
ting
T (
o C)
H1: Purely Proximate
IPMDH
natural homologs
artificial?
Tradeoff exists for all enzymes.
Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225.
p-nitrobenzyl esterase (pNBE)S
tabi
lity
(A
r /A
i)
Activity at 25oC (Ai)
Sta
bili
ty
Activity at 25oC
No enzyme’s land
p-nitrobenzyl esterase (pNBE)
Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225.
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
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.
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.
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.
• 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
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.
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.
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
p-nitrobenzyl esterase (pNBE)
Sta
bili
ty
Activity at 25oC
No enzyme’s land
Sta
bili
ty
Activity at 25oC
Most mutations are deleterious or nearly neutral.
Sta
bili
ty
Activity at 25oC
Mutations that improve either property are rare.
p = O()
p = O(
Sta
bili
ty
Activity at 25oC
Mutations that improve both properties are very rare
p = O()
Sta
bili
ty
Activity at 25oC
Consistent with p(S, A) = p(S) p(A)
p(S>WT) = p(A>WT) = O( << 1
p = O()
p = O()p = O(
Proteins in nature are well-adapted:
S&A are far above average
S/AWT
frequency
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.
Sta
bili
ty
Activity at 25oC
Consistent with p(S, A) = p(S) p(A)
p(S>WT) = p(A>WT) = O( << 1
p = O()
p = O()p = O(
Giver, L. et al. (1998) PNAS 95, 12809-12813.
Directed Evolution: Improved S&AA
ctiv
ity
(mm
ol/m
in/m
g)
Melting T (oC)
pNBE
5
1 22
1
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.
Sta
bili
ty
Activity at 25oC
Viable Lethal
H3: Mutation-Selection
Threshold Selection
• Gu(Th) = kTh
– KD/N = e-
– Proteins typically have > 7
– No reason (or evidence) to believe higher S has selective advantage
Threshold Selection• Gu(Th) = kTh
– KD/N = e-
– Proteins typically have > 5– No reason (or evidence) to believe higher S has
selective advantage
• A(Th) = – With low flux control coefficient, higher A may offer
no advantage– When important for control, higher A may be
disadvantageous
Sta
bili
ty
Activity at 25oC
Viable Lethal
H3: Mutation-Selection
Sta
bili
ty
Activity at 25oC
Viable Lethal
Mutation brings S&A to thresholds
A(Th)
20oC
37oC 75oC
S/A for H3 (Mutation-Selection)
Gu(Th)kTh
50
55
60
65
70
75
80
85
90
0 2 4 6 8 10 12
kcat (s-1) at 20oC
mel
ting
T (
o C)
IPMDH
Svingor, A. et al. (2001) J. Biol. Chem. 276, 28121-28125.
20oC
37oC
75oC
S/A in Nature
= A(To)
A
TTh
Arrheniusmelting
A
20oC
37oC
75oC
T
Th
20oC
37oC
75oC
T
To
A
20oC
37oC
75oC
A(To)
Gu(Th)kTh
S/A for H3 (Mutation-Selection)
Gu/kT TTh
0
Tm
20oC 37oC 75oC
0
T20oC 37oC 75oCGu/kT
0
Gu/kT Tm Tm Tm20oC 37oC 75oC
S/A for H3 (Mutation-Selection)
20oC
37oC
75oC
A(To)
Tm
50
55
60
65
70
75
80
85
90
0 2 4 6 8 10 12
kcat (s-1) at 20oC
mel
ting
T (
o C)
IPMDH
Svingor, A. et al. (2001) J. Biol. Chem. 276, 28121-28125.
20oC
37oC
75oC
S/A in Nature
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
Performance Tradeoffs
• Pervasive in biological thinking
• Resource allocation (time, energy, mass)
• Design tradeoffs
• Biochemistry: Stability/Activity
• Behavior: Foraging, Fight/Flight
• Physiology: Respiration, Biomechanics
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