Transcription Kinetics in Bacteria. Ido Golding Department of Molecular Biology Princeton University Johan Paulsson Edward C. Cox. Cellular life as a set of discrete events. Transcription (initiation, elongation, termination) Translation RNA & protein degradation
Transcription Kinetics in Bacteria
Department of Molecular Biology
Edward C. Cox
To Reliably detect and quantify the kinetics of these processes
(Usually obscured by population averaging etc.)
“The central dogma of molecular biology”
DNA RNA PROTEIN
Miller et al (1970)
In vivo / Whole population:
In vitro / Single molecule:
Optical trapping setup for studying RNA polymerase
J. Shaevitz et al, Nature426: 684 - 687 (2003)
Record of RNA polymerase motion
Following transcription in real-time
Gene of interest:
Golding et al, Cell (2005)
Spot intensity ~ 70 GFPs
Golding and Cox, PNAS (2004); Golding and Cox, Phys. Rev. Lett. (2006)
RNA copy number:
1st peak =
50-100 X GFP =
Gene induction kinetics:
Indicators of gene activity
+ additional tests
QPCR: S. Zawilski
Lux: Lutz & Bujard 1997
2. mRNA & protein numbers:
mRNA number of bound MS2-GFP proteins
photon flux from localized green fluorescence
Protein number of mRFP1 proteins
photon flux from whole-cell red fluorescence
mRNA per cell
Approach to steady state
Constant rate of production k1 ; first-order elimination with rate constant k2:
dn/dt = k1 – k2n
n(t) = k1 /k2 (1 – e - k2t)
n(t) = mRNA/cell
k1= transcription rate = 0.14 min-1 (fit)
k2= dilution rate = ln 2 / 50 min-1
Average kinetics consistent
with Poisson process.
mRNA copy-number histogram
Variance vs mean
Fraction of cells with no mRNA:
k1 (measured) 0.03 min-1
rate of N0 decline << transcription rate!
Probability of zero events
Variance to mean ratio:
Poisson:s2 / n = 1
measured:s2 / n 4
with Poisson process!
Gene in the OFF state switches ON with a constant probability (k1).
Gene in the ON state either switches OFF (k2),
or makes a transcript with constant probability (ktrans).
Can result in transcriptional bursting (burst size b ~ ktrans / k2)
Golding & Cox, Curr. Biol. (2006).
(analytical results, simulations)
P0(t)declines with ratek1
mRNA number histogram
Measured transcription rate
k1eff = k1 * b
Thattai and van Oudenaarden 2001;Paulsson 2004
RNA kinetics in individual cells
# mRNA vs time
Distribution of on & off times
Distribution of burst sizes
RNA bursts geometrically distributed
On & off times exponentially distributed
Chubb JR, Trcek T, Shenoy SM, Singer RH.
Curr. Biol. 2006 May 23;16(10):1018-25.
See also: Golding & Cox, Curr. Biol. (2006).
Yu J, Xiao J, Ren X, Lao K, Xie XS
Science. 2006 Mar 17;311(5767):1600-3.
Cai L, Friedman N, Xie XS
Nature. 2006 Mar 16;440(7082):358-62.
See also: Golding & Cox, Genome Biology (2006).
DN = difference in RNA numbers between 2 daughter cells.
Binomial statistics - consistent with independent segregation of individual molecules.
1) Protein copy number is proportional to mRNA copy number
2) How many proteins are made from one transcript?
IG = (nRNA*N) * fGFP
IR= nPROTEIN* fRFP
IG = green fluorescence level (of spots)
IR = red fluorescence level (of cell)
fGFP = flux from one GFP molecule
fRFP = flux from one RFP molecule
N ~ 50-100, IR / IG = 3.10.2
fRFP /fGFP 31
p = nPROTEIN / nRNA= N * (fGFP /fRFP ) * (IR / IG) 60-110
protein vs mRNA
+ single cells:
Golding and Cox, PNAS (2004)
constrained motion punctuated by large jumps
Golding & Cox,
Phys. Rev. Lett. (2006)
a=1 (in vitro)
a=0.7 (in vivo)
slope = -(1+a) = -1.77
slope = -1.96
Motion is sub-diffusive:
d2 = a ta , a = 0.70±0.07
(in vitro: a = 1.04 ±0.03)
Similar motion observed in eukaryotic cells
(lipid granules, dextran etc)
Power spectrum of position:
P(f) ~ f -(1+a) , a = 0.77±0.03
Sub-diffusion arising from long-tailed distribution of waiting times:
w(t) ~ t-(1+a)with 0 < a< 1
(Metzler & Klafter 2000)
Interaction with heterogeneous medium
MreB & FtsZ mutants exhibit sub-diffusion similar to wild-type
(“Mixed” results in eukaryotes: Weiss et al 2004,
Tolic-Norrelykke et al 2004, Dauty and Verkman 2005)
(2) Molecular crowding?
Large volume fraction of cell taken by
~300 mg/ml (Zimmerman & Trach 1991)
~1 mm DNA
* Sub-diffusion coefficient decreases with growth rate
* Deleting RBS leads to faster motion
* In vitro results (Banks and Fradin 2005)
* Monte-Carlo simulations
(Saxton 1994, Weiss et al 2004)
What hinders motion in the cytoplasm?
Exponent a is insensitive to system parameters:
presence of RBS, length of RNA molecule, growth rate, presence of antibiotics (Cm,Tet), cytoskeletal elements (MreB,FtsZ)…
a =al +(1-al)e-f/f0
(Banks & Fradin 2005)
F0 =threshold density for S.D. = ?
al =asymptotic value of a ≈ 0.74
Values for E. coli :
F* ≈ 0.4 (Zimmerman & Trach 1991)
a*≈ 0.74 (this study)
E. coli :
F* >> F0
(F* , a*)
(von Hippel & Berg 1989).
(Warren & ten Wolde 2004).
p ~ (a/r)3-2/a (p→1 for a →2/3)
where a = target size, r = initial distance
(Golding & Cox 2006, Halford & Marko 2004).
infected with phage l
DNA, RNAP, ribosomes, cytoskeleton…
D. Peabody, H. Diamant, R. Segev, Y. Zhang,
R. Austin, P. Wolanin, J. Puchalla
& all members of the Cox lab