in this drawing of the lac operon, which molecule is an inactive repressor?
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Figure 1.
Three models for stochastic gene expression.
(A) Burst model in which transcription of the Dna is always agile. (B) Two-state model in which the Deoxyribonucleic acid switches with constant rates betwixt active and repressed states. (C) Inducible genetic switch in which an inducer both controls the charge per unit of switching betwixt agile and inactive transcription states and is likewise positively regulated by the protein product – a positive feedback loop (PFB). The greyness dotted connection indicates a weak effect of the inducer in promoting the unbinding of repressor at high inducer concentrations.
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Figure 2.
Overview of the lac genetic circuit in Eastward. coli.
(A) In the absence of inducer, the lac repressor (LacI) binds to the lac operator preventing transcription of genes in the lac operon. (B) Following an increment in the extracellular inducer concentration, inducer enters the cell via both diffusion beyond the membrane and active transport by lactose permease (LacY). Once within, inducer binds free LacI molecules preventing them from binding to the operator. (C) Afterward the intracellular inducer concentration reaches a threshold, any jump repressor is "knocked-off" the operator leading to expression of the lac genes. (D) At loftier intracellular inducer concentrations the genes for lactose metabolism are fully induced. (E) Afterward inducer is removed, repressor rebinds to the operator preventing further expression of the lac operon and the enzymes for lactose metabolism are either degraded or diluted through cellular segmentation.
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Tabular array 1.
Reactions and rate constants used in the stochastic model of the lac circuit.
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Figure three.
Fits of rate constants for IPTG binding to the lac repressor.
(A) Pseudo first guild rate constants observed during stochastic simulations of IPTG binding to (bluish) repressor and (red) repressor-operator complex. At each inducer concentration 1000 simulations starting with 2 free (or operator-complexed) repressor dimers in a volume of L were performed. The mean fraction of free repressor monomers as a function of time was fit to a unmarried exponential to obtain the observed rate constant for binding at the inducer concentration. 10 and o are data from Dunaway et al. [75]. (B) Equilibrium binding of IPTG to (blue) repressor and (carmine) repressor-operator complexes. In a stochastic simulation at each inducer concentration, 20 complimentary (or operator-complexed) repressor dimers in
Fifty were kickoff equilibrated with inducer to reach the steady state. Following, 5 minutes of data were collected from which the equilibrium fraction of inducer bound repressor monomers was calculated. x and o are data from O'Gorman et al. [74].
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Tabular array 2.
Obstacle affluence in in vivo spatial models.
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Effigy 4.
Markov diagram for transcriptional bursting in the lac circuit.
Under low-to-moderate inducer concentrations, a flare-up begins when the operator enters the state and ends when it transitions to a repressor bound land.
.
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Figure 5.
Parameter space of repressor binding parameter .
(A) Hateful burst size every bit a office of inducer concentration for diverse values of , where
. Parameters used were
=
G,
=
Chiliad,
=
, and
=
. (B) The charge per unit of change in the flare-up size with respective to the inducer concentration.
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Effigy half-dozen.
Linear fit of flare-up size to inducer concentration.
x are data from Choi et al. [22].
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Figure seven.
Outburst analysis of stochastic simulations of a uncomplicated two-state process.
The two-state process was described by: . Rate constants were chosen such that on average
bursts of Z with a constant burst size
were produced during Z'south mean lifetime with the mean duration of each burst lasting for the indicated fraction of the lifetime. At each point, 250 stochastic simulations were run until the probability density was stationary and so the distributions of Z were fit to gamma distributions to obtain the
and
parameters. The ratios of (A)
/
and (B)
/
as a part of the burst duration bear witness the range of burst durations for which a gamma distribution fit can reliably recover the original parameters. In this example
and
.
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Figure eight.
Parameter plumbing equipment for inducer–repressor–operator interactions.
(A) Fraction of operator regions bound by a repressor as a part of time following an increase of IPTG to the indicated concentration. In these simulations, . (B) Number of bursts over the mean poly peptide lifetime as a office of inducer concentration for a variety of values of the
parameter. x are data from Choi et al. [22].
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Figure ix.
Steady state LacY distributions from the well-stirred NPF model.
Distributions at inducer concentrations of (A) 0, (B) 100, and (C) 200 TMG. Shown are (greyness bars) histograms from x,000 Gillespie trajectories and (red dash) gamma distributions from Choi et al. [22]. (D) Hateful LacY equally a function of inducer concentration along with 95% ranges. (Eastward) The noise in the LacY distributions as quantified by the Fano factor (variance over the mean). (F) The fraction of time spent in the transcriptionally active state.
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Figure x.
Response of an uninduced PFB population to the addition of external inducer.
(A) Probability density (arbitrary units, darker = higher) of the number of LacY in a cell over the course of 24 hours. Shown are representative responses for populations in the uninduced range (0–10
; left), the bimodal range (10–25
; heart), and the concerted induction range (>25
; right). Lines evidence the mean value of the (green) uninduced and (red) induced subpopulations. (B) Fraction of the cells in each of the subpopulations. (C) The (solid) mean and (dotted) variance of LacY in the uninduced subpopulation.
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Figure eleven.
Effect of positive feedback on GRF noise.
(A) Mapping of the mean internal inducer concentration for a given external concentration for the (light-green) uninduced and (red) induced subpopulations. (black dotted) The values for the lac excursion without positive feedback are shown for reference. (B) The hateful number of LacY in the subpopulations as a part of internal inducer concentration. (C) The noise in the LacY distribution.
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Figure 12.
The effect of in vivo crowding on repressor rebinding.
Each line represents the hateful of 5000 trajectories. (A) The observed diffusion coefficient, , every bit a function of time calibration for a repressor diffusing in a volume with the indicated fraction occupied by in vivo obstacles. (B)
–exponent arising from fitting
to a model of anomalous diffusion,
. (C) The probability for a repressor to rebind with the operator before diffusing into the majority (64 nm from operator) following unbinding, every bit a function of the in vivo packing. (D) The distribution of escape times for repressors that diffuse to bulk rather than rebind, at 3 packing values.
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Figure 13.
LacY PFB+IV in vivo distributions.
(A) The distribution of LacY in (orange bars) 100 modeled E. coli cells at 13 TMG concentration compared with (light-green dotted) the PFB well-stirred distribution. (B) Mean number of LacY proteins in the (circles) PFB+Iv and (light-green dotted) PFB models. (C) The noise in the distributions.
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Figure 14.
Analysis of cryoelectron tomography based jail cell model.
(A) Slow growth E. coli cell model based in part on data from a tomographic reconstruction. Shown are (orange) ribosomes, (light gray) membrane, (dark grey) condensed nucleoid, and (scarlet) lac operator. (B+C) Distribution of repressor–operator complex lifetimes for the fast and tedious growth models, respectively. Curves show fits to an exponential distribution with the given mean. (D) Position of mRNA–membrane contact after diffusion of mRNA produced at the lac operon in (blue x) fast growth and (red o) slow growth models. Dotted lines evidence the length of the respective cells.
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Figure fifteen.
Maximum-likelihood fitting of 2 models for gene expression to stochastic simulations of an inducible genetic circuit.
(A and B) Parameter fits from the flare-up model. (C–F) Parameter fits from the two-state model. Shown are fits for (black dotted) NPF simulations, (green dotted) PFB simulations, and (orange circles) PFB+Four simulations. Also shown are (blue solid) actual parameter values calculated from the simulation data. Shaded areas indicate the 95% confidence intervals for ML fits using distributions from 50 and 200 NPF cells.
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Effigy 16.
Probability landscape of protein–mRNA abundances in the inducible lac switch model.
(A) Steady-land probability landscape (arbitrary units, darker = higher) for the NPF model at 500 TMG. The dotted line shows the trajectory of a representative cell during a ∼iii hour interval starting at the open up circumvolve and catastrophe at the closed circle. (B) Probability landscape of the PFB circuit over a period of 24 hours post-obit the addition of external TMG to 16
. The line follows a single cell switching from the uninduced to the induced state over the class of ∼13 hours.
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Source: https://journals.plos.org/ploscompbiol/article/figures?id=10.1371%2Fjournal.pcbi.1002010
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