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A variational approach to the stochastic aspects of cellular signal transduction
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10.1063/1.2353835
/content/aip/journal/jcp/125/12/10.1063/1.2353835
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/12/10.1063/1.2353835
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

An inactive receptor , when activated by a signal, activates downstream protein .

Image of FIG. 2.
FIG. 2.

Comparison of the computed distributions for at for the two-step cascade: Gillespie simulation (circles), one-term basis (dash dotted line), integral form basis (solid line), expansion (dotted line), and Langevin equation (dashed line). (a) , , , and with initial conditions and (b) , , , and with .

Image of FIG. 3.
FIG. 3.

Comparison of the computed distributions for at and for the two-step cascade: Gillespie simulation (circles), integral form basis (solid line), expansion (dotted line), and Langevin equation (dashed line). , , , and with initial conditions .

Image of FIG. 4.
FIG. 4.

Comparison of the average and variance computed for the two-step cascade in the time interval : Gillespie simulation (circles), one-term basis (dash dotted line), integral form basis (solid line), expansion (dotted line), and Langevin equation (dashed line). , , , and with initial conditions .

Image of FIG. 5.
FIG. 5.

Comparison of the computed distributions for at for the three-step cascade without (a) and with (b) negative feedback: Gillespie simulation (circles), integral form basis (solid line), and Langevin equation (dashed line). , , , , , , and with initial conditions .

Image of FIG. 6.
FIG. 6.

Comparison of the average computed for the three-step cascade without (a) and with (b) negative feedback in the time interval : Gillespie simulation (circles), integral form basis (solid line), and Langevin equation (dashed line). , , , , , , and with initial conditions .

Image of FIG. 7.
FIG. 7.

Comparison of the variance computed for the three-step cascade without (a) and with (b) negative feedback in the time interval : Gillespie simulation (circles), integral form basis (solid line), and Langevin equation (dashed line). , , , , , , and with initial conditions .

Image of FIG. 8.
FIG. 8.

An inactive receptor , when activated by a signal, activates downstream protein , which in turn activates protein . In a negative feedback loop, downregulates the activation.

Image of FIG. 9.
FIG. 9.

Comparison of the computed distributions for at for the four-step cascade: Gillespie simulation (circles), integral form basis (solid line), and Langevin equation (dashed line). , , , , , , , and with initial conditions .

Image of FIG. 10.
FIG. 10.

Comparison of the average and variance computed for the four-step cascade in the time interval : Gillespie simulation (circles), integral form basis (solid line), and Langevin equation (dashed line). , , , , , , , and with initial conditions .

Image of FIG. 11.
FIG. 11.

Comparison of the computed distributions for at for the two-step cascade: Gillespie simulation (circles), integral form basis (solid line), expansion (dotted line), and Langevin equation (dashed line). , , , and with initial conditions . (a) and calculated by integrating the ODEs derived from Eq. (20). (b) and estimated by best fitting the exact solution. Shown in the picture is only the distribution profile on [0, 60] with other part close to zero.

Image of FIG. 12.
FIG. 12.

Comparison of the computed distributions for at (a) and (b) for the binding-dissociation reactions given by Eq. (A1): Gillespie simulation (circles), variational approach with simple basis, Eq. (A4), (solid line). and with initial condition .

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/content/aip/journal/jcp/125/12/10.1063/1.2353835
2006-09-27
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: A variational approach to the stochastic aspects of cellular signal transduction
http://aip.metastore.ingenta.com/content/aip/journal/jcp/125/12/10.1063/1.2353835
10.1063/1.2353835
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