Biochemical Signaling and Its
Energy Cost:
Protein phosphorylation, DNA replication,
enzyme cooperativity and kinetic proofreading
Hong Qian
Department of Applied Mathematics
University of Washington
A car can not run without fuel. Most biochemical processes in a
living cell can not function without a sufficient amount of active
energy utilization. Textbook tells us that the three major energy
sinks inside a cell are (i) biosynthesis, (ii) ionic and neutral
molecular pumping, and (iii) mechanical movement. But how much
energy is dissipated in normal cellular information processing? It is
surprising that we do not know at all the answer to this simple
question.
In this talk, I try to establish this "signal-energy
connection". I shall introduce the concept of open chemical
systems; and discuss several key cellular processes and the role of
energy in their functioning: (1) protein phosphorylationdephosphorylation as a signaling switch; (2) DNA replication
checkpoint with high fidelity; (3) sigmoidal cooperativity in
monomeric enzyme with dynamic disorder, and (4) kinetic
proofreading as a mechanism for specificity amplification.
A Little Quiz on Energy
☺
• A light bulb, 110V, how much energy it
consumes?
• If there is no label, but you are given a
meter that measures the current in the
light bulb, can we figure out the
wattage?
• The answer is voltage × current (amp) =
power (watt), the energy per unit time.
What is the difference between a tube
of chemicals and a cell in Petri dish?
In a cell, the chemical reaction system
continuously exchanges materials with its
environment!
Then, what is the difference between a
cell in Petri dish and a dialysis bag?
The chemicals in cell culture medium
contain calories, releasing energy when
broken down. The chemicals in the buffer
are in equilibrium.
Closed vs. Open Chemical
Systems
• A dialysis tube reaches a chemical equilibrium
(i.e., Gibbs grand canonical ensemble)
• An open chemical system exchanges chemicals
with its surrounding that sustains a chemical
gradient. It is driven (i.e., Schördinger).
• It reaches a nonequilibrium steady-state (i.e.,
Prigogine).
Nonequilibrium Steady-State
(NESS)
NESS = miracle
in Hebrew
NESS in a test tube: a driven
reaction
A+B
C+D
In a thought experiment, an “agent” continuously
keeps the concentrations of A, B, C, and D at
constant, sustaining the chemical reaction in a
steady-state. In reality, this can be done by a
regenerating system or excess (approximately).
What are the consequences of an
open chemical system and what
are the characteristics of a driven
chemical reaction in NESS?
Before studying open systems, we first
have to characterize a closed system
• It reaches a chemical equilibrium; it becomes
a “pile of dirt”.
• There is no flux in each and every reactions.
• The forward flux = backward flux (G.N.
Lewis’s principle of detailed balance, 1925).
• The system is “time-reversible”: One can run
a “recording tape” backward!
In More Quantitative Terms:
A+B
o
k+1
o
k-1
C+D
forward flux = backward flux:
k [ A] [ B] = k [C ] [ D]
o
+1
eq
eq
o
−1
eq
k
[ A] [ B]
1
=
=
eq
eq
[C ] [ D]
k
K eq
eq
eq
o
−1
o
+1
eq
For a driven reaction, how much is the
energy from the surrounding medium?
From elementary biochemistry, the free
-RT
ln
K
eq
energy difference
o
Notk+1
at their
of a reaction:
C+D
A+B
o
Equilibriumk in a cell!
-1
[ A][ B]
ΔG = ΔG + RT ln
[C ][ D]
o
≠ 0 in a cell!
living part
[S ]
ΔG = ΔG + RT ln
cell
[ P]
cell
o
dead part
And …
A+B
C+D
the free energy difference, i.e., chemical
“voltage” multiplies the flux, i.e. chemical
“current”: ΔG × J, is the amount of
chemical “power” going to the reaction.
voltage × current = power!
(same as for the electricity)
A Role of Open Chemical
Systems in Cellular Biology and
Signal Transduction?
Currently, Molecular Cellular
Biology Focus on …
The molecules and their atoms
The pathways and their logics
EGF Signal Transduction Pathway
A cell is a little machine. The
cellular logics are carried out by
molecules, via biochemical
reactions in aqueous(?), chemically
open environment.
The cellular signaling networks are
very complex. But complexity is not
everything. If you don’t change the
medium in a long time, cells die. The
chemical reactions approach to
equilibrium. Without gas, a car can
not run, even with all the hardware
being there!
Let us start with a simple, small
reaction network in an open
chemical system…
Thermodynamic Box and Enzyme
Reactions in Equilibrium
P
S
E
k3
EP
o
o
k-3
k-1
k-2
k2
k1
ES
k k k [S ]
=1
k k k [ P]
o
1 2 3
o
−1 −2 −3
k kk
[ P]
=
eq
[S ]
k k k
eq
o
1 2 3
o
−1 −2 −3
= K eq
Open Chemical Systems and
Its Energy Input
P
S
E
k k k [S ]
> 1,
k k k [ P]
o
1 2 3
o
−1 −2 −3
[ P]
eq
>K
cell
[S ]
cell
EP
ES
k k k [S ]
K [S ]
= RT ln
RT ln
cell
cell
k k k [ P]
[ P]
o
1 2 3
o
−1 −2 −3
cell
eq
cell
= ΔG
cell
SP
This energy has to do with the cellular
concentrations of the S and P! One has
to constantly feed the cells to keep the
cellular [S] and [P] away from relaxing
to their equilibrium. In a test tube
experiment without regenerating
system, a reaction always goes to
equilibrium.
Phosphorylation-dephosphorylation
Cycle as an Open Chemical System
neglecting the
catalysts:
T
Pi
E
k3
E+T
E*
1
E*+D
1
E*2
E+Pi
E2*
k-3o o
k-1
k-2
k2
o
k1
E1*
D
Inside Living Cells
• The ATP and ADP/Pi concentrations
determine the relevant energy level of
the PdPC, not the energy in the
phosphate bond per sc.
• The mitochondria work hard to keep the
ATP concentration high while the ADP
concentration low.
Inside Living Cells
• The available energy relevant to a normal living
cell is from the sustained high concentration of
ATP (~1mM) and low concentrations of ADP
(~10μM). With an equilibrium constant of 4.9
x 105 M for ATP hydrolysis and Pi of ~1mM,
the phosphorylation potential in a normal cell is
about 12 kcal/mol.
• The Pacific Ocean could be filled with an
equilibrium mixture of ATP, ADP and Pi, but
the ATP would have no capacity to perform
signal transduction via PdPC.
In a Cell, Where did the Energy Go?
According to Textbooks,
Inside Living cells
(Biochemistry, Stryer. p. 240)
• (i) Biosynthesis
• (ii) Ionic and neutral molecular
pumping
• (iii) Mechanical movement.
• They are collectively known as the
three major energy sinks at the
cellular level.
All the above three are
chemical/mechanical functions.
How much free energy is
dissipated in normal cellular
information processing? Can there
be a fourth sink for cellular
energy?
Why has protein
phosphorylation evolved to be
the ubiquitous mechanism for
regulating enzyme activities in
living organisms?
Phosphorylation Energy Hypothesis
Protein phosphorylation is not merely a chemical
signal in terms of a structural tag. Energy
derived from the hydrolysis reaction, in a living
cell, is used to ensure the proper function of
biochemical signaling. The energy is necessary
for overcoming intrinsic biochemical “noise”
from thermal agitations, small copy numbers, and
limited affinities, guaranteeing precise and robust
cell development and functions.
Qian, H. & Reluga, T.C. Phys. Rev. Lett. Vol. 94, 028101 (2005).
Open Chemical-systems Analysis
of Cellular Systems
• Theory of biochemical switches in signal
transduction
• Enzyme kinetics and dynamic cooperativity
• Kinetic proofreading and energy driven
specificity amplification
• Polymerase rate driven high fidelity in DNA
replication
Open Chemical-systems
Analysis of Cellular Systems
(1)
Theory of Biochemical
Switches in Signal Transduction
Qian, H. Biophys. Chem. vol. 105, pp. 585-593 (2003);
Qian, H. & Cooper, J.A. Biochem. vol. 47, pp. 2211-2220 (2008).
biologically active forms
of signaling molecules
[ B*]
[ B] + [ B*]
A*
A
1.0
B
in cell
B*
in test tube
0.0
[A*]
Biologically active forms
of signaling molecules
*
A
A
k1 [A*]
k-1[A*]
*
B
B
k-2
k2
k1, k-1, k-2 are rate
constants containing
[ATP], [ADP], and [Pi]
Introducing the amplitude of a switch
(AOS):
⎛ [ B*] ⎞
⎛ [ B*] ⎞
−⎜
AOS = ⎜
⎟
⎟
⎝ [ B ] + [ B*] ⎠[ A*]=∞ ⎝ [ B ] + [ B*] ⎠[ A*]=0
k1
k −2
γ −1
=
−
=
k1 + k−1 k2 + k−2 ( k1 / k−1 + 1)( k2 / k−2 + 1)
γ −1
⎛ ΔG ⎞
≤
= tanh ⎜
⎟
γ + 2 γ +1
⎝ 4 RT ⎠
Amplitude of the switch as a
function of the intracellular
phosphorylation potential
Response of a Switch
B activation as a function [A*]
= k1[ A*] k2
Cellular Nonequilibrium Condition
Phosphorylation Potential: Δ G = RT ln γ
γ
1010
104
103
102
ΔG (kcal/mol)
13.8
5.5
4.1
2.8
WE1
a1
d1
W
k1
q1
q2
d2
k2
W*
a2
W*E2
Qian, H., Biophys. Chem., vol. 105, pp. 585-593 (2003)
A. Goldbeter & D.E. Koshland, PNAS, vol. 78,
pp.6840-6844 (1981)
Zero-order Ultrasensitivity
First-order and Zero-order PdPC:
Sigmoidal and Ultasensitivity
The kinetic isomorphism between
PdPC and GTPase
No energy, no switch!
Open Chemical-systems
Analysis of Cellular Systems
(2)
Enzyme Kinetics and Dynamic
Cooperativity
Qian, H. Biophys. J., vol. 94, to appear (2008).
Fluctuating Enzyme and Dynamic
Disorder
Recent work in single-molecule
enzymology, by Xie and coworkers,
has convincingly demonstrated that
many enzymes have a slow
conformational fluctuations.
Single Channel Conductance
First Concentration Fluctuation
Measurements (1972)
(FCS)
Fast Forward to 1998
Stochastic Biochemical Kinetics
0.2mM
2mM
Lu, P.H., Xun, L.-Y. & Xie, X.S. (1998) Science, 282, 1877-1882.
Mean Product Waiting Time
k1[S]
E
k-1
ES
k2
E+
From S to P, it first form the complex ES with
mean time 1/(k1[S]), then the dwell time in state
ES, 1/(k-1+k2), after that the S either becomes P
or goes back to free S, with corresponding
probabilities k2 /(k-1+k2) and k-1 /(k-1+k2). Hence,
T =
1
1
k2
k-1
+
+
+
0
T
k 1 [S ] k - 1 + k 2 k - 1 + k 2
k- 1 + k2
Mean Waiting Time is the Double
Reciprocal Relation!
k −1 + k 2
1
+
T =
k 1k 2 [ S ] k 2
KM 1
1
=
+
v max [ S ] v max
k1
E+S
k-1
(A)
k2
ES
k-2
E+P
k1 [S]
k-1
ES
E
(B)
k2
k-2[P]
(A)
P
(B)
o
k3
k3
E1
k
E1
1 [S
]
k-1
β α
ES
]
S
[
k2
k-2
E2
o
k4
P
β
k
1 [S
]
α
E2
ES
S]
[
k2
% of maximal velocity
100
80
60
40
20
0
0
10
20
substrate concentration [S]
30
• Pathways in parallel is dictated
by average flux (rate)
• Pathway in serial order is
dictated by average time
From Cooperativity to
Specificity: The Square-law
v
vmax
∝
k1 k2 [S]2
Specificity Based on Off-rates:
Hopfield-Ninio’s Kinetics
Proofreading
o
E1S
k1 [S]
E
k-1
k-2
o
k2 [S]
P
k4
α
β
E2S
(A)
o
k1 [S]
k-1
E
k-2
k4
E1S
α
β
E2S
(B)
Open Chemical-systems
Analysis of Cellular Systems
(3)
Kinetic Proofreading and Energy
Driven Specificity Amplification
Qian, H. J. Mol. Biol. vol. 362, pp. 387-392 (2006).
The Original Kinetic Proofreading
Theory
In protein biosynthethesis, t-RNA
binding to corresponding codons:
the binding constants only have 100
fold difference, but there are fewer
errors in polypeptides in cells, ~1 in
every 10,000 residues.
Receptor–mediated Signal
Transduction and Specificity
GGTP
RL*
R+L
GGDP
RL
G
Two Ligands for a Receptor
L
R
L’
k1
k−1
RL
R
k1
,
k−1
RL’
The difference in the affinities is determined
by the dissociation constant
k−1
[ RL]eq
= Kd =
eq
eq
[ R ] [ L]
k1
With cyclic kinetics in ligand(s)
binding, in equilibrium:
L
R
k3
to down-stream
L
RL*
k−3 k
−1
k−2
k2
k1
RL
k1k 2 k3
=1
k −1k −2 k−3
In an open system, the ratio of
[RL*] to that of [R]:
[ RL*]
=
[ R][ L]
k1k 2 + k −1k −3 + k 2 k −3
k 2 k3 + k − 2 k −1 + k3k −1
if: k −1k −3 << k1k 2, or k 2 k −3
k3 k −1 >> k − 2 k −1 and k2 k3 .
k1k 2 k3
[ RL*]ness
1
>> 1 and
then
∝
2
ness
ness
[ R] [ L]
k −1k − 2 k −3
( Kd )
Energy can be used to amplify
specificity!
Open Chemical-systems
Analysis of Cellular Systems
(4)
Polymerase Rate Driven High
Fidelity in DNA Replication
Cady, F. & Qian, H. manuscript in preparation
DNA Polymerase Kinetics
Step 1
E + DNA
Step 2
E•DNA
Step 3
E•DNA•dNTP
E*•DNA•dNTP
Step 4
Step 6
E•DNA+1
k2
B
k
dNTP
k-2
o
1
k-1
k −o3
A
Step 5
E•DNA+1•PPi
E*•DNA+1•PPi
C
k3
PPi
A: E•DNA
B: E•DNA•dNTP
C: E•DNA+1•PPi
Cycle kinetics of DNA polymerase
with correct and wrong base
Bg
k2
k-2
k-1 k3
k1
Cg
p g k −3
A
r1
Bb
r3
r-1
r2
r-2
g
(1 − p )r− 3
Cb
Equilibrium vs. Kinetic Selectivities
prob. error
prob. correct
lnθ
lnη
η (1-p )/p
g
1
0.1
g
normalized relative error
For low equilibrium selectivity
(η=2)
θ = 10
θ = 100
θ = 1000
0.01
0.001
0
0.5
1
1.5
Δ G/RT
2
2.5
For high equilibrium selectivity
(η=100)
normalized relative error
η (1-pg)/pg
1
0.1
θ = 200
θ = 1000
θ = 10000
0.01
0
0.5
1
1.5
ΔG/RT
2
2.5
Conclusions
(1) We have present an open chemical
system theory as well as its
applications to several key
components in cellular systems,
including phosphorylation signaling,
switch, monomeric dynamic
cooperativity, kinetic proofreading
and specificity amplification, and
DNA replication fidelity.
Cont.
Currently, major efforts are being
directed toward elucidating the
complexity in biochemical
networks. However, without free
energy input, cellular networks
cannot function however complex
a chemical reaction system is.
(2) We have introduced nonequilibrium
steady-state (NESS) models that
quantitatively account for the energetics in
phosphorylation-dephosphorylation
switches and specificity amplification. It is
the chemical energy derived from ATP and
GTP hydrolysis that establishes the NESS
of a cell, and makes the cell ─ a tiny
biochemical reaction system that consists of
a collection of thermally driven fluctuating
macromolecules ─ a genetically
programmed chemical machine.
(3) As a biochemical machine, a cell
exhibits complex temporal behavior. Free
energy inputs assure that the important
biochemical reactions inside cells, not
dictated by thermal noise but dictated by
evolution, execute robust temporal
dynamics. Information processing in
cellular biology requires free energy
expenditure for its accuracy. It is thus
natural that evolution has chosen the
energy-rich phosphorylation reactions as
the ubiquitous mechanism for signal
transduction inside cells.
(4) In the light of current interests in
epigenetics, it is not unreasonable to
suggest that many cellular processes, such
as cell cycle, differentiation, and apoptosis
are all linked to cellular energy.
Acknowledgements
Thank You!