Biochemical Frequency Control by Synchronisation of Coupled Repressilators: An <i>In Silico</i> Study of Modules for Circadian Clock Systems

<table>Typical temporal course towards synchronisation of two marginally different initial frequencies (solid lines) converging to a common value (dashed curves). Coupling strength: <svg height="11.0125" id="M37" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 73.6875 11.0125" width="73.6875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.0125)">
<g transform="translate(72,-63.19)">
<text transform="matrix(1,0,0,-1,-71.95,63.41)">
<tspan style="font-size: 12.50px; " x="0" y="0">d</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">i</tspan>
<tspan style="font-size: 12.50px; " x="9.727334" y="0">ﬀ</tspan>
<tspan style="font-size: 12.50px; " x="24.930983" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="36.958866" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="43.210369" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="46.336117" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="52.58762" y="0">1</tspan>
</text>
</g>
</g>
</svg>, ratio of initial frequencies: <svg height="11.1" id="M38" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 176.2375 11.1" width="176.2375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="21.880251" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="28.13175" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="34.383251" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="40.63475" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="46.88625" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="50.362083" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="56.613583" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="59.739334" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="65.990837" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="72.242332" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="78.493835" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="84.745331" y="0">7</tspan>
<tspan style="font-size: 12.50px; " x="90.996834" y="0">8</tspan>
<tspan style="font-size: 12.50px; " x="100.71166" y="0">≈</tspan>
<tspan style="font-size: 12.50px; " x="112.75205" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="119.00356" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="122.1293" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="128.3808" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="134.63231" y="0">2</tspan>
</text>
</g>
</g>
</svg>. Synchronous frequency: 0.001616.</table>

Computational Intelligence and Neuroscience

fig4

Figure 4

Figure 4: Biochemical Frequency Control by Synchronisation of Coupled Repressilators: An <i>In Silico</i> Study of Modules for Circadian Clock Systems 

Computational Intelligence and Neuroscience

Biochemical Frequency Control by Synchronisation of Coupled Repressilators: An In Silico Study of Modules for Circadian Clock Systems

Figure 4