# Florescence Lifetime Imagining Microscopy (FLIM)

**Florescence Lifetime Imaging (FLIM)**

This wiki is on “Imaging Proteins In Vivo using Florescence Lifetime Microscopy” by Fredic Festy, Simon M Ameer-Beg, Tony Ng, and Klaus Suhling.

**Introduction to FLIM:** FLIM allows you to deduce information about the environment around the florescent label without having to know the local probe concentration or florescent intensity. The sensitivity of florescence is at the single molecule level. This imagining technique is commonly applied to live cells.

**How FLIM Works:** Incident light (usually from a pulsing laser) excites the first electronically excited singlet state. When the electron lowers its energy state, it will radiate light. While an electron (from florescent marker) will usually only emit one photon, a lifetime is measured because many electrons are excited and by inspecting the photons detected vs time graph one can determine the lifetime. In addition to lifetime, wavelength and polarization of emitted light from the florescent markers will depend on local environment parameters. Therefore, these local parameters can be calculated form lifetime, wavelength or polarization of emitted light.

The reason that the lifetime is shorter in the presence of other molecules is because other molecules give the excited electron an alternate pathway to release energy. Hueristicaly speaking, it is equivalent to N0 being a function of time (since electrons are falling to lower energy states without radiating light). If the lifetime of the excited electron from radiative pathways only has lifetime <math>\tau_1 </math>, and form non-radiative pathways has lifetime <math>\tau_2</math>, then we see:

<math> N^\prime_{0} e^{\frac{-t}{\tau_1}} = N(t) e^{\frac{-t}{\tau_1}} = N_{0} e^{\frac{-t}{\tau_1}} e^{\frac{-t}{\tau_2}} = N_{0} e^{-t \frac{\tau_1 + \tau_2}{\tau_1 \tau_2}} = N_{0} e^{\frac{-t}{\tau_{new}}}</math>

Notice that <math> \tau_{new} = \frac{\tau_1 \tau_2}{\tau_1 + \tau_2} < \tau_1 </math>. This is mathematically identical to adding resistors in parallel. Any finite valued <math>\tau_2</math> will make <math>\tau_{new}</math> smaller than <math>\tau_1 </math>. Therefore the measured lifetime in the presence non-radiative pathways is smaller than without the radiative pathways. Note again that τ_new is not a property of concentration, fluorophore intensity, photobleaching, light pathlength, or scattering.

**Data Analysis of FLIM:**
The preferred method of data analysis will depend on the statistical accuracy of the data and the time frame for the data to be analysed. In addition to single florescent species being measured, two species can be measured using the bi-exponential equation: <math> I(t) = A_i e^{\frac{t}{\tau_i}} + A_{ii} e^{\frac{t}{\tau_{ii}}} + B </math>

Here I(t) is the intensity as function of time, <math>A_i </math> and <math>A_{ii} </math>are measure of the relative concentration of species i and ii. <math>\tau_i </math> and <math>\tau_{ii} </math> are the lifetimes of each specie. By fitting I(t) one get the relative concentrations (<math>A_i </math>and <math>A_{ii}</math>) and information about the local environment (<math>\tau_i </math> and <math>\tau_{ii}</math>).