Influence of conformational changes in complex molecules on photon statistics of single molecule fluorescence

Abstract

A single complex molecule with conformational changes (conformations 0 and 2) is considered. When such a molecule is irradiated by cw-laser light it can randomly change the intensity or polarization of its fluorescence due to jumps from one conformation to another. In fact, the molecule manifests itself either like the 0-type or the 2-type emitter. An expression for the matrix ${s}_{\ensuremath{\alpha}\ensuremath{\beta}}(t)$ called the start-stop correlator (waiting time distribution) in which $\ensuremath{\alpha}=0,2$ and $\ensuremath{\beta}=0,2$ is derived. An expression for the matrix ${p}_{\ensuremath{\alpha}\ensuremath{\beta}}(t)$ called the full correlator is derived as well. It determines the density of the probability of finding an event of $\ensuremath{\alpha}$ type and an event of $\ensuremath{\beta}$ type separated by time interval $t$. A relation between matrices ${s}_{\ensuremath{\alpha}\ensuremath{\beta}}(t)$ and ${p}_{\ensuremath{\alpha}\ensuremath{\beta}}(t)$ is found. A mathematical expression for the distribution ${w}_{N}(T)$ of events measured in time interval $T$ is derived. It is expressed solely via the matrix ${s}_{\ensuremath{\alpha}\ensuremath{\beta}}(t)$. Numerical calculations of the event distribution function for various rates of intra- and interconformational jumps are carried out with the help of the formula for ${w}_{N}(T)$ and by the Monte Carlo method. Both methods of the calculation yield identical distributions. Fluctuating fluorescence intensity $I$($t$) for a bin time of 5 ms is calculated for slow and fast interconformational jumps. A relation is found between the autocorrelation function ${g}^{(2)}(t)$ of fluorescence measurable in experiments and the matrix ${p}_{\ensuremath{\alpha}\ensuremath{\beta}}(t)$ calculated theoretically.