DSSA Simulations: Exploring the Effects of <i>h</i>

<p>The horizontal dotted line marks <i>P</i>₀, mRNA is represented by the solid line, and protein by the dashed line.</p

Mean Oscillation Frequencies for Different Delay Values (<i>P</i>₀, <i>h</i>, <i>μ_m, μ_p</i> Are Fixed)

<p>Mean Oscillation Frequencies for Different Delay Values (<i>P</i>₀, <i>h</i>, <i>μ_m, μ_p</i> Are Fixed)</p

DSSA Simulations: Exploring the Effects of <i>P</i>₀

<p>The horizontal dotted line marks <i>P</i>₀, mRNA is represented by the solid line, and protein by the dashed line.</p

DDE Solution: Exploring the Effect of Large <i>P</i>₀

<p>DDE Solution: Exploring the Effect of Large <i>P</i>₀</p

DSSA Simulations: Exploring the Effects of Delay

<p>The horizontal dotted line marks <i>P</i>₀, mRNA is represented by the solid line, and protein by the dashed line.</p

DSSA Simulations for <i>P</i>₀ = 100, <i>h</i> = 3, <i>τ</i> = 10 (Top) and <i>P</i>₀ = 100, <i>h</i> = 4, <i>τ</i> = 15 (Bottom) over 12 h and 2 h

<p>Left, more than 12 h. Right, more than 2 h. The dotted horizontal line corresponds to <i>P</i>₀. Solid lines represent mRNA, dashed lines protein populations.</p

Sensitivity Analysis: DSSA Simulations with Perturbed Rate Constants

<div><p>(A) <i>α_m</i><b>.</b></p><p>(B) <i>α_p</i><b>.</b></p><p>(C) <i>μ_m</i><b>.</b></p><p>(D) <i>μ_p</i>.</p></div

DDE Solution: Exploring the Effect of Delay on Protein

<p>DDE Solution: Exploring the Effect of Delay on Protein</p

APD dispersion at forty-eight equally spaced nodes in [0.06 cm, 1 cm] for ten different values of <i>α</i>.

<p>For a fixed <i>α</i>, the APD is computed from the AP solution profile recorded at each considered node in the spatial interval. Dispersion of APD is then defined as the difference between the computed value of APD at that node and the maximum APD value recorded for the same value of <i>α</i> over the entire spatial domain.</p

Temporal evolution for <i>t</i> ∈ [0,400 ms] of the standard solution with reduced conductivity and the fractional solution with unit conductivity parameter at three equally spaced nodes <i>P</i>₁, <i>P</i>₂, <i>P</i>₃, in the spatial domain [0, 1 cm].

<p>The continuous blue line corresponds to the standard solution obtained with <i>α</i> = 2, <i>D</i> = 0.093 mS⋅cm⁻¹. The dashed red line represents the fractional solution obtained by setting <i>α</i> = 1.5, <i>D</i> = 1 mS⋅cm⁻¹. In both cases the stimulus <i>I</i>_stim = 40 <i>μ</i>A⋅cm⁻³ was applied on [0,0.05 cm] at <i>t</i>_stim = 10 ms for two consecutive milliseconds and then removed.</p