10 research outputs found

    Monte Carlo simulations and ODE solutions of the market shares for symmetric appeals.

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    <p>The Monte Carlo simulations involved 10<sup>4</sup> realizations of the system for nine different set of parameters (grey lines). In all cases we used <i>q</i><sub>1</sub> = 1, the appeal used for both products were the same (<i>A</i><sub>1</sub> = <i>A</i><sub>2</sub>) and both products start with zero purchases, <i>d</i><sub>1</sub>(<i>t</i> = 0) = <i>d</i><sub>2</sub>(<i>t</i> = 0) = 0. Although the Monte Carlo simulations produce discrete dots in the (<i>d<sub>T</sub></i>, <i>MS</i><sub>2</sub>) space, we plot each simulation with straight lines that link consecutive dots to follow trajectories easily.</p

    Monte carlo simulations and ODE solutions of the market shares for asymetric appeals.

    No full text
    <p>The Monte Carlo simulations involved 10<sup>4</sup> realizations of the system for nine different sets of parameters (grey lines). In all cases, <i>q</i><sub>1</sub> = 1 and both products start with zero purchases, i.e., <i>d</i><sub>1</sub>(<i>t</i> = 0) = <i>d</i><sub>2</sub>(<i>t</i> = 0) = 0. Although Monte Carlo simulations produce discrete dots in the (<i>d<sub>T</sub></i>, <i>MS</i><sub>2</sub>) space, we plot each simulation with straight lines that link consecutive dots to follow trajectories easily.</p

    Monte Carlo simulations and ODE solutions of the market shares for symmetric appeals.

    No full text
    <p>The Monte Carlo simulations involved 10<sup>4</sup> realizations of the system for nine different set of parameters (grey lines). In all cases we used <i>q</i><sub>1</sub> = 1, the appeal used for both products were the same (<i>A</i><sub>1</sub> = <i>A</i><sub>2</sub>) and both products start with zero purchases, <i>d</i><sub>1</sub>(<i>t</i> = 0) = <i>d</i><sub>2</sub>(<i>t</i> = 0) = 0. Although the Monte Carlo simulations produce discrete dots in the (<i>d<sub>T</sub></i>, <i>MS</i><sub>2</sub>) space, we plot each simulation with straight lines that link consecutive dots to follow trajectories easily.</p

    Hill function dose-response.

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    <p>Schematic representation of Hill-type dose-response curves, in log-linear (A) and log-log scale (B). The EC10 and EC90 are the inputs needed to produce an output of 10% and 90% of the maximal response (<i>O</i><sub><i>max</i></sub>), respectively. The <i>Hill working range</i>, HWR, is the input range relevant for the calculation of the system’s <i>n</i><sub><i>H</i></sub>. For isolated modules, the HWR = [EC10, EC90]. Panel (C) displays the local ultrasensitivity (the response coefficient R) as a function of input. Note that for Hill functions, inputs much smaller than the EC50 have Rs around the Hill coefficient.</p

    Market share of product 2 (<i>MS</i><sub>2</sub>) as a function of <i>Q</i><sub>2</sub> and <i>A</i><sub>2</sub>, for different values of <i>A</i><sub>1</sub> and , assuming <i>q</i><sub>1</sub> = 1.

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    <p>Market share of product 2 (<i>MS</i><sub>2</sub>) as a function of <i>Q</i><sub>2</sub> and <i>A</i><sub>2</sub>, for different values of <i>A</i><sub>1</sub> and , assuming <i>q</i><sub>1</sub> = 1.</p

    Dose-response analysis for the dual step phosphorylation model.

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    <p>Transfer functions for each of the three layers of the MAPK cascade (A-C), obtained considering for each layer i) the isolated module (Is, dotted blue), ii) a mechanistic implementation of the model (Seq, dashed-turquoise) and iii) the mathematical composition of isolated response functions (Non-Seq, continous red). The corresponding response coefficient curves are shown in panels (D-F). Turquoise dashed vertical lines show the <i>X</i>10<sub><i>i</i></sub> and <i>X</i>90<sub><i>i</i></sub> values of each layer (i.e. mechanistic scheme), while red solid vertical lines mark the layer’s <i>X</i>10<sub><i>i</i></sub> and <i>X</i>90<sub><i>i</i></sub> associated to the composition of response curves of each module (i.e. <i>F</i><sup><i>non</i>—<i>seq</i></sup>).</p

    Schematic response function diagrams for two different compositions of two GK ultrasensitive modules are shown in panels (A) and (B).

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    <p>Axes were arranged as explained in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180083#pone.0180083.g002" target="_blank">Fig 2</a>’s caption. In panel (A) <i>O</i><sub>1,<i>max</i></sub> ≫ <i>EC</i>50<sub>2</sub>, and module-1’s HWR covers the input region below <i>EC</i>50<sub>1</sub>, a region in which the curve shows no local ultrasensitivity (<i>R</i><sub>1</sub> = 1). In panel (B) we show a special scenario where the <i>O</i><sub>2,<i>max</i></sub>/<i>EC</i>50<sub>2</sub> ratio was tuned in order to set module-1’s HWR in its most ultrasensitive region.</p

    Equivalence between a single-step layer in O’Shaughnessy model and a covalent modification cycle.

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    <p>O’Shaughnessy et al. single-step layer (A) and the equivalent covalent modification cycle (B). (C) Steady state transfer functions of ERK layer in isolation of the O’Shaughnessy single-step cascade (blue dashed line), compared to a centered Goldbeter-Function with equivalent parameters (red solid line) (<i>K</i><sub>1</sub> = 0.04 and <i>K</i><sub>2</sub> = 1000, see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180083#pone.0180083.s001" target="_blank">S1 Text</a>).</p

    Schematic diagrams of the response function when composing a Hill function in module-1, with a linear function (in green) or a power function (in blue) in module-2.

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    <p>Schematic diagrams of the response function when composing a Hill function in module-1, with a linear function (in green) or a power function (in blue) in module-2.</p

    Hill functions composition.

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    <p>Schematic response function diagrams for two different compositions of a pair of Hill-type ultrasensitive modules. In each panel, the dose-response function of the first module is displayed in the lower semi-plane: the downward vertical axis representing the first module’s input signal while its response function, which corresponds to the second module’s input, is displayed along the horizontal axis. The dose-response curve for the second module is displayed in the upper-plane. In (A) the maximum output of the first module is higher than the EC50 of the second module (<i>O</i><sub>1,<i>max</i></sub> ≫ <i>EC</i>50<sub>2</sub>), while in (B), it is lower than that value (<i>O</i><sub>1,<i>max</i></sub> < <i>EC</i>50<sub>2</sub>).</p
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