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A variational approach to the stochastic aspects of cellular signal transduction
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10.1063/1.2353835
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Affiliations:
1 Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290
2 Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California 92093-0371
3 Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599-3290
a) Electronic mail: gpapoian@unc.edu
J. Chem. Phys. 125, 124106 (2006)
/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

FIG. 1.

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

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 .

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 .

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 .

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 .

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 .

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 .

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.

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 .

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 .

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.

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 .

/content/aip/journal/jcp/125/12/10.1063/1.2353835
2006-09-27
2014-04-16

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