Principles of FRET-based (Bio)Sensors
Auke Jisk Kronemeijer
RijksUniversiteit Groningen
Contents
1. Introduction............................................................................................................................................ 3
2. General Principles of Resonance Energy Transfer (RET)..................................................................... 3
2.1 Förster Energy Transfer......................................................................................................... 4
2.2 Dexter Energy Transfer......................................................................................................... 7
2.3 Reversibility of Energy Transfer........................................................................................... 7
3. Measuring Fluorescence Resonance Energy Transfer (FRET).............................................................. 8
4. FRET- Based (Bio)Sensors.................................................................................................................... 9
4.1 Molecular FRET (Recognition) Biosensor............................................................................ 9
4.2 Quantum Dot FRET (Recognition) Biosensor.................................................................... 11
4.3 FRET Sensors Based on Distance Changes between Donor and Acceptor........................ 14
4.4 FRET Sensors Based on Spectral Overlap Changes Between Donor and Acceptor.......... 16
4.5 Tailor Made Sensors........................................................................................................... 17
5. Conclusion................................................................................................................ ........................... 17
6. References................................................................................................................ ........................... 18
2
1. Introduction
In current day research, many effort is made to search for sensitive and reusable measurement devices for
recognition of specific chemicals or toxins. For the research in biomolecular sciences, the quest is even
more ambitious, because the search is concentrated at small sensors capable of continuously monitoring
specific species in vivo (1). The basic idea of these sensors is that some specific interaction with only the
target species gives rise to a signal, which can be turned into an electric signal for processing in an
integrated circuit.
Many applications of these biosensors have been proposed. The real time measurement of biological toxins,
when soldiers in armies are fighting enemies with potential threat of using chemical weapons or the real
time analysis of food produced in factories, to give two extremes. Furthermore, many diseases stem from
the presence of some bacteria or virus which produce specific molecules. When there are sensors available
for determining these species in vivo, a diagnosis is quick and easy made.
Besides making measurements in vivo, the sensors currently in research are simple systems, possibly
particular useful for mass production and thus cheap. This is an advantage above the time consuming,
expensive analytical methods used today. New sensors can be useful for more easy detection of scientific
interesting properties.
Of course, there are still many difficulties to overcome. Present day sensors are very temperature dependent
and have a limited range in which the devices are really reliable. Also the stability of the devices is low (2).
One particular interesting concept for (bio)-sensors is based on the principle of resonance energy transfer
(RET). This mechanism involves the transfer of energy from an excited donor to an acceptor without the
intervention of a photon. The excited acceptor then emits light with longer wavelength. Sensors based on
this principle often contain a donor species specifically tuned to an acceptor and a specific binding site for
the target species. When no acceptor is present close to the donor, fluorescence of the acceptor will not be
observed, while when the acceptor has come close because the target species (which by itself can be the
acceptor) is present, fluorescence will be observed. Furthermore, because RET occurs only at certain
donor-acceptor distances, RET can also gives some spatial information when needed. A general advantage
of using the RET-principle for sensors is that light can easily made in an electrical signal by photodetectors.
2. General Principles of Resonance Energy Transfer (RET)
Many different approaches are taken to account for energy transfer between donors and acceptors and
several different mechanism are currently known. All mechanism account for the fact that an excited donor
gives up energy to an unexcited acceptor, leaving the donor in its ground state and the acceptor in the
excited state. The energy can be exchanged by the two species in two different kinds of processes, radiative
and non-radiative processes.
The radiative processes are easy understandable. The excited species spontaneously emits a photon of a
certain energy which is absorbed by the other species. In this process, the acceptor can be an identical
molecule as the emitter, but also another species provided that the energy of the emitted photon
corresponds to a transition in the acceptor.
Another possibility is non-radiative energy transfer. It differs from radiative transfer in that the distance
over which the energy is transferred is far more smaller. Radiative transfer can occur over distance longer
than 10 nm while this is impossible for non-radiative transfer. Another difference is that for non-radiative
transfer a coherent state of the system is needed. This means that the whole system is described by one
single wavefunction whereas in the radiative processes every donor and acceptor is described by its own
wavefunction. For this non-radiative transfer two different kinds of models are set up (3). The mechanisms
of both models are different and are shown in Figure 1. The first model is a dipolar interaction between the
two species and is called Förster Energy Transfer (Figure 1a). The second model is an expansion of the
Förster Energy Transfer mechanism. This model incorporates not only dipole-dipole interaction terms
between species as the Förster model does, but also incorporates higher order interaction terms. This model
is called Dexter Energy Transfer. Dexter Energy Transfers is often important in triplet-triplet interactions
between species and is often shown as a triplet electron exchange from and to the two species. (Figure 1b).
3
Figure 1: Two Resonance Energy Transfer Mechanisms. (a) Förster
Energy Transfer by a dipole-dipole interaction between donor and
acceptor. (b) Dexter energy transfer by higher order interaction terms,
often important for triplet-triplet interactions.
2.1 Förster Energy Transfer
The theory of energy transfer between molecules was first set up by Förster in the late 1940’s (4). As this is
the case, the process if often called Förster Resonance Energy Transfer. However, when the acceptor is a
fluorophore, also the term Fluorescence Resonance Energy Transfer is used. The theory is based on the
theory of delocalised electronic states first made by Frenkel (5) and extended by Davydov (6). Here the
theory of delocalised excitation will be considered in its most basic form as done by Förster (7).
Consider N molecules with fixed distance between each other. The Hamiltonian of the system can then be
written as
N
H   Hn 
n 1
1
Vmn
2 n,m
(1)
Here the first term is the Hamiltonian of the free molecules and the second term is the interaction between
the different molecules. If now the demand for antisymmetrized wavefunctions is neglected, the ground
state wavefunction of the electrons in the system can be described as
N
 g   n
(2)
n 1
where the ground state wavefunctions in simply the product of all ground state eigenfunctions of the free
molecules. This ground state wavefunction can be inserted into the Schrödinger equation. Then the energy
of this ground state wavefunction is found to be
N
E g   Eng 
n 1
1
Vmn
2 n,m
(3)
In this equation, the first term is the sum of all ground state energies of the free molecules and the second
term is the interaction between the electrons which can be evaluated as
Vmn  mn Vmn  m n
(4)
4
Now an excitation has to brought into the system. This excitation can be described as a local excitation of
one free molecule. The wavefunction of a particular configuration of the system with one particular single
molecule exited is
1excited  l'    n
(5)
n l
where the prime indicates the excited state wavefunction of the free molecule excited. The total
wavefunction of the whole system with one excitation is the system is then described by a linear
combination of all the wavefunctions of the form of equation (5):
 k   C kl l'   n
l
(6)
n l
The whole system of equations consisting of N equations of the form of equation (6) can be solved by
means of the eigenvalue equation
 *l H  k  E k  lk
(7)
With the Hamiltonian operator equation (1), this eigenvalue problem can be expressed by two other
interaction matrices which are essentially decompositions of the interaction term of the Hamiltonian:
'
Vmn
  m'  n Vmn  m'  n
(8)
U mn   m'  n Vmn  m n'
(9)
The second integral is called the resonance integral between configurations with one molecule excited or
another. Here it is already possible to see that there is some interaction between the excited states of the
different molecules.
The terms in the resonance integral can be expanded into point multipole series. These expansion will lead
to a multipole-multipole expansion. Often when the resonance integral is calculated, only the dipolar terms
are taken into account and any higher terms in the expansion are neglected. Therefore, Förster energy
transfer is often referred to as an dipolar interaction between the excited states of molecules. However,
higher terms in the expansion can also be taken into account giving rise to e.g. quadrupole-dipole terms.
In principle, now all wavefunctions and the Hamiltonian are known, it is possible to calculate the energy
transfer rate from one molecule to another. For this, the time dependent Schrödinger has to be considered.
Eventually, the energy transfer rate can be calculated. However, in the approach followed above, no nuclear
vibrations or differences in equilibrium positions are considered and to calculate the energy transfer rate a
more extended calculation than the one shown above has to be done.
The complete theory leads too far to describe here, however, it has been shown that the energy transfer rate
between molecules can also be calculated with a classical theory (8). Here the starting point is a classical
harmonic oscillator model with eigenfrequency
0 
0
1

2 2
k
m
(10)
The one dimensional equation of motion of an electron in a molecule which is driven with light is
(11)
m  x  k  x  e  E0  cos(  t )
where damping of the motion is ignored. The solution of this equation in the case of resonance can be
approximated by
x
e  E0
 sin( 0  t )
2  m  0
(12)
The energy of the oscillator can then be calculated. This is done by noting that in a turning point of an
oscillator, all energy the oscillator posseses is potential energy:
W
1 2
kx
2
(13)
and combining equations (10), (12) and (13) gives the total energy of the oscillator
e 2 E02 2
W
t
8m
(14)
5
where only the first term of the expansion of the square of the sine function is retained. It is seen that the
energy of the oscillator increases quadratically with time. Now we consider the interaction between a donor
species and an acceptor species. The way to do this is to consider the excited donor as source for an electric
field. The energy of the acceptor species can then be calculated by using equation (14) together with the
strenght of the electric field of the donor at the acceptor. The strength of this electric field at the acceptor,
more precise the amplitude of this electric field, can be calculated as
 e A
E acc 
(15)
n2 R3
where A is the amplitude of oscillation of the donor harmonic oscillator, n is the refractive index of the
medium around and R is the distance between the two species and comes into the equation cubed because
the electric field of a dipole falls off this way. κ is a dimensionless quantity in the order of 1 which
accounts for the relative orientation of the two harmonic oscillators. The amplitude of the oscillation of the
donor A can be calculated via
Wdonor 
1 2 1
kA  m 2 A 2
2
2
(16)
For the case of resonance, the energy which the acceptor obtains from the donor can be calculated by
combining equations (14), (15) and (16):
Wacc
2
e 2 E acc
 2 e 4 A2 2
 2e4
2

t 
t 
 Wdonor  t 2
4 6
2 4 2 6
8m
8m  n R
4m n  R
(17)
This equation is the case for exact resonance. To calculate the energy transfer between two species, the
‘amount’ of resonance has to be calculated. This is done by using the emission function of the donor and
the absorption function of the acceptor. The two functions describe the emission, respectively the
absorption, of the species as function of the frequency. Also one has to determine when resonance occurs at
one single emission frequency. The width of this resonance zone around one single frequency is 2 t . The
total number of oscillators in resonance is the equal to how many acceptor oscillators are present in the
frequency zone 2 t around a single frequency of a donor, summed over all possible frequencies of the
donor. This can be put in an integral form as

2
 f aAcceptor ( )d
t
N   f eDonor ( ) 
0
Donor
Acceptor
Here f e
and f a
(18)
are the emission and absorption functions of the donor and the acceptor. The
total energy of the acceptor can now be calculated by using equations (17) and (18), knowing that each pair
of oscillators of the donor and acceptor in resonance contribute an amount equal to equation (17) to the
energy of the acceptor and the number of pairs is given by equation (18):
Wacc 

   2e4
2
4
2m n R
6
 Wdonor  t   f eDonor ( ) f aAcceptor ( )
0
d
2
(19)
which can be put in differential form as

dWacc
   2e4
d
Donor


W
( ) f aAcceptor ( ) 2
donor  f e
2 4 6
dt
2m n R

0
(20)
The rate of energy transfer from donor to acceptor is now defined through
dWacc
 nd a  
dt
(21)
And from equation (20) it can be seen that
n d a 

   2e4
2
4
2m n R
6
f
0
Donor
e
( ) f aAcceptor ( )
d
2
(22a)
6
Or
n d a 

 2e4
16 m n R
2
2
4
6
f
Donor
e
( ) f aAcceptor ( )
0
d
2
(22b)
It can be seen that Forster Energy transfer depends essentially on two important variables. The rate of
energy transfer decrease with the sixth power of the distance between donor and acceptor. This means that
the process is restricted to small distances between donor and acceptor, otherwise the process will become
too small to observe or other processes which occur become more probable to happen. Second, the transfer
depends on the spectral overlap of the emission of the donor and the absorption of the acceptor. These two
variables give rise to tunability of energy transfer between specific donor and acceptor species.
Forster energy transfer, the complete theory, is regarded as a good description of energy transfer
phenomena, especially in singlet energy transfer (3). However, a limitation of Förster’s theory is that the
initial and final electronic states are not exact eigenstates of the system and some other theories are being
developed to take this into account (9).
2.2 Dexter Energy Transfer
The second, expanded model for energy transfer between donor and acceptor species is by including higher
multipole interactions between donor and acceptor (10). A standard result from quantum mechanic time
dependent pertubation theory is Fermi’s Golden Rule (11), which gives the probability for a system to go
from an initial electronic state to a final one :
ni  f 
2
 i H Pert  f

2
E
(23)
where the states Ψi and Ψf are of the same energy and ρE is the density of states at that energy. If electron
spin is taken into account, the matrix element of the pertubation can be written out explicitly in terms of
the spatial wave functions and the spin wavefunctions. The matrix elements will lead to two terms. The first
term is the Coulomb integral between the initial and the final states and the second term is the so-called
exchange integral. This exchange integral can be seen as an interaction which exchanges the positions of
two electrons if the integral is non-zero. The integral is only non-zero if the electron’s spins have equal
signs and therefore Dexter energy transfer is often important in triplet-energy transfer. Because the two
states should have the same energy, an integral of the same form as equations (18) has to be considered to
account for the number of states which can be in resonance and eventually the transition probability varies
as (3,10):

nd  a
2
e4

 Y  2 2  exp(  2R )   f eDonor ( E ) f aAcceptor dE
L

 R0
0
(24)
where the dependences mainly come from approximate solutions of the exchange integrals. L is an
effective radius of the excited and unexcited states and Y is a dimensionless number. The most important
issue is that Dexter Energy transfer depends exponentially on the distance between donor and acceptor.
2.3 Reversibility of Energy Transfer
In principle both energy transfer mechanism account for energy transfer between two species with states of
the same energy. No specific property is needed for the species to be donor or acceptor, so no directionality
is imposed by the different species. When no other mechanism come to play in such system this would be
correct and the energy transfer would be completely reversible. However, in real molecules, competition
exists between energy transfer to another molecule and e.g. spontaneous emission of a photon or vibrational
relaxation. Because of this competition, when these processes are considerable fast for one of the species,
energy transfer back will be less probable, because before energy transfer could occur, relaxation has
already taken place. Then the energy of the initial donor will be higher than the energy of the acceptor
which has relaxed (Ed > Ea) and resonance energy transfer cannot occur. Now the reversibility is lifted and
is it often possible to specific say what is the donor and what is the acceptor as the acceptor’s relaxation is
fast and (almost) no energy will transferred from this species to the donor. These relaxation processes also
account for the shift in wavelength of the initial excitation wavelength and the fluorescence wavelength
(Figure 2).
