Skip to main content
Figure 1 | Theoretical Biology and Medical Modelling

Figure 1

From: Relating a calcium indicator signal to the unperturbed calcium concentration time-course

Figure 1

a: Dependence of the time-constant τ1 of the linearized system on the two dimensionless kinetic parameters Rb and Rf, shown as a contour plot in the Rb-Rf plane. Numbers on the iso-τ lines indicate the value of the time-constant in seconds. b: Time-course of the calcium-bound indicator signal y(t) in the linear regime, i.e. when eqs. (15) and (16) apply. The inset shows the parameters for the two exponential functions describing the time course: y ( t ) = y ( 0 ) ( c 1 e t / τ 1 + c 2 e t / τ 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEcqGGOaakcqWG0baDcqGGPaqkcqGH9aqpcqWG5bqEcqGGOaakcqaIWaamcqGGPaqkcqGHflY1daqadaqaaiabdogaJnaaBaaaleaacqaIXaqmaeqaaOGaeyyXICTaemyzau2aaWbaaSqabeaacqGHsislcqWG0baDcqGGVaWliiGacqWFepaDdaWgaaadbaGaeGymaedabeaaaaGccqGHRaWkcqWGJbWydaWgaaWcbaGaeGOmaidabeaakiabgwSixlabdwgaLnaaCaaaleqabaGaeyOeI0IaemiDaqNaei4la8Iae8hXdq3aaSbaaWqaaiabikdaYaqabaaaaaGccaGLOaGaayzkaaaaaa@5404@ for the decay, and y ( t ) = y ( 0 ) ( 1 c 1 e t / τ 1 + c 2 e t / τ 2 ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWG5bqEcqGGOaakcqWG0baDcqGGPaqkcqGH9aqpcqWG5bqEcqGGOaakcqaIWaamcqGGPaqkcqGHflY1daqadaqaaiabigdaXiabgkHiTiabdogaJnaaBaaaleaacqaIXaqmaeqaaOGaeyyXICTaemyzau2aaWbaaSqabeaacqGHsislcqWG0baDcqGGVaWliiGacqWFepaDdaWgaaadbaGaeGymaedabeaaaaGccqGHRaWkcqWGJbWydaWgaaWcbaGaeGOmaidabeaakiabgwSixlabdwgaLnaaCaaaleqabaGaeyOeI0IaemiDaqNaei4la8Iae8hXdq3aaSbaaWqaaiabikdaYaqabaaaaaGccaGLOaGaayzkaaaaaa@55E1@ for the increase. If not subject to variation, the parameters in both a and b were as follows: kb = 100.0 [1/sec], kf = 0.1 [1/(nMol*sec)], γ = 20.0 [1/sec], ymax = 1000.0 [nMol] and α0 = 100.0 [nMol/sec]. Consequently, the KD = 1000 nMol, and the dimensionless kinetic parameters Rb and Rf both were 5.0.

Back to article page