Transcript Force vs. Velocity Profiles for Single Molecules of RNAP

Force vs. Velocity Profiles for Single
Molecules of RNAP
Transcription Mechanisms
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Transcription: Synthesis of
RNA from a DNA Template.
Requires DNA-dependent
RNA polymerase plus the
four nucleotides (ATP, GTP.
CTP and UTP).
Synthesis begins at a the
initiation site on DNA
The template strand is read
3' to 5' and the mRNA is
synthesized 5' to 3'
Aims of Investigation
The force vs. (steady state) velocity curve
gives a fundamental characterization of
the enzyme mechanism:
Mechanical loads opposing the forward
motion are applied to preturb selectively
rates of translocation steps
Experimental Design I
The Low Force Regime
Open loop mode
 Bead is held in weak trap of fixed stiffness,
subject to variable force
Experimental Design II
The High Force Regime
Closed loop mode
 Bead is held at low trap stiffness until clamp limit is
reached. After feedback circuit is triggered, position
of bead is actively maintained as trap stiffness rises
to compensate force produced by RNAP
Transcription at Low and High Loads
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Bead
displacement
and trap
stiffness gives
values of timevarying force
and RNAP
position along
template, which
can be used to
calculate RNA
transcript
lenght
Stall Forces of RNAP
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Assuming every
reaction cycle carries
RNAP forward app. By a
single base unit the
fraction of free energy
converted into
mechanical work near
stall is estimated at
44%, comparable to
50% of kinesin near
stall
Force-Velocity relations for RNAP
Parametrization of variables to obtain
ensemble data (before averaging):
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Dimensionless velocity v was
normalized to unloaded speed V0
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Dimensionless force f was
normalized to force at half of the
maximal velocity, F(1/2)
Assumption:
Large class of tightly coupled
enzymatic mechanisms for
elongation:
V(f) = 1/(1+a^(f-1))
Comparison with Theory
From fitted values of x and {F(1/2)}, a
characteristic distance δ over which load acts
can be computed according to eq. δ =
kbTln(a)/{F(1/2)}
Physical interpretation of δ depends on the
biochemical model invoked (5-10bp in present
paper)
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Biochemical Approaches
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Conformational changes taking place within a flexible
RNAP molecule cause it to alternate between
stressed and relaxed states, deforming by a variable
distance corresponding to 0 to 8 base pairs
The 3´-end of the RNA undergoes thermal
fluctuations against a physical barrier presented by
catalalytic site of enzyme. Rectification of this
random motion driven by free energy of nucleotide
condensation produces a Brownian ratchet that can
exert a significant force
Theoretical Approaches behind RNA
Elongation Mechanisms I
•Translocation rate kN is governed
by Arrhenius/Eyring kinetics – it
depends exponentially on the height
of the energy barrier between two sites
•Application of an external load F raises the
barrier by FΔ and slows the rate
•For this class of models, the distance δ
corresponds to Δ, the distance from the
initial site to the position of the barrier
maximum
Theoretical Approaches behind RNA
Elongation Mechanisms II
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One among the states 1 to N is a load
dependent composite of two
sequential substrates that are in rapid
equilibrium and located at adjacent
physical sites along the DNA
The rate of enzyme progress is
proportional to the relative occupancy
of the forward and reaward sites, p+
and pδ is identified as d, the physical
distance between the forward and
reaward sites on the DNA
Theoretical Approaches behind RNA
Elongation Mechanisms III
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Fully reversible reactions, with
an elongation – incompetent
state p branching off the main
pathway, transition to which is
load dependent
Here, δ = d, where d
characterizes the physical extent
of the conformational change
between the competent and
incompetent states (may not be
an integral multiple of base
pairs)
Force – Velocity Analysis
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All three mechanochemical models lead to the
F-V relation of the general Boltzmann form:
V(F) = V0(1+A)/(1+Aexp(Fδ/kbT))
This equation may be used to derive a scaling
formula permitting the single molecule
measurements of RNAP to be normalized and
hence compared, thus in dimensionless
variables: