Journal: PLoS ONE

Article Title: A novel optogenetically tunable frequency modulating oscillator

doi: 10.1371/journal.pone.0183242

Figure Lengend Snippet: Two parameter bifurcation for HOTFM against the parameters for the repressor downstream of the two component light system (CcaS-CcaR); the x-axis corresponds to the repression coefficient K and y-axis corresponds to the degradation coefficient γ . The boundary of the shaded region represents the branch of hopf solutions; the unshaded region below the hopf branch corresponds to parameter values for which there exits a stable steady state and oscillations are absent. Whereas, the shaded region above the hopf branch represents parameter values for which stable oscillations exist. a) The two parameter bifurcation plot with the shaded region representing a heatmap for the period of oscillation. At each point in this region, the color represents the period of oscillation. Points farther away from the hopf branch in the shaded region show higher period (lower frequency), while the points closer to the hopf branch exhibit lower period (higher frequency). b) The two parameter bifurcation plot with the shaded region representing a heatmap for the period of oscillation. At each point in this region, the color represents the period of oscillation. Points farther away from the hopf branch in the shaded region show higher amplitude, while the points closer to the hopf branch exhibit lower amplitude.

Article Snippet: In this work, numerical bifurcation analysis has been employed for this purpose; the change in behavior of the HOTFM oscillator is tracked in the two parameter space of K and γ using numerical bifurcation performed with the Matlab package DDE-BIFTOOL [ ].

Techniques:

Journal: PLoS ONE

Article Title: A novel optogenetically tunable frequency modulating oscillator

doi: 10.1371/journal.pone.0183242

Figure Lengend Snippet: Robustness analysis with respect to Integrated Absolute Synchronization Error (IASE). Two parameter bifurcation plots are presented for HOTFM and the Danino oscillators in the γ I - γ A parameter space for IASE. The blue (red) curve respresents the hopf branch for HOTFM (Danino). Region above the hopf branch corresponds to parameter values where oscillations occur, while for regions below the hopf branch oscillation dies and steady state solution arises. For a comparative analysis of robustness between HOTFM and Danino we consider 520 points in the region of oscillations common to both HOTFM and Danino. At each point the system of equations (containing a linear array of 6 cells for both HOTFM and Danino) is numerically integrated for 500 minutes. From the obtained solutions IASE is calculated. For points which have IASE Danino − IASE HOTFM > 0, HOTFM is more robust compared to Danino, while for IASE Danino − IASE HOTFM < 0 Danino is more robust. a) Heatmap representing IASE Danino − IASE HOTFM at the 520 points in the oscillatory region common between HOTFM and Danino. Positive values suggest that HOTFM is more robust for IASE compared to Danino and vice versa. b) Heatmap for part a. thresholded at the value 0. Regions with positive values in a. have dark red color here, while regions with negative values in a. are colored blue. c) Heatmap for the effect sizes for individual points calculated using bootstrap estimates for the distribution for IASE Danino − IASE HOTFM Robustness Analysis for IASE. If IASE Danino − IASE HOTFM > 0, effect size is reported for greater robustness of HOTFM, while if IASE Danino − IASE HOTFM < 0, effect size (cohen’s d ) is reported for greater robustness of Danino. The color scheme is as follows—Blue (negligible effect, d < 0.2), Cyan (small effect, 0.2 ≤ d < 0.5), Yellow (medium effect, 0.5 ≤ d < 0.8) and Dark Red (large effect, d ≥ 0.8). d) Heatmap for the presence or absence of 0 in the 95% bootstrapped confidence interval. Dark red means absence of 0 while blue represents presence.

Article Snippet: In this work, numerical bifurcation analysis has been employed for this purpose; the change in behavior of the HOTFM oscillator is tracked in the two parameter space of K and γ using numerical bifurcation performed with the Matlab package DDE-BIFTOOL [ ].

Techniques:

Journal: PLoS ONE

Article Title: A novel optogenetically tunable frequency modulating oscillator

doi: 10.1371/journal.pone.0183242

Figure Lengend Snippet: Robustness analysis with respect to Rate of Synchronization ( r ). Two parameter bifurcation plots are presented for HOTFM and the Danino oscillators in the γ I - γ A parameter space for r . The blue (red) curve respresents the hopf branch for HOTFM (Danino). Region above the hopf branch corresponds to parameter values where oscillations occur, while for regions below the hopf branch oscillation dies and steady state solution arises. For a comparative analysis of robustness between HOTFM and Danino we consider 520 points in the region of oscillations common to both HOTFM and Danino. At each point the system of equations (containing a linear array of 6 cells for both HOTFM and Danino) is numerically integrated for 500 minutes. From the obtained solutions r is calculated. For points which have r Danino − r HOTFM < 0, HOTFM is more robust compared to Danino, while for r Danino − r HOTFM > 0 Danino is more robust. a) Heatmap representing r Danino − r HOTFM at the 520 points in the oscillatory region common between HOTFM and Danino. Negative values suggest that HOTFM is more robust for r compared to Danino and vice versa. b) Heatmap for part a. thresholded at the value 0. Regions with negative values in a. have dark red color here, while regions with positive values in a. are colored blue. c) Heatmap for the effect sizes for individual points calculated using bootstrap estimates for the distribution for r Danino − r HOTFM Robustness Analysis for Rate of Synchronization ( r ). If r Danino − r HOTFM < 0, effect size is reported for greater robustness of HOTFM, while if r Danino − r HOTFM > 0, effect size (cohen’s d ) is reported for greater robustness of Danino. The color scheme is as follows—Blue (negligible effect, d < 0.2), Cyan (small effect, 0.2 ≤ d < 0.5), Yellow (medium effect, 0.5 ≤ d < 0.8) and Dark Red (large effect, d ≥ 0.8). d) Heatmap for the presence or absence of 0 in the 95% bootstrapped confidence interval. Dark red means absence of 0 while blue represents presence.