7
Figure 2: Mechanism for Red-shifted Fluoresence through (Fluorescence)
Resonance Energy Transfer. 1. Absorption at the donor, 2. Energy Transfer,
3. Vibrational Relaxation, 4. Emission from the acceptor
3. Measuring Fluorescence Resonance Energy Transfer (FRET)
Measurements of RET are often based on the Forster mechanism and called Forster Resonance Energy
Transfer or Flourescence Resonance Energy Transfer (FRET). Because the rather easy relationship between
transfer rate and the distance and spectral overlap between donor and acceptor, many information about
systems can be obtained using FRET. Measurement of FRET can also give information whether or not an
specific acceptor is present because its emission is present of not. To quantitatively know how much of this
specific acceptor is present, quantitative FRET measurements have to be done. Detection of FRET can be
divided into two classes of approaches: fluorescence decay kinetics-based measurements and intensitybased measurements (12).
In kinetics-based measurements, the kinetics of the excited states of the donor or acceptor are determined.
Two different kinds of measurements can again be distinguished (13). The first is photobleaching FRET
(pbFRET). In this method the donor is continuously exposed to light and normally this leads to a slow
destruction of the donor, called photobleaching. This photobleaching is irreversible and can occur by
several different mechanism, e.g. photo-oxidation. Photobleaching leads to a decay in the fluorescence
observed from the donor. When now a FRET acceptor is present, the energy transfer to this acceptor
reduces the average time the donor is excited and as a consequence the decay rate of the fluorescence due
to photobleaching decreases. How much this rate has decreased then depends on the amount of energy
transfer which occurs. This technique has one important drawback, which is the irreversible photobleaching
process which destroys the fluorophores making new or duplicate measurements impossible.
A second type of kinetics-based measurements is fluorescence lifetime imaging microscopy (FLIM), which
measures the donor excited state lifetime decrease as a result of the energy transfer process. An important
advantage of this technique is that the emission of the donor and acceptor need not to be separated to
minimize crossover effects. Because when the fluorescence overlap, with this technique it is possible to
look at the combined fluorescence. When energy transfer takes places, this leads to an temporal increase in
the fluorescence from the acceptor, which is called in-growth. This FRET induced in-growth can then be
detected in the increase of the lifetime of the combined fluorescence (14). The absence of this criteria for
non-overlapping fluorescence is an advantage over intensity-based measurements where this is the case
(See below).
The intensity based measurement of FRET obtains information by measuring the FRET induced changes in
donor and/or acceptor emission (also called donor sensitized emission, seFRET) or the variation of the
donor emission with acceptor photobleaching (also called acceptor depletion FRET, adFRET) (12).
Detecting by seFRET can be done by measuring the decrease in the intensity of the donor emission or the
increase in acceptor emission. An advantage of this methods in that it is non-volatile, however, when using
this method, corrections have to be taken into account for some processes that can account for large errors
in the measurements (15).
A first problem is called spectral bleed-through in excitation. This bleed-through in excitation is that the
acceptor is also excited by the donor excitation wavelength. In this way already part of the acceptor is
excited, making in difficult to determine how many acceptors are excited by FRET.
8
A second problem is called cross-talk. This is a sort of spectral bleed-through in the detection. It is the
unwanted contribution of donor and/or (direct) acceptor emission to the emission which is actually created
by the FRET mechanism, e.g. when acceptor emission is measured to determine FRET but also donor
emission is in the same area of the spectrum, giving difficulties in determining how much emission is
actually caused by FRET.
Detection by adFRET is based on the fact that when the acceptor is bleached, it can no longer accept
energy from the donor. A consequence is the increase of donor emission as a function of the increase of
photobleaching of the acceptor, from which the amount of energy transfer can be calculated. This methods
has also the problem with spectral bleed-through, the acceptor emission into the donor emission. Also a
problem can arise by photobleaching the donor also instead of the acceptor only. Furthermore, the method
inherently destroys the samples.
Figure 3: Summary of FRET detection measurements
4. FRET- Based (Bio)Sensors
The need for real-time measuring sensors already discriminates between the detection methods used for
FRET based sensors. Because kinetics-based measurements take normally more time to analyze, often
intensity based detection methods are preferred. Also for biological in vivo measurements, destructing of
the target is not desired for obvious reasons and therefore photobleaching measurements are not available
to use. This means that often the best choice for the detection of FRET is the intensity-based seFRET
detection, where still a choice can be made between measuring donor or acceptor emission. By choosing
this kind of detecting, the problems of spectral bleed-through become important to make a reliable
quantitative sensor and have to be overcome.
