DNA Melting: Model function and parameter estimation by nonlinear regression

This subject matter will be explained in lecture, in tutorials, and in the lab.

Photobleaching

Excited fluorescent dye molecules may react chemically with compounds in their environment and permanently lose their ability to fluoresce — a phenomenon called photobleaching. LED and ambient light illuminate the SYBR Green dye for 15 or more minutes over the course of a single melting and annealing cycle, which results in measurable photobleaching. Bleaching can be diminished by lowering the illumination; however, the signal is also proportionally reduced. Photobleaching can also be corrected by a mathematical model.

Model assumptions

Photobleaching is a complicated phenomenon. The model proposed here adheres to Dr. George E. P. Box's excellent advice on modeling. Some of the assumptions are more suspect than others.

Which assumptions are probably significant sources of systematic error?

• The dye is divided into two populations, bleached and unbleached, with concentrations S and S
• The initial dye concentration is S + S
• Only dye molecules bound to dsDNA may be excited.
• Only excited fluorophore molecules bleach
• An excited fluorophore will either bleach with probability $ p $ or return to the ground state with probability $ 1-p $.
  • The constant $ 1-p $ encompasses all of the mechanisms by which the fluorophore returns to the ground state unbleached, including fluorescence, phosphorescence, and non-radiative relaxation.
• Bleaching is irreversible.
• The number of molecules in the excited state is proportional to fluorescence.
• Bleached and unbleached molecules bind to dsDNA with the same affinity.

Model

Under these assumptions, bleaching is proportional to fluorescenct.

$ \frac{\partial \bar{S}}{\partial t} = p f_{total}(t) $

• Magnitude of the illumination is equal to I_Total = I_Ambient + I_LED, the intensities of ambient light and LED illumination, respectively.
  • Total fluorescence, $ f_{total} $ is proportional to $ I_{total} $
  • The lock-in amplifier only detects the portion of the fluorescence proportional to $ I_{LED} $
  • $ I_{Ambient} $ is approximately constant