Article Snippet: In this work, numerical bifurcation analysis has been employed for this purpose; the change in behavior of the HOTFM oscillator is tracked in the two parameter space of K and γ using numerical bifurcation performed with the Matlab package DDE-BIFTOOL [ ].

Techniques:

Journal: PLoS ONE

Article Title: A novel optogenetically tunable frequency modulating oscillator

doi: 10.1371/journal.pone.0183242

Figure Lengend Snippet: Robustness analysis with respect to Integrated Absolute Synchronization Error (IASE). Two parameter bifurcation plots are presented for HOTFM and the Danino oscillators in the γ H - γ A parameter space for IASE. The blue (red) curve respresents the hopf branch for HOTFM (Danino). Region above the hopf branch corresponds to parameter values where oscillations occur, while for regions below the hopf branch oscillation dies and steady state solution arises. For a comparative analysis of robustness between HOTFM and Danino we consider 1510 points in the region of oscillations common to both HOTFM and Danino. At each point the system of equations (containing a linear array of 6 cells for both HOTFM and Danino) is numerically integrated for 500 minutes. From the obtained solutions IASE is calculated. For points which have IASE Danino − IASE HOTFM > 0, HOTFM is more robust compared to Danino, while for IASE Danino − IASE HOTFM < 0 Danino is more robust. a) Heatmap representing IASE Danino − IASE HOTFM at the 1510 points in the oscillatory region common between HOTFM and Danino. Positive values suggest that HOTFM is more robust for IASE compared to Danino and vice versa. b) Heatmap for part a. thresholded at the value 0. Regions with positive values in a. have dark red color here, while regions with negative values in a. are colored blue. c) Heatmap for the effect sizes for individual points calculated using bootstrap estimates for the distribution for IASE Danino − IASE HOTFM Robustness Analysis for IASE. If IASE Danino − IASE HOTFM > 0, effect size is reported for greater robustness of HOTFM, while if IASE Danino − IASE HOTFM < 0, effect size (cohen’s d ) is reported for greater robustness of Danino. The color scheme is as follows—Blue (negligible effect, d < 0.2), Cyan (small effect, 0.2 ≤ d < 0.5), Yellow (medium effect, 0.5 ≤ d < 0.8) and Dark Red (large effect, d ≥ 0.8). d) Heatmap for the presence or absence of 0 in the 95% bootstrapped confidence interval. Dark red means absence of 0 while blue represents presence.

Article Snippet: In this work, numerical bifurcation analysis has been employed for this purpose; the change in behavior of the HOTFM oscillator is tracked in the two parameter space of K and γ using numerical bifurcation performed with the Matlab package DDE-BIFTOOL [ ].

Techniques:

Journal: PLoS ONE

Article Title: A novel optogenetically tunable frequency modulating oscillator

doi: 10.1371/journal.pone.0183242

Figure Lengend Snippet: Robustness analysis with respect to Rate of Synchronization ( r ). Two parameter bifurcation plots are presented for HOTFM and the Danino oscillators in the γ H - γ A parameter space for r . The blue (red) curve respresents the hopf branch for HOTFM (Danino). Region above the hopf branch corresponds to parameter values where oscillations occur, while for regions below the hopf branch oscillation dies and steady state solution arises. For a comparative analysis of robustness between HOTFM and Danino we consider 1510 points in the region of oscillations common to both HOTFM and Danino. At each point the system of equations (containing a linear array of 6 cells for both HOTFM and Danino) is numerically integrated for 500 minutes. From the obtained solutions r is calculated. For points which have r Danino − r HOTFM < 0, HOTFM is more robust compared to Danino, while for r Danino − r HOTFM > 0 Danino is more robust. a) Heatmap representing r Danino − r HOTFM at the 1510 points in the oscillatory region common between HOTFM and Danino. Negative values suggest that HOTFM is more robust for r compared to Danino and vice versa. b) Heatmap for part a. thresholded at the value 0. Regions with negative values in a. have dark red color here, while regions with positive values in a. are colored blue. c) Heatmap for the effect sizes for individual points calculated using bootstrap estimates for the distribution for r Danino − r HOTFM Robustness Analysis for Rate of Synchronization ( r ). If r Danino − r HOTFM < 0, effect size is reported for greater robustness of HOTFM, while if r Danino − r HOTFM > 0, effect size (cohen’s d ) is reported for greater robustness of Danino. The color scheme is as follows—Blue (negligible effect, d < 0.2), Cyan (small effect, 0.2 ≤ d < 0.5), Yellow (medium effect, 0.5 ≤ d < 0.8) and Dark Red (large effect, d ≥ 0.8). d) Heatmap for the presence or absence of 0 in the 95% bootstrapped confidence interval. Dark red means absence of 0 while blue represents presence.

Article Snippet: In this work, numerical bifurcation analysis has been employed for this purpose; the change in behavior of the HOTFM oscillator is tracked in the two parameter space of K and γ using numerical bifurcation performed with the Matlab package DDE-BIFTOOL [ ].

Techniques: