2PEF

Two-photon emission fluorescence microscopy is a powerful imaging technique used to visualize structures and processes in biological tissues with high spatial resolution. This technique allows for deeper tissue penetration and reduced phototoxicity compared to traditional single-photon fluorescence microscopy. Here, we'll explore the principles, mathematical framework, and applications of two-photon microscopy.

Principles of Two-Photon Microscopy

Fluorescence Excitation: Two-photon microscopy involves the simultaneous absorption of two photons of lower energy (typically infrared light) by a fluorophore to excite it to a higher energy state. The energy sum of the two photons is equivalent to the energy of one photon in traditional fluorescence microscopy.

Schematic of two-photon absorption process

Advantages:

• Deeper Tissue Penetration: Infrared light used in two-photon microscopy penetrates deeper into tissues (up to 1 mm or more) compared to visible light.
• Reduced Photodamage: The longer wavelength light causes less photodamage and photobleaching, preserving the viability of living tissues during imaging.
• Intrinsic Optical Sectioning: Two-photon absorption only occurs at the focal plane, providing intrinsic optical sectioning and reducing background fluorescence.

Applications:

• Neuroscience: Imaging of neuronal structures and activity in live brain tissues.
• Developmental Biology: Visualization of embryonic development in model organisms.
• Cancer Research: Study of tumor microenvironments and metastasis.

Mathematical Framework

The probability of two-photon absorption depends on the intensity of the excitation light. Mathematically, this can be described as:

${\mathrm{\$P\_\{\backslash text\{2-photon\}\}\; \backslash propto\; I^2\$}}_{}$

where $P_{\text{2-photon}}$ is the probability of two-photon absorption and $I$ is the intensity of the excitation light.

The fluorescence intensity $F$ from a two-photon excitation process is given by:

$\mathrm{\$F\; \backslash propto\; \backslash delta\; \backslash cdot\; \backslash Phi\; \backslash cdot\; I^2\$}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}$

where:

$$

• $\delta$ is the two-photon absorption cross-section of the fluorophore.
• $\Phi$ is the quantum yield of the fluorophore.
• $I$ is the intensity of the excitation light.

Instrumentation

1. Laser Source: Two-photon microscopes typically use femtosecond pulsed lasers (e.g., Ti lasers) that provide high peak intensities necessary for two-photon excitation.

2. Objective Lens: High numerical aperture (NA) objectives are used to focus the laser light tightly into the sample.

3. Detection System: The emitted fluorescence is collected by photomultiplier tubes (PMTs) or other sensitive detectors. Non-descanned detection is often employed to maximize signal collection from deeper tissues.

References

1. Denk, W., Strickler, J. H., & Webb, W. W. (1990). Two-photon laser scanning fluorescence microscopy. Science, 248(4951), 73-76.
2. Svoboda, K., & Yasuda, R. (2006). Principles of two-photon excitation microscopy and its applications to neuroscience. Neuron, 50(6), 823-839.
3. Helmchen, F., & Denk, W. (2005). Deep tissue two-photon microscopy. Nature Methods, 2(12), 932-940.