Fluorescent Macromolecular Sensors of Enzymatic Activity for In Vivo Imaging - Progress in Molecular Biology and Translational Science - page 370

bloodstream enables slow buildup of PGC sensor at the sites of enhanced
vascular permeability. The presence of vascular barrier, which is usually com-
promised in solid tumors and inflammatory lesions, is not freely permeable even
in the case of relatively small (5-10 nm sized) molecules such as PGC carriers.
According to the Kedem-Katchalsky equation, 102 the transport rate of a
solute, that is, in our case a macromolecular sensor ( J s ) across the blood vessel
wall, can be described as

Þ C ,

J s ¼o RT C v ð C e Þþ J v 1 ð s ½ 9 : 1

where C

, that is, the average concentration of the sensor in
vascular and extravascular spaces; J v is the fluid volume flux; s is the solute
reflection;

¼ 1 = 2 C v þ ð C e Þ

are the solute permeability coefficients; and RT is the gas
constant-thermodynamic temperature product. The first term takes into
account the diffusive transport, and the second term describes the rate of
convection. Assuming the temperature to be constant,

o

o RT ¼ PS ,

where PS is the permeability-surface area product.
The vast majority of all fluorescence imaging methods are based on mea-
suring the change of fluorescence intensity in the target organ over time. In
general, the total fluorescence intensity measured in the organ is

where I o is the total measured fluorescence, I e is the fluorescence intensity of
extravascular compartment, and I v is the intravascular fluorescence intensity.
However, for quenched long-circulating macromolecular sensors, I v

I o t ðÞ¼ I e t ðÞþ I v t ðÞ , ½ 9 : 2

0,

and therefore Eq. (9.2) is simplified as

I o t ðÞ I e t ðÞ:

The change of extravascular, that is, target organ, fluorescence ( I e ) in the
absence of the intracompartmental self-quenching of enzyme-liberated fluo-
rescent products will be proportional to the buildup of the concentration of
free fluorophore ( L ) that is cleaved off a macromolecular carrier. In case the
buildup proceeds at a linear rate, that is, the release rate of the fluorophore
mediated by the enzyme from the carrier is linear, the fluorescence intensity
change rate can be written as

d I o
d T ¼

d I e
d t ¼

d L
d T

A