Often to make the sensors very specific, biomolecules are used. This is because the molecules, e.g.
enzymes, are tailor-made over the years of evolution to specifically bind a target molecule. Therefore, at
the current stage of research development, these molecules perform very good for recognizing target
molecules. So with the use of biomolecules, already the sensitivity which is needed is introduced. However,
still problem arise with non-specific binding, but these molecules perform better than others.
4.1 Molecular FRET (Recognition) Biosensor
For the recognition of molecules often biomolecules are used, as mentioned above. These molecules are
however then somewhat modified to be compatible with the FRET mechanism and the detection. For the
sensors, intensity based seFRET detection is used. The principle of the detection is actually very simple.
The target molecules is acceptor or donor. The biomolecular sensor molecule is then modified to be the
opposite of the target molecule, so respectively donor or acceptor in the present case. This modification is
9
Figure 4: Fluorescence of a (modified) biomolecule without
and with the presence of a target molecule. The intensity
differences can be measured from either the blue or the red
fluorescence and contain the same information.
often a difficult step. Not because it is impossible to put a donor or acceptor moiety on the biomolecules,
but to change the fluorescence characteristics of the moiety to the target molecule.
When now the whole sensing device, here probably still a solution, is irradiated with the light which excites
the donor, only the donor fluorescence will be observed when no acceptor is present. When now the target
molecule is present, by means of the FRET mechanism, the acceptor get excited too (Figure 4). So now
also the fluorescence of the target will also be observed, accompanied by a decrease in fluorescence of the
donor. By measuring one or both intensities of the fluorescence, first of all the presence of the target can be
determined, if the number of target molecules present is not too small. Furthermore, when the sensing
device is calibrated for different amounts of target molecules present, in principle also quantitative
measurements can be done with the device. The quantitative measurements with this device are still tricky.
This is because the problems of spectral bleed- through are very pronounced in this configuration with two
molecules as donor and acceptor. This is because the species are both molecules with very strict determined
energy levels and consequently have a narrow excitation band. However, for FRET, these energy levels
always have to coincide with energy levels of the respective acceptor. This means that in almost every case
the acceptor is excited too with the excitation wavelength and thereby making it very difficult to determine
the total energy transfer by the FRET mechanism. Also the emission often has a large tail to the red side of
the spectrum (vibronic progression), which introduces extra cross-talk in the detection (16).
One way to solve the problem of bleed-through in these systems is linear spectral unmixing or spectral
fingerprinting (17). It should be stressed here that this is a method to overcome difficulties in this particular
measurement, not changing the measurement setup at all.
The procedure of spectral unmixing is based on prior known fluorescence of the different isolated species.
It is assumed that the total emission detected is a linear combination of the isolated donor emission, isolated
acceptor emission and emission from acceptors in donor-acceptor complexes, excited by FRET. The
procedure enables the calculation of the contributions of the different contributions to the total emission
detected. This is done by solving a system of linear equation in which the concentrations of free donor, free
acceptor and donor-acceptor complex appear. It is then assumed that the FRET mechanism only occurs
between donors and acceptors in a complex. Still this method is in development and often approximations
have to be taken. This must always be done in present case because otherwise the system is unsolvable. The
reason for this is the following. We consider the linear system of equations
I  A x
(25)
in which I is the component of fluorescence measured, which summed should give the total measurement
and x is the concentration considered (free donor, free acceptor, complex). Because in matrix A, one
column always is a linear combination of the other two is, this system of equations is unsolvable when a
10
Figure 5: Several fluorophores which can be used as donor and acceptor
for FRET. (a) AMCA (b) MACA (c) TRITC (d) FITC. Optimized pairs
are respectively as donor / acceptor (18): 1. AMCA / FITC 2. DMACA /
FITC 3. FITC / TRITC
single excitation is used. This can be circumvented by introducing additional spectroscopic data into the
calculation, but often the assumption is made that only the donor is excited by the incoming radiation. Also
it is often assumed that almost no free acceptor is present anymore. However, in this way it is still difficult
to say something about the current measurement. It started out by e.g. wanting to know the spectral bleedthrough in excitation but in the calculation it is assumed that there is none.
A problem which also arises in making these recognition system is tuning the donor and acceptor to each
other. For FRET to occur, considerable spectral overlap is needed (equations (22),(23)). In principle this
seems good and it is rather understandable. However, tuning the species is not always easy. Tuning the
emission is mostly done by attaching electron donating or withdrawing side groups to a known fluorophore.
Examples of tuned flourophores are found in literature but this tuning should not be overlooked to easily
(Figure 5).
Another disadvantage until now is that the sensor is a solution in which the sensing molecules and also the
target molecules are dissolved in. Of course, this kind of measurements are of practical interest in
laboratories but not in quick in-field measurements. Making the sensing molecules on a surface could
improve these sensors. The idealistic view of this is that some kind of small plate will show one color or
another, showing the person who uses it what is happening. This demand, and the problem of spectral
bleed-through can possibly be handled better by introducing quantum dots as donor species in these kinds
of sensors.
4.2 Quantum Dot FRET (Recognition) Biosensor
Quantum dots are very small crystallites of a certain inorganic semiconductor. Their size often ranges from
2-10 nm. A quantum dot structure is a confined structure and may be considered as 0-dimensional (19).
Electrons in the quantum dot are confined in all three directions in the structure. The energy levels of an
ideal quantum dot are completely discrete. As for a basic problem in quantum mechanics, the particle in a
box, the more the electrons are confined in a structure, the higher their lowest energy becomes and the
higher the distance becomes between different energy levels. This means that the onset of absorption, the
lowest energy at which absorption can take place just over the band gap of the quantum dot, changes with
the size of the quantum dot. This absorption onset is for a large part also the energy of the emission of the
quantum dot. Absorption of light by the quantum dot is broad because once the energy of the light is
increased to over the energy of the gap, still new states come available where electrons can jump to after
absorption. Also phonons can take part in the excitations. Relaxation of these higher excited states is rapid
and ends up at the electronic state just above the band gap (20). Therefore, most emission is from this state
and is therefore narrow. Moreover, because the wavelength of this emission is determined by the band gap,
11
Figure 6: Normalized absorption of molecular
material (solid line) and a quantum dot with its
size tuned to the emission of the molecular
material (dotted line). It can be seen that the
absorption of the quantum dot is broader (16).
which itself is determined by the size of the quantum dot, the wavelength of emission can be tuned by
changing the size of the dot. This is a big advantage over molecular materials. Quantum dot synthesis is
well known and can be controlled very good (21,22,23) and so an rather easy way is found for tuning a
FRET donor to an acceptor.
Another advantage of quantum dots as FRET donors is the fact that the absorption of quantum dots is so
broad while their emission is narrow. This means that a quantum dot can be excited relatively far away
from the emission wavelength. This means that bleed-through in excitation of the acceptor in minimized
and quantitative energy transfer can be measured more exact. Also the assumption for linear spectral
unmixing that almost only the donor is excited is more valid. Since a batch quantum dots made in a
procedure never have exactly the same optical properties because of spreading in the size of the dots, still
all quantum dots can be excited together with the same wavelength, because their absorption is so broad.
Also the quantum dots are photochemically stable.
Now it is established that quantum dots can be used as FRET donor, they have to be made compatible with
the basic measurement procedures of sensors. For sensors to be sensitive, still biomolecules are used for
their specificity. However, the donor quantum dot and the acceptor have to come close together for energy
transfer between them. This is done by surface manipulation.
Often a surface capping layer is introduced around the quantum dots which are prepared. This capping
layer is often a semiconductor with a wider band gap than the quantum dot. This leaves the surface
passivated and prevents that excitons leave the quantum dot via a relaxation pathway that does not
contribute to the energy transfer such as charge transfer (24). Surface passivation is believed to be useful
because the process decreases the number of surface states at the surface of the quantum dot. Surface states
or vacancies in it are believed to be traps for luminescence (25). Therefore, reducing the number of surface
states enhances the luminescence of the dot. Excitons are bound electron-hole pairs in the quantum dot
which are responsible for the luminescence / energy transfer when the electron and the hole recombine.
There is a competition in the quantum dots between energy transfer and charge transfer and when the
excitons can leak away in to the outer regions of the quantum dot and interact with the surroundings, there
is a higher chance that these excitons will form a charge tranfer state with the surroundings. Therefore,
trapping these excitons inside the quantum dot will enhance the luminescence of the dot.
Furthermore, the capping layer can be chosen such that chemical functionalization is made more easy.
Chemical functionalization is needed to bring the molecules close to the quantum dot. In this way the
energy transfer between the quantum dot donor and the acceptor is optimized. Also for the use in biological
system, it is used to make the quantum dots water soluble. The procedures followed to change the surfaces
of quantum dots often make use of the concept of self-assembly. In these processes the whole system in
consideration by itself makes the linkage of the inorganic semiconductor and the molecules, like a goldsulfur bond. During these processes the biomolecule which needs to be used can also be linked to the dot.
12
Figure 7: A capped quantum dot (often ZnS capped CdSe) made water soluble
by self-assembly of mercapto acetic acid on its surface and functionalized with a
biomolecule (27). Here the sensor can be based on two different principles. First,
it is possible that there is already energy transfer from the quantum dot to the
biomolecule. Then when the target molecule binds to the complex, this energy
transfer is quenched. The sensor would ‘see’ the presence of the target by a
decrease in fluorescence at the wavelength of the fluorophore incorporated in the
recognition molecule. Second, it is possible that there is no resonance energy
transfer before the target molecule is present. When it is present, energy transfer
to the target will occur and it will be possible to detect by means of an increase
of fluorescence at the wavelength of the target molecule.
Several examples of a linkage of a biomolecule to a quantum dot are a bifunctional linker, an electrostatic
interaction or a hydrophobic interaction (26). The biomolecule in consideration here does not have to be
altered anymore to act as FRET species. The molecule is now only there for specific recognition of the
target while the quantum dot acts as FRET donor.
Apart from the advantages of excitation of quantum dots and there stability against photobleaching, another
advantage of quantum dots as donors is that they can be synthesized on a surface. Control of the emission
of the quantum dots formed at these surfaces and their lateral arrangement has been reported (28,29,30), but
is also still under research. However, when these quantum dots can be synthesized on a surface, one could
think about small sensor devices which can be carried by persons.
The quantum dots could be assembled on a surface, with molecules assembled on the quantum dots
themselves. A small laser, e.g. a small semiconductor laser, could excite the quantum dots. Maybe it will be
possible to excite the quantum dots electronically. Photodetectors, possibly also quantum dots, could
determine the emission from the quantum dots or the target species and this is then turned in an electrical
signal. Probably, however, such kind of device would only work for target molecules dissolved in some
solvent but this seems to met the targets, because most often one wants to measure liquids or solutions with
Figure 8: AFM image of Si8Ge2 pyramidical quantum dots on a Si (001)
surface. It demonstrates the growth of quantum dots on surfaces and the
potential to use quantum dots assemblies as templates of FRET donors
in sensors (31).
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this method. However, sensors based on the FRET principles with quantum dots give an promising view for
the development of sensitive measurement devices. Problems with the molecular sensor seem possible to
overcome. The biggest challenge then remains finding good biomolecules which specificly bind the target
set, and which is compatible with FRET sensing.
4.3 FRET Sensors Based on Distance Changes between Donor and Acceptor
Further away from the potential application of FRET sensors in daily life, sensor based on this principle can
be used by the scientific community to make their research more easy or towards the detection of yet
undetected properties. Because of the variety of FRET donors and acceptors and the optimized pairs used in
literature, this information can be used for measuring properties of specific interest of a researcher.
One principle which is somewhat more sophisticated than only the detection of a species, is based on
measuring the course of certain chemical reactions. This can be done by using the sensitivity of energy
transfer between two species for the distance between the species. When the distance between these species
is changed by some means, this is directly seen in the output of light from donor or acceptor.
This principle for measuring the distance changes between donor and acceptor species can be used very
elegantly in measurements for determining activities of enzymes in the field of biochemistry. Enzymes are
biomolecules which perform all kinds of chemical reactions in living cells. However, also bacteria or
virusses can cause that different enzymes are present in living cells which should not be present there and
cause harm to the living species. Therefore it is quite important to understand how certain families or
Figure 9: (a) Molecule used for the determination of the activity of the
enzyme phosphodiesterase with (b) fluorescence before and (c) fluorescence
after cleaving of the phophodiester bond by the enzyme (33). The enzyme
phosphodiesterase cleaves phosphodiester bonds. Before cleavage of the
molecule shown in (a), the donor and acceptor moieties are close to each
other and energy transfer occurs when the sample is irradiated at the
absorption wavelength of the donor. Therefore, fluorescence from the donor
will be observed as seen in (b). After cleavage by the enzyme, the donor and
acceptor are further away from each other and thereby making energy
transfer impossible. When irradiated, now only the fluorescence of the donor
will be observed as seen in (c). By carefully choosing linkers and analyzing
the fluorescence coming from the sample, the number of phosphodiester
bond cleaved can be determined. In this way the activity, how fast the
enzyme cleaves diester bonds, of the enzyme can be determined with
different substrate molecules.
14
specific enzymes work and what kinds of substrate molecules they convert into other harmless or harmful
molecules. This information can then also be used for the inhibition of these enzymes, which is making the
enzyme incapable of doing its original function by (more or less) permanently binding an inhibitor to
binding site of the enzyme. There are several methods for determining the mechanisms of enzymes, one of
them being kinetics studies.
The principle of fluorescence resonance energy transfer can be used to determine the action of an enzyme
to a substrate. Enzymes can couple two molecules to one or cleave one molecule in two parts. If an enzyme
is considered which breaks down certain molecules into parts, this speed can be determined. On one end of
the cleavage point a donor is attached and at the other end an acceptor is attached. The rate at which the
cleavage process occurs can then be determined by the rate at which the FRET-based acceptor signal
decreases or the donor signal increases (32). By calibration of the device with known concentrations of
both donor and acceptor, the rate of concentration increase or decrease can be determined.
Of course, because these are quantitative measurements, the same problem as with the quantitative
measurements from the sensors described above occur. Here quantum dots would probably give the same
advantages as before. A problem could possibly arise with getting the quantum dots close enough to the
acceptor species. However, when quantum dots are incorporated, spectral bleed-through would be
decreased and more accurate measurements of the activity of these enzymes could be done.
The procedure described here for enzymes could also be used for other chemical reactions. However, one
should already know something about the chemical reaction before one knows where to attach the different
donor and acceptor side groups to the molecules considered. Therefore, it looks like these techniques are
most useful for biochemical purposes. For biochemical analyses, it is often the case that many sorts of little
modified molecules are used to test an enzyme for which molecules it works best and worst. For a
biochemist this leads to information about the mechanism of the reaction and about other properties of
interest.
The principle of the distance dependence of FRET can also be used in another way. In a certain setup it can
be used to determine the isomeric form of a molecule. As an example of this cis-trans isomers are
considered (Figure 10). In one form of the molecule, the cis form, the donor and acceptor are close to each
other and as a consequence of the FRET mechanism the emission of the acceptor will be observed. In the
other form, the trans form, the donor and acceptor are far away from each other and no emission of the
acceptor will be observed. This principle can also be used to determine the presence of specific molecules.
It is known that cis-trans isomerisation can be initialised due to the presence of certain molecules. If it is
known to which target molecules the sensor molecules are sensitive, the presence of these molecules can be
determined by the change in the FRET efficiency and thus the emission which comes from the sample.
Figure 10: Two different isomeric forms a 2-butene
derivative, functionalised with a donor D and an acceptor A.
(a) Cis form. (b) Trans form. (c) Isomerisation between cis
and trans form initialised by an initiator molecule. The
presence of this initiator molecule can thus be determined by
the change in the FRET efficiency between the donor and the
acceptor as a consequece of the isomerisation.
15
Another interesting application which uses the distance dependence of FRET, is using FRET for
measurements of pressure. This is done by incorporating the donor and acceptor species in a matrix and if
pressure is exhibited on this matrix, the donors and acceptors become closer to each other, while, of course,
the ratio between donor and acceptor does not change in the material. By changing the distance the
efficiency of the FRET mechanism changes and this can be detected. The principle is incorporated in
coatings and shows promising results. Also it has been suggested that these coating sensor could be used to
measure shear stresses (34). A large problem in these system would probably be to produce sensor without
differences between them. However, first all sensor could be calibrated seperately. Also there should be
attention to the absorption spectrum of the matrix and how it influences the emission in to the FRET
detection channel.
4.4 FRET Sensors Based on Spectral Overlap Changes Between Donor and Acceptor
Another property of FRET which can be explored is the spectral overlap of the donor and the acceptor.
Also this property can be used to distinguish several situations from each other in quantitative FRET
measurements. This approach uses photochromic compounds. It gives also an addition to the determination
methods for FRET but can also determine structural changes in molecules.
Photochromic compounds transform between two different structure if illuminated with the correct
wavelength of light. An advantage of these compounds is that the transformation is reversible. Normally,
the two different structures have both a different absorption spectrum. In this way the two structures can be
distinguished using FRET. However, if a donor and a photochromic acceptor is used, in which only one of
the two structures has spectral overlap with the donor, also the energy transfer mechanism can be turned on
and off with the use of the correct wavelength of light which switches the photochromic compounds
between the two structures (35). By using this design of donor and acceptor pairs, a solution possibly can
(a)
(b)
Figure 11: (a) Photochromic convertable FRET pair with in (b) its fluorscence and
aborption spectra (36). In the upper part the absorption and fluorescence of the donor
moiety is shown. In the lower part the absorption of the open (O) and closed (C) form of the
molecule is shown. After opening of the ring with UV light, spectral overlap between the
two parts of the molecules is established and energy transfer can occur. Ring closure can be
done by illumination with visible light or heat.
16
be found in the quantitative measurements of FRET. As said above, problems always arise with spectral
bleed-through, making it difficult to determine what is the contribution of the FRET mechanism to the total
fluorescence and what is the result of other processes in the system. By using photochromic donors or
acceptors, this separation can be made and the determination of the efficiency of the FRET mechanism will
become easier.
The reversibility of the photochromic conversion gives an opportunity to repeat quantitative FRET
measurements and the off-state represents an internal reference of the system. Problems with these
approaches can be that the excited state of the usable structure can return to the ground state of the
unwanted structure during the FRET mechanism. This thus leads to a decrease in FRET efficiency because
the number of species present for energy transfer decrease while the energy transfer is occuring.
A possible application of almost the same principle can again be the determination of the activity of certain
enzymes. Where it is impossible to get two fluorophores too far away from each other after the enzyme has
done its work, a donor or an acceptor can be designed which obtains or looses its FRET character during
the reaction with the enzyme. Now the conversion mostly is permanent but during the enzyme action the
FRET efficiency changes which can be used to determine the speed at which the enzyme does the
conversion.
4.5 Tailor Made Sensors
Basic principles for FRET based sensors are given above. However, for every specific case these general
principles are used in many different manners or new design principles are tried to be used. There are
numerous systems known for determining a specific quantity using energy transfer. The system are all
made for measuring different properties and different problems rise in the realization of the sensors.
Therefore, all sensors have their own advantages and disadvantages. The principle of FRET can be used for
many purposes and probably new sensor systems are developed in the future.
5. Conclusion
Fluorescence resonance energy transfer is an interaction between excited states of different molecules or
materials. It can be used for many purposes and specifically small measurement sensors are under
development. Problems in the quantification of FRET efficiency are rather known and solutions to them are
being developed. Many different setups are used for measuring a quantity with FRET. All of them have
their specific problems and advantages. However, introduction of quantum dots as FRET donors seems to
have many advantages. In the use of these