Force vs. Velocity Profiles for Single Molecules of RNAP

Transcription Mechanisms 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 IThe Low Force Regime

Open loop mode Bead is held in weak trap of fixed

stiffness, subject to variable force

Experimental Design IIThe 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

Bead displacement and trap stiffness gives values of time-varying force and RNAP position along template, which can be used to calculate RNA transcript lenght

Stall Forces of RNAP

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 RNAPParametrization of variables to

obtain ensemble data (before averaging):

Dimensionless velocity v was normalized to unloaded speed V0

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)

Biochemical Approaches 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

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 p-

δ is identified as d, the physical distance between the forward and reaward sites on the DNA

Theoretical Approaches behind RNA Elongation Mechanisms III

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 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: