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284 Cell-Penetrating Peptides: Processes and Applications
one time point. The benefit of simplicity, speed, and small amount of used material
is lost in the fact that a single point experiment will not give kinetic constants and,
consequently, information obtained might be useful only for rough evaluation. Similar,
to some enzyme kinetics studies in which the time interval of quasi-linear
dependence of the amount of transformed substrate per time is independently determined
and then only one point inside this interval is routinely used, 17 this approach
has been sometimes used for comparison of the initial rates of internalization of
various analogues of CPPs. However, if the initial rate of internalization is substantially
different for different analogues, the linear interval of internalization rate must
be separately determined for each analogue; otherwise the comparison is not justified.
An alternative solution would be the choice of two time points in the expected
linear interval at which the amount of internalized CPP is determined; if the rates
of internalization calculated at each of two points do not differ substantially, the
obtained result could be considered the proper initial rate.
13.3.2 UPTAKE MEASUREMENTS AS A FUNCTION OF TIME
A better approach is to monitor the concentration of the internalized CPP as a
function of time. In order to obtain reliable results, kinetic data should be collected
over a time interval long enough to approach concentration equilibrium between
CPP internalized in the cells and that in the surrounding solution. This can be done
at one fixed concentration of CPP or, better, at several concentrations of CPP. When
a fixed concentration of CPP is used, the obtained data allow for calculation of the
rate constant of internalization and also the yield of internalization at the chosen
concentration of CPP. The quality of the calculated kinetic parameters depends
greatly on the number and reliability of the measured experimental points. Since the
mechanism of CPP internalization is not known, any analysis of kinetic data is either
phenomenological or model based. As a first approximation, first-order kinetics of
internalization can usually be assumed and kinetic parameters are obtained by fitting
Equation 13.1 to the experimental points:
[ ]= [ ] −
( )
A A e kt −
1
∞
(13.1)
where [A] is the concentration of internalized CPP at time point t, [A] ∞ is the final
concentration of CPP inside the cells, and k is the first-order rate constant. Parameters
that are fitted are k and [A] ∞. The latter is the maximal concentration of CPP
internalized at given initial concentration of CPP outside the cells ([A] 0) and makes
possible calculation of the internalization yield expressed by ([A] ∞/[A] 0) × 100.
Sometimes it is more illustrative to convert the first-order rate constant into halftime
of internalization (t 0.5) using the equation t 0.5 = ln2/k.
Goodness of fit should be tested for the whole time interval of the progress curve
and analysis of residuals should be carried out (the algorithm for this is usually
incorporated into the fitting program) in order to observe possible trends in discrepancy
between the calculated curve and experimental points. If goodness of fit is not