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. 2010 Oct 13;5(10):e11207. doi: 10.1371/journal.pone.0011207

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Hassan M. Fathallah-Shaykh.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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To avoid the complications of numerical integration over long periods, the integration of these experiments is performed from 0 to 24 hr while computing measurements only at two fixed time points, and 24 hr; corresponds to either the time of the peak (), trough () of each direct target gene or . The procedure is then repeated with the last vector of the previous cycle as initial condition. The numerical integration methods are based on an explicit Runge-Kutta formula, the Dormand-Prince pair (ode45, Matlab), and on a variable order solver based on the numerical differentiation formulas (ode15s, Matlab). Relative error tolerance is . Data from ode45 are shown here, the results from ode15s are shown in Figure S4. (a) and (b) plot the jitter of per at in the wt and cwo-mutant models in LD, respectively (see Equation 3). (c) and (d) plot the network jitter of the wt and cwo-mutant models in LD, respectively. Notice that the limits converge and that per and network jitters are larger in the cwo-mutant model as compared to wt. Similarly, tim, cwo, pdp1 and vri jitters are also larger in the cwo-mutant models as compared to wt (Figures S1, S2, and S3). Network jitter is lower in the presence of CWO at , where refers to direct target genes. These times include ZT = 2.91, 4.19, 4.22, 5.2, 5.22, 8.68, 10.07, 10.15, 10.8, 10.99, 14.44, 15.95, 16.4, 16.77 and 19.09 in the wt model and ZT = 6.42, 7.58, 7.88, 7.94, 8.98, 12.19, 13.31, 13.75, 13.76, 14.97, 17.96, 19.04, 19.623, 19.57 and 20.97 in the cwo-mutant model (see Figures S1, S2, and S3).

Inline graphic — To avoid the complications of numerical integration over long periods, the integration of these experiments is performed from 0 to 24 hr while computing measurements only at two fixed time points, and 24 hr; corresponds to either the time of the peak (), trough () of each direct target gene or . The procedure is then repeated with the last vector of the previous cycle as initial condition. The numerical integration methods are based on an explicit Runge-Kutta formula, the Dormand-Prince pair (ode45, Matlab), and on a variable order solver based on the numerical differentiation formulas (ode15s, Matlab). Relative error tolerance is . Data from ode45 are shown here, the results from ode15s are shown in Figure S4. (a) and (b) plot the jitter of per at in the wt and cwo-mutant models in LD, respectively (see Equation 3). (c) and (d) plot the network jitter of the wt and cwo-mutant models in LD, respectively. Notice that the limits converge and that per and network jitters are larger in the cwo-mutant model as compared to wt. Similarly, tim, cwo, pdp1 and vri jitters are also larger in the cwo-mutant models as compared to wt (Figures S1, S2, and S3). Network jitter is lower in the presence of CWO at , where refers to direct target genes. These times include ZT = 2.91, 4.19, 4.22, 5.2, 5.22, 8.68, 10.07, 10.15, 10.8, 10.99, 14.44, 15.95, 16.4, 16.77 and 19.09 in the wt model and ZT = 6.42, 7.58, 7.88, 7.94, 8.98, 12.19, 13.31, 13.75, 13.76, 14.97, 17.96, 19.04, 19.623, 19.57 and 20.97 in the cwo-mutant model (see Figures S1, S2, and S3).