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