stability-activity tradeoffs: proximate vs. ultimate causes jeffrey endelman university of...
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Stability-Activity Tradeoffs: Proximate vs. Ultimate Causes
Jeffrey Endelman
University of California, Santa Barbara
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Causation in Biology
• Proximate (physicochemical)
• Ultimate (evolutionary)
Mayr, E. (1997) This is Biology. Cambridge: Harvard Univ. Press.
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Enzyme Activity
• Enzymes catalyze reactions, e.g.
• Active site is where reaction occurs
LDHpyruvate + NADH + H+ lactate + NAD+
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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+
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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.
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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.
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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.
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Enzyme Stability
• Enzymes denature (ND) as T inc.
• Gu = GD-GN
• Tm: Gu(Tm) = 0
• Residual activity (Ar /Ai)
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Wintrode, P.L & Arnold, F.H. (2001) Adv. Prot. Chem. 55, 161-225.
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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
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50
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65
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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.
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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)
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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.
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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
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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.
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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.
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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.
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• 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
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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.
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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.
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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
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p-nitrobenzyl esterase (pNBE)
Sta
bili
ty
Activity at 25oC
No enzyme’s land
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Sta
bili
ty
Activity at 25oC
Most mutations are deleterious or nearly neutral.
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Sta
bili
ty
Activity at 25oC
Mutations that improve either property are rare.
p = O()
p = O(
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Sta
bili
ty
Activity at 25oC
Mutations that improve both properties are very rare
p = O()
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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(
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Proteins in nature are well-adapted:
S&A are far above average
S/AWT
frequency
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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.
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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(
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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
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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.
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Sta
bili
ty
Activity at 25oC
Viable Lethal
H3: Mutation-Selection
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Threshold Selection
• Gu(Th) = kTh
– KD/N = e-
– Proteins typically have > 7
– No reason (or evidence) to believe higher S has selective advantage
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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
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Sta
bili
ty
Activity at 25oC
Viable Lethal
H3: Mutation-Selection
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Sta
bili
ty
Activity at 25oC
Viable Lethal
Mutation brings S&A to thresholds
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A(Th)
20oC
37oC 75oC
S/A for H3 (Mutation-Selection)
Gu(Th)kTh
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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)
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A
TTh
Arrheniusmelting
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A
20oC
37oC
75oC
T
Th
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20oC
37oC
75oC
T
To
A
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20oC
37oC
75oC
A(To)
Gu(Th)kTh
S/A for H3 (Mutation-Selection)
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Gu/kT TTh
0
Tm
20oC 37oC 75oC
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0
T20oC 37oC 75oCGu/kT
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0
Gu/kT Tm Tm Tm20oC 37oC 75oC
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S/A for H3 (Mutation-Selection)
20oC
37oC
75oC
A(To)
Tm
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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
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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
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Performance Tradeoffs
• Pervasive in biological thinking
• Resource allocation (time, energy, mass)
• Design tradeoffs
• Biochemistry: Stability/Activity
• Behavior: Foraging, Fight/Flight
• Physiology: Respiration, Biomechanics