Phase Differential Enhancement of FLIM to Distinguish FRET Components of a Biosensor for Monitoring Molecular Activity of Membrane Type 1 Matrix Metalloproteinase in Live Cells

Abstract

Fluorescence lifetime-resolved imaging microscopy (FLIM) has been used to monitor the enzymatic activity of a proteolytic enzyme, Membrane Type 1 Matrix Metalloproteinase (MT1-MMP), with a recently developed FRET-based biosensor in vitro and in live HeLa and HT1080 cells. MT1-MMP is a collagenaise that is involved in the destruction of extra-cellular matrix (ECM) proteins, as well as in various cellular functions including migration. The increased expression of MT1-MMP has been positively correlated with the invasive potential of tumor cells. However, the precise spatiotemporal activation patterns of MT1-MMP in live cells are still not well-established. The activity of MT1-MMP was examined with our biosensor in live cells. Imaging of live cells was performed with full-field frequency-domain FLIM. Image analysis was carried out both with polar plots and phase differential enhancement. Phase differential enhancement, which is similar to phase suppression, is shown to facilitate the differentiation between different conformations of the MT1-MMP biosensor in live cells when the lifetime differences are small. FLIM carried out in differential enhancement or phase suppression modes, requires only two acquired phase images, and permits rapid imaging of the activity of MT1-MMP in live cells.

Appendices

Appendices

Although the derivations of frequency-domain methods [26, 28, 29], the polar plot [44, 49, 50] and homodyne detection [26, 27, 30, 31, 33, 34] have been presented elsewhere, the following appendices are provided here to assist the reader.

Appendix A: Frequency-Domain Lifetime Measurements for Systems with Sets of Discrete Lifetimes

The fluorescence response of a sample with more than one lifetime component that is illuminated with a very short excitation pulse is described by F _δ (t),

$$ {F_{{_{\delta }}}}(t) = \sum\limits_i {{a_i}{e^{{\frac{{ - t}}{{{\tau_i}}}}}}} $$

(A.1)

The fluorescence emission of each component with species fraction (a _i ) decays with a lifetime (τ _i )_.

The fundamental fluorescence response from a multi-component sample excited by excitation light E(t) repetitively modulated at radial frequency ω _E , arises from the convolution of the F _δ (t) with E(t) to give the resulting function S(t),

$$ S(t) = {E_o}\sum\limits_i {{a_i}} {\tau_i} + {E_{\omega }}\sum\limits_i {\frac{{{a_i}{\tau_i}}}{{\sqrt {{1 + {{\left( {{\omega_E}{\tau_i}} \right)}^2}}} }}} \cos \left( {{\omega_E}t - \left( {\varphi_i^F - {\varphi_E}} \right)} \right) $$

(A.2)

The measured modulation depth (the AC amplitude) of S(t) and its phase delay relative to E(t) are dependent on all the separate lifetimes of the sample and the frequency of light modulation. The phase delay and modulation ratio of the multi-component fluorescence response are defined and calculated as in Eqs. 3 and 4 of the text; however, there is no simple relation between phase and modulation and the fluorescence lifetimes.

In the analysis of frequency-domain data, S(t) is normalized by the DC fluorescence, ${E_o}\sum\limits_i {{a_i}} {\tau_i}$, which normalizes the measurement for the sample concentration and brightness.

Appendix B: The Polar Plot

The analysis of S(t) on the polar plot begins by normalizing S(t) by its DC offset yielding the function S(t)/SS (SS = steady-state intensity averaged over a complete period of oscillation, which can be referred to as the DC offset),

$$ \frac{{S(t)}}{{SS}} = 1 + \frac{{{E_{\omega }}}}{{{E_o}}}\sum\limits_i {{\alpha_i}{M_i}} \cos \left( {{\omega_E}t - {\varphi_i}} \right) $$

(B.1)

In this equation, (α _i ) is the fractional contribution that each lifetime component (i) has to the measured steady-state intensity,

$$ {\alpha_i} = \frac{{a{}_i{\tau_i}}}{{\sum\limits_i {a{}_i{\tau_i}} }} $$

(B.2)

This function S(t)/SS can also be described by Eq. (B.3), where (M) and (ϕ) are the measured modulation ratio and phase delay of the fluorescence signal due to all the contributing fluorescence components.

$$ \frac{{S(t)}}{{SS}} = 1 + \frac{{{E_{\omega }}}}{{{E_o}}}M\cos \left( {{\omega_E}t - \varphi } \right) $$

(B.3)

A simple re-arrangement of terms will then lead to following two equations,

$$ \frac{{{E_o}}}{{{E_{\omega }}}}\left( {\frac{{S(t)}}{{SS}} - 1} \right) = M\cos \left( {{\omega_E}t - \varphi } \right) $$

(B.4)

$$ \frac{{{E_o}}}{{{E_{\omega }}}}\left( {\frac{{S(t)}}{{SS}} - 1} \right) = \sum\limits_i {{\alpha_i}{M_i}} \cos \left( {{\omega_E}t - {\varphi_i}} \right) $$

(B.5)

The coordinate transforms of the polar plot stem from the equivalence of Eq. (B.4) and Eq. (B.5). By applying a trigonometric identity, Eq. (B.4) can be written as,

$$ M\cos \left( {{\omega_E}t - \varphi } \right) = M\cos \left( {{\omega_E}t} \right)\cos \left( \varphi \right) + M\sin \left( {{\omega_E}t} \right)\sin \left( \varphi \right) $$

(B.6)

Taking Eq. (B.6), the M cos (ω _E t) cos (ϕ) term is in phase with the excitation light’s modulation, and the M sin (ω _E t) sin (ϕ) term is out of phase with (orthogonal to) the excitation light’s modulation. Thus, M cos (ω _E t−ϕ)can be represented on a Cartesian [x,y] coordinate plot: this is called the polar plot. We only need to consider the amplitudes of the in-phase and out-of-phase components, which can be represented as a vector,

$$ x = M\cos \left( \varphi \right) $$

(B.7)

$$ y = M\sin \left( \varphi \right) $$

(B.8)

Likewise, any term (j) in the sum in Eq. (B.5) can also be re-written as shown below,

$$ {\alpha_j}{M_j}\cos \left( {{\omega_E}t - {\varphi_j}} \right) = {\alpha_j}{M_j}\left( {\cos \left( {{\omega_E}t} \right)\cos \left( {{\varphi_j}} \right) + \sin \left( {{\omega_E}t} \right)\sin \left( {{\varphi_j}} \right)} \right) $$

(B.9)

By applying a similar argument, each constituent lifetime of a measured multi-component lifetime can be represented as a vector on the polar plot. In this case, the resulting vector is weighted by the fractional contribution of lifetime (j) to the steady-state intensity (α _j ).

Therefore, since $\sum\limits_i {{\alpha_i}{M_i}} \cos \left( {{\omega_E}t - {\varphi_i}} \right) = M\cos \left( {{\omega_E}t - \varphi } \right)$, one can see that the vector on the polar plot describing $M\cos \left( {{\omega_E}t - \varphi } \right)$is the sum of the vectors of each lifetime component (i) weighted by its corresponding fractional contribution to the steady-state intensity (α _i ).

Appendix C: Homodyne Detection for Measuring Lifetimes in the Frequency Domain

The acquisition of the phase delay and modulation ratio reflected by the lifetimes in the frequency domain is often accomplished by mixing the intensity-modulated fluorescence response of the sample S(t) with a harmonic signal injected in the detector G(t),

$$ G(t) = {G_o} + {G_{\omega }}\cos \left( {{\omega_G} + {\varphi_G}} \right) $$

(C.1)

The signal that acquired by the detector is product of S(t) and G(t). This multiplication results in a DC offset term, several high frequency terms (with frequencies ω _E , ω _G and ω _G + ω _E ) and a term oscillating at a frequency equal to difference between ω _G and ω _E , as shown below,

$$ \left[ {G(t)*S(t)} \right] = {G_o}{E_o}\sum\limits_i {{a_i}{\tau_i}} + {G_o}{E_{\omega }}\sum\limits_i {\frac{{{a_i}{\tau_i}}}{{\sqrt {{1 + {{\left( {{\omega_E}{\tau_i}} \right)}^2}}} }}} \cos \left( {{\omega_E}t + {\varphi_E} - \varphi_i^F} \right) + {G_{\omega }}{E_o}\sum\limits_i {{a_i}{\tau_i}\cos \left( {{\omega_G}t + {\varphi_G}} \right)} + \frac{{{G_{\omega }}{E_{\omega }}}}{2}\sum\limits_i {\frac{{{a_i}{\tau_i}}}{{\sqrt {{1 + {{\left( {{\omega_E}{\tau_i}} \right)}^2}}} }}} \left( {\cos \left( {\left( {{\omega_G} + {\omega_E}} \right)t + {\varphi_G} + {\varphi_E} - \varphi_i^F} \right) + \cos \left( {\left( {{\omega_G} - {\omega_E}} \right))t + {\varphi_G} - {\varphi_E} + \varphi_i^F} \right)} \right) $$

(C.2)

The homodyne detection method included in this paper applies a signal to our detector that has the same frequency as the waveform which modulates the intensity of the excitation light (ω _G = ω _E ). When averaged for times in the millisecond range, the high frequency terms in [G(t)S(t)], go to zero and consequently, the terms that remain have no time dependence,

$$ {\left[ {G(t)*S(t)} \right]_{{LF,Homo}}} = {G_o}{E_o}\sum\limits_i {{a_i}{\tau_i} + \frac{{{E_{\omega }}{G_{\omega }}}}{2}} \sum\limits_i {\frac{{{a_i}{\tau_i}}}{{\sqrt {{1 + {{\left( {{\omega_E}{\tau_i}} \right)}^2}}} }}} \cos \left( {{\varphi_G} - {\varphi_E} + \varphi_i^F} \right) $$

(C.3)

To define various points on this sinusoid (Eq. (C.3)) so that the modulation ratio and phase delay indicative of the sample can be found, the phase of the detector (ϕ _G ), is changed through a set of angles over a full period of cosine. All other parameters are kept constant throughout the acquisition. Hence, the varying phase of G(t) applied in this process is often written relative to the constant phase of E(t) as (ϕ _E -ϕ _G ). The intensity of the sample ([G(t)S(t)]_{LF, Homp}) is then collected at each phase sampled in the detector. A fitting, normalization to the DC offset and comparison to a known reference standard are then performed on the data collected by homodyne methods to determine the phase delay and the modulation ratio of the sample.

In this paper, [G(t)S(t)]_{LF, Homp} refers to a discrete intensity collected for a single pixel in a lifetime image or something similar to a cuvette-based sample in a fluorometer. The entire lifetime image containing these types of curves at each pixel is denoted by D(ϕ _E -ϕ _G ) as shown in Supplemental Figure 1.