Under these simplifications, population densities of PQ molecules at each level and photoproduct can be solved and written as Display Formula
$N0(t)=NA\u2009exp(\u2212qUV0\rho UVt),$(7)
Display Formula$N1(t)=qUV0\rho UV\tau 121\u2212qUV0\rho UV\tau 12NA[exp(\u2212qUV0\rho UVt)\u2212exp(\u2212t/\tau 12)],$(8)
Display Formula$N2(t)=qUV0\rho UVNA\u2009exp[\u2212(qUV2\rho UV+qR\rho R)t](\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12)+qUV0\rho UV(1\u2212qUV0\rho UV\tau 12)NA\u2009exp(\u2212qUV0\rho UVt)(\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)\u2212qUV0\rho UV\tau 12(1\u2212qUV0\rho UV\tau 12)NA\u2009exp(\u2212t/\tau 12)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12),$(9)
Display Formula$N3(t)=NAqR\rho RqUV0\rho UV\u2009exp(\u2212Mk3Pt)(1\u2212\tau 12Mk3P)(qUV0\rho UV\u2212Mk3P)(qUV2\rho UV+qR\rho R\u2212Mk3P)\u2212qR\rho RqUV0\rho UVNA(qUV2\rho UV+qR\rho R\u2212Mk3P)\u22121exp[\u2212(qUV2\rho UV+qR\rho R)t](\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12)\u2212qUV0\rho UV(qUV0\rho UV\u2212Mk3P)1(1\u2212qUV0\rho UV\tau 12)qR\rho RNA\u2009exp(\u2212qUV0\rho UVt)(\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)+qUV0\rho UV\tau 12(1\u2212qUV0\rho UV\tau 12)qR\rho RNA(1/\tau 12\u2212Mk3P)\u22121exp(\u2212t/\tau 12)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12),$(10)
Display Formula$NB(t)=NAqUV2\rho UVqUV0\rho UV\u2009exp(\u2212MkBPt)(1\u2212\tau 12MkBP)(qUV0\rho UV\u2212MkBP)(qUV2\rho UV+qR\rho R\u2212MkBP)\u2212qUV2\rho UVqUV0\rho UVNA(qUV2\rho UV+qR\rho R\u2212MkBP)\u22121exp[\u2212(qUV2\rho UV+qR\rho R)t](\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12)\u2212qUV0\rho UV(qUV0\rho UV\u2212MkBP)11\u2212qUV0\rho UV\tau 12qUV2\rho UVNA\u2009exp(\u2212qUV0\rho UVt)(\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)+qUV0\rho UV\tau 121\u2212qUV0\rho UV\tau 12qUV2\rho UVNA(1/\tau 12\u2212MkBP)\u22121exp(\u2212t/\tau 12)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12),$(11)
Display Formula$NP(t)=NA\u2212NAqR\rho RqUV0\rho UV\u2009exp(\u2212Mk3Pt)(1\u2212\tau 12Mk3P)(qUV0\rho UV\u2212Mk3P)(qUV2\rho UV+qR\rho R\u2212Mk3P)\u2212NAqUV2\rho UVqUV0\rho UV\u2009exp(\u2212MkBPt)(1\u2212\tau 12MkBP)(qUV0\rho UV\u2212MkBP)(qUV2\rho UV+qR\rho R\u2212MkBP)+[Mk3PqR\rho R(qUV2\rho UV+qR\rho R\u2212Mk3P)+MkBPqUV2\rho UV(qUV2\rho UV+qR\rho R\u2212MkBP)]\xd7qUV0\rho UVNA\u2009exp[\u2212(qUV2\rho UV+qR\rho R)t](qUV2\rho UV+qR\rho R)(\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12)+[qR\rho RMk3P(qUV0\rho UV\u2212Mk3P)+qUV2\rho UVMkBP(qUV0\rho UV\u2212MkBP)]\xd71(1\u2212qUV0\rho UV\tau 12)NA\u2009exp(\u2212qUV0\rho UVt)(\u2212qUV0\rho UV+qUV2\rho UV+qR\rho R)+[\u2212qR\rho RMk3P(1/\tau 12\u2212Mk3P)\u2212qUV2\rho UVMkBP(1/\tau 12\u2212MkBP)]\xd7qUV0\rho UV\tau 12\tau 12NA\u2009exp(\u2212t/\tau 12)(1\u2212qUV0\rho UV\tau 12)(\u22121+qUV2\rho UV\tau 12+qR\rho R\tau 12).$(12)