How Does Reaction vs Diffusion Regulate ROS/RNS Biology?

Sunrise Free Radical SchoolSociety for Free Radical Biology and Medicine

14th Annual MeetingNov. 16, 2007

J. R. Lancaster, Jr.Center for Free Radical BiologyDepartments of Anesthesiology,

Environmental Health Sciences, and Physiology & Biophysics

The University of Alabama at Birmingham

•Diffusibility

•Kinetics of Reaction

Two Properties Characteristic of Small, Uncharged, Highly Reactive Molecules

Kinetics of Reaction•Rate vs Rate Constant

•How Reactions Really Occur: Importance of Solvent Diffusion

•Sources and Sinks

•Crowding in the Cytoplasm

•Spatial Confinement of NO

•Net Movement of Collections of Molecules

•Significance of zero order kinetics

Diffusibility

How Reactions Really Occur 

In order for two molecules to react, they must collide. However, of the billions of chemical reactions, only a handful are rapid enough that the reaction will occur after only a few collisions. Thus, virtually all reactions occur only after the two molecules collide in “just the right way.”  In the gaseous phase, the distance between molecules is great enough to insure that molecules will separate rapidly after the collision. In the condensed phase, however (in aqueous solution or in tissue), individual molecules are surrounded by a “cage” of solvent (H2O) molecules. Thus, parts of the “walls” of these cages must move away from two solutes (reactants) in order for collisions to occur:

 Once this happens, however, the molecular pair is surrounded by the solvent cage which means that during the lifetime of the cage (which is 10-10 – 10-8 sec) the reactant molecules are colliding repeatedly. This is termed an “encounter.”

If the probability of the reaction is high enough that the reaction will occur every time there is an encounter, then the rate of the reaction (the overall rate) will depend only on how fast the two molecules will form an encounter. This is called the “diffusion limit.” No reaction can occur more rapidly than this limit.

This limit is in the range 109-1010 M-1s-1 (this is the value for k). Many reactions of radicals occur at this diffusion limit.

Dk T

r4

S tokes ’ L aw :

For N O (r = 1.4 x 10 m) in H O at 37 C , D = 2740 m /s

-10

o

22

D (m 2 /s ) N O (H 2O ) 3 3 0 0

N O (B ra in ) 3 8 1 0E th a n o l 11 0 0G lu co se 5 7 0S u crose 4 6 0

M yo g lo b in 11 3H em og lo b in 6 9

Temperature (kinetic energy)

Viscosity (solvent mobility)

Solute size

The Diffusion Constant: How Fast a Molecule Moves

Compartment A

Probability for NO moving from A to B:k x [NO]aProbability for NO moving from B to A:k x [NO]bIf [NO] = [NO], No Net Movement(NO's will just "change places")If [NO] > [NO], Net Movement from A to BIf [NO] > [NO], Net Movement from B to A

a b

a bb a

NOa

NOb

Compartment B

CONCLUSION: The only thing that "makes"molecules move from one place to anotheris the presence of concentration gradients.Molecules will move "downhill".always

kk

Net Movement of Collections of Molecules

Theoretical Predictions of Diffusion in Aqueous Solution

Method 1: Analytical SolutionsMethod 2: Numerical Solutions

Analytical Solutions: based on Fick’s Laws

An Example: Diffusion away from a sphere:

The Bible: Crank “The

Mathematics of Diffusion”:

][][][ 2

NOkr

NOD

t

NO

2/1

2ln

e][

][ tDr

o

r

NO

NO

[NO]o

[NO]r

r

For a given half-life of NO, what is r if [NO]r is 50% of [NO]o?

(the shorter the half-life the faster NO disappears as it travels, and so r will decrease)

Steady-State:

.

Point Source (2 µm diameter cell)

.

0 2 4 6 8 100

1x105

2x105

3x105

4x105

5x105

Num

ber

of C

ells

Aff

ecte

d

Half-Life (sec)

For cells 2 m diameter (3.35 x 10-14 L/cell); [NO]r/[NO]o

= 0.5:

For a half-life of 5 seconds, one NO-producing cell will affect 150,000 others

0.00 0.05 0.10 0.15 0.200

200

400

600

800

1000

1200

1400

Num

ber

of C

ells

Aff

ecte

d

Half-Life (sec)

For a half-life of 0.05 seconds, one NO-producing cell will affect 150 others

Leone et al. BBRC 221:37 (96)

Porterfield et al. AJP 281:L904 (01)

Malinski et al. BBRC 193:1076 (93)

175 m

Experimental:

Cell

100 µm

Beckman in “Nitric Oxide: Principles and Actions” Lancaster, ed. (1996)

Comparison with Other Reactive Species:

NO(N+1)NO(N-1)

N-1 N N+1

k3 k3

A Numerical Solution: Illustration of the Effect of Diffusion on Reaction:

Lancaster Meth. Enz. 268:31(96)

Entry or exit will affect ONLY the concentration of the species

k4NO(N)

NO3-

NOxk2

kf

How do we incorporate diffusion?:

)(42

)()1(3)1(3)(

)(

2

Nf

NNNN

NOkkk

NONOkNOkdt

NOd

k4NO(N)

NO3-

NOxk2

kfNO(N+1)NO(N-1)

N-1 N N+1

k3 k3

Lancaster in “Nitric Oxide Biology and Pathobiology” LJ Ignarro, ed. (00)

Lancaster Meth. Enz. 268:31(96)

Sources and Sinks:

Khan et al. PNAS 101:15944(04)

Stamler et al. Cell 106:675(01)

Spatial Confinement of NO

Lancaster Meth. Enz. 268:31(96)

Only way to spatially confine NO: Change its r (reaction)

Polarographic Measurement of D:

The Ilkovic Equation:

DA only in the Nernst layer!

Is Measurement of D with Electrodes Truly Reflective of Diffusion in Cells?:

“Macromolecular Crowding: an Important but neglected Aspect of the Intracellular Environment” Curr. Opin. Struct. Biol. 11:114(01)

Crowding in the Cytoplasm

Four factors that account for slowed diffusion:-- Slowed diffusion in fluid-phase cytoplasm-- Probe binding to intracellular components-- Probe collisions with intracellular components (crowding)

What are the data?

Verkman “Solute and Macromolecule Diffusion in Cellular Aqueous Compartments” Trends Biochem Sci 27:27 (02)

Kao et al. “Determinants of the Translational Mobility of a Small Solute in Cell Cytoplasm” J Cell Biol. 120:175 (93)

Two determinants of how fast a reaction occurs: Concentrations of reactants and rate constant: kA B

Akdt

Bd

For many reactions involving radicals, rate constants (k) are very large:

Rate ConstantRate

RATE VS. RATE CONSTANT:

Kirsch et al. Chem. Eur. J. 7:3313 (01)

109

k23

k24

k22

k30

k31

k32

k33

k34

k35k-32

k27

k28

k29

k25

k26 GS

GSOOGSSG -

[GSO ]xO + Products42 -

O + Products52 -

GSH

GSOH + NO2-

GSNO +H + NO+ -

2ONOO-

GSNO

GSSG[GSOONO]

GSOONO2GSONO2

GSSG

GSNO2

NO +H

2-

+

NO2

NO2

NO2

NO2

O2

GSOO

GS

HCO3-

GSH

GS-

N O2 3

GSOH 86%14%

CO 3-

O 2-O2

NO

NO

“All” Reactions:

Most Important Biologically:

k23

k24

k22

k30

k31

k32

k33

k34

k35k-32

k27

k28

k29

k25

k26 GS

GSOOGSSG -

[GSO ]xO + Products42 -

O + Products52 -

GSH

GSOH + NO2-

GSNO +H + NO+ -

2ONOO-

GSNO

GSSG[GSOONO]

GSOONO2

GSONO2

GSSG

GSNO2

NO +H

2

-

+

NO2

NO2

NO2

NO2O2

GSOO

GS

HCO3-

GSH

GS -

N O2 3

GSOH 86%14%

CO 3-

O 2-O2

NO

NO

B

A

C

WHY?

RATE VS. RATE CONSTANTLancaster Chem Res Toxicol 19:1160 (06)

An example: Reactions of GSH with RNS

NO2

NO + O2

GS

GSNO GSNO

N O2 3

NO

NO

GSH

GSHNO2-

RATE VS. RATE CONSTANT:

109 M-1s-12 x 107 M-1s-

1

Rate Constants

1 M5000 M

Rate = 2 x 107 x 5 x 10-3 = 105 M/s

Rate = 109 x 10-

6 = 103 M/s

3 x 109 M-1s-

16.6 x 107 M-1s-

1

Rate of C formation is independent of concentration of B (“zero order” in [B]). Only determined by the rate of formation of A.

k1k2

AB

C

1

12

21

2

0

kv

kBAk

BAkkdt

Ad

BAkdt

Cdv

Significance of Zero Order Kinetics:

0 10 20 30 40 50 600

20

40

60

80

RS

NO

(pm

ol/m

g)(

)

Time (min)

0

300

600

900

[NO

] (nM

)(

)

0 10 20 30 40 50 60 700

50

100

150

200

O2 (

M)

Time (min)

0 15 30 45 600.0

2.5

5.0

7.5

10.0

O2 (M

)

Time (min)

An Experimental Example: Measurement protein RSNO in cells treated with NO donor (Sper/NO); Simultaneous measurement of O2 and NO:

Rate of RSNO Formation is Zero Order in [NO]

0 10 20 30 40 50 600

20

40

60

80

RS

NO

(pm

ol/m

g)(

)

Time (min)

0

300

600

900

[NO

] (nM

)(

)

0 10 20 30 40 50 60 700

50

100

150

200

O2 (

M)

Time (min)

0 15 30 45 600.0

2.5

5.0

7.5

10.0

O2 (M

)

Time (min)

An Experimental Example: Measurement protein RSNO in cells treated with NO donor (Sper/NO); Simultaneous measurement of O2 and NO:

Also not dependent on [O2]

Inconsistent with2NO + O2

NO +NO2

2NO2

N O2 3

N O + RSH2 3 RSNO + NO + H2- +

Consistent with

RS + NO RSNO

Charles BosworthHarry MahtaniJose ToledoBill Gates

American Cancer SocietyNIH

Sunrise Free Radical School, 2007

Society for Free Radical Biology and Medicine

14th Annual Meeting

Washington, D.C.