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.

☺
• 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).

in Hebrew

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!

o k
+1
A+B k
-1 o
C+D forward flux = backward flux: k o
+ 1
A B eq = k o
− 1
C D eq
A B eq
C D eq
= k o
− 1 = k o
+ 1
K
1 eq

For a driven reaction, how much is the energy from the surrounding medium?
From elementary biochemistry, the free
-RT ln
K of a reaction: A+B k o
C+D k
-1
Δ = Δ
G o +
RT ln ≠
0 in a cell!

living part
G o
RT ln
S cell
P cell dead part

A+B
C+D the free energy difference, i.e., chemical
“voltage” multiplies the flux, i.e. chemical
“current”: Δ
G × J
, is the amount of chemical “power” going to the reaction.
(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

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…

P k
3
o k
-3 k
-2 k
-1
k
2 o k
1
S o [ ] k k k o
− 3
[ ]
= 1
P eq
S eq o
= k k k o
− 1 − 2 − 3
=
K eq

P
S o [ ]
− 1 − 2
− o k k k P
3
[ ]
> 1,
P cell
S cell
>
K eq o [ ] cell
RT ln k k k o
− 3
[ ] cell
=
RT ln
K eq [ ] cell
P cell
= Δ cell
G
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 k
3
E *
2
E k o
-3 k
-2 o k
-1 o k
1
E *
1 k
2
D

• 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.

• The available energy relevant to a normal living cell is from the sustained high concentration of
ATP (~1mM) and low concentrations of ADP
(~10 μ M). With an equilibrium constant of 4.9 x 10 5 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?

?

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

(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
A A
*
B B
*
1.0
0.0
in cell in test tube
[
A*
]

Biologically active forms of signaling molecules
A A
*
B k
-1
[A*]
B
* k
-2 k
2 k
1
[A*] k
1
, k
-1
, k
2 are rate constants containing
[ATP], [ADP], and [Pi]

Introducing the amplitude of a switch
(AOS):
AOS
=
⎛
⎝ +
⎞
⎠
=
≤ k
1 k
+
1 k
− 1
− k
2 k
+
− 2 k
− 2
γ − 1
γ + 2 γ + 1
= tanh
=
=∞
−
⎛
⎝
( k
1
/ k
− 1
+
⎞
⎠
+
γ
)(
− 1
1 k
2
/ k
− 2
+ 1
)
Δ
G
4
RT

Amplitude of the switch as a function of the intracellular phosphorylation potential

Response of a Switch
B activation as a function [A*]
= [ *] k
2

Cellular Nonequilibrium Condition
Phosphorylation Potential: G RT ln γ
γ Δ
G
(kcal/mol)
10 10 13.8
10 4 5.5
10 3 4.1
10 2 2.8

W k a
1
2
WE
1 k
1 q d
1
2
W*E
2 q
1 d
2 a
2
W*
Qian, H., Biophys. Chem.
, vol. 105 , pp. 585-593 (2003)

First-order and Zero-order PdPC:
Sigmoidal and Ultasensitivity

The kinetic isomorphism between
PdPC and GTPase

(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.

E k
1
[S] k
-1
ES k
2
E +
From S to P, it first form the complex ES with mean time 1/( k
1
[S]), then the dwell time in state
ES, 1/( k
-1
+ k
2
), after that the S either becomes P or goes back to free S, with corresponding probabilities k
2
/( k
-1
+ k
2
) and k
-1
/( k
-1
+ k
2
).
Hence,
T
= k
1
1
[ S ]
+ k
1
1
+ k
2
+ k
1 k
+
2 k
2
0 + k
1 k
-
+
1 k
2
T

Mean Waiting Time is the Double
Reciprocal Relation!
T
= k k
−
1
1 k
2
+
[ k
S
2
]
+
1 k
2
=
K
M v max
1
[ S ]
+
1 v max

E + S
(A) k
1 k
-1
ES k
1
[S] k
2 k
-2
E + P k
-1
E ES
(B) k
2 k
-2
[P]

P
(A) k
3 o
E
1 k
1
[S
]
β
E
2
α k
-1 k
2
[S
] k
-2
ES k
4 o
P
(B) k
3
β
E
1
α k
1
[S
]
ES
E
2 k
2
[S
]

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

v v max
k
1 k
2
[
S
] 2

Specificity Based on Off-rates:
Hopfield-Ninio’s Kinetics
Proofreading
P k
1 o
[S]
E
1
S k
-1
E k
2 o
[S] k
-2
α β
E
2
S k
4
(A)
E k
1 o
[S] k
-1
α
E
1
S
β k
4 k
-2 E
2
S
(B)

(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
G GTP
R+L
RL *
G GDP
RL G

L ’ L
k
1 k
−1
k
1
, k
−1
L
The difference in the affinities is determined by the dissociation constant
[
RL
] eq
R L eq
=
K d
= k
− 1 k
1

With cyclic kinetics in ligand(s) binding, in equilibrium: to down-stream
L
k
3
*
L
k
−3 k
−2 k
−1 k
1
k
2 k
1 k
2 k
3 k
− 1 k
− 2 k
− 3
= 1

In an open system, the ratio of
[
RL*
] to that of [
R
]:
[
RL
*]
= k
1 k k
2 k
3
2
+
+ k
− 1 k
− 3 k
− 2 k
− 1
+
+ k
2 k
− 3 k
3 k
− 1 if: k
− 1 k
− 3
<< k
1 k
2 , or k
2 k
− 3 k
3 k
− 1
>> k
− 2 k
− 1 and k
2 k
3
.
then k
1 k
2 k
3 k
− 1 k
− 2 k
− 3
>> 1 and
[
RL
*] ness
R L ness
∝
1
2

Energy can be used to amplify specificity!

(4)
Polymerase Rate Driven High
Fidelity in DNA Replication
Cady, F. & Qian, H. manuscript in preparation

DNA Polymerase Kinetics
E + DNA
Step 1
E•DNA
Step 2
E•DNA
+1
Step 6
E • DNA • dNTP
Step 3
E* • DNA • dNTP
Step 4
E • DNA
+1
• PPi
Step 5
E* • DNA
+1
• PPi dNTP k
2
B k
1 o k
-1 k
-2 k o
−
3
A
C k
3
PPi
A: E•DNA
B: E•DNA•dNTP
C: E•DNA
+1
•PPi

Cycle kinetics of DNA polymerase with correct and wrong base k
2
B g k
-1 k
-2 k
3 k
1
A
C g p g k
−
3
B r
1 b r
-1 r
2 r
-2 r
3
( 1
− p g ) r
−
3
C b

Equilibrium vs
. Kinetic Selectivities
ln θ ln η

For low equilibrium selectivity
(
=2
)
1
0.1
0.01
0.001
0 0.5
1 1.5
Δ
G/RT
2
θ = 10
θ = 100
θ = 1000
2.5

For high equilibrium selectivity
(
=100
)
1
0.1
θ = 200
θ = 1000
θ = 10000
0.01
0 0.5
1 1.5
2 2.5
Δ
G/RT

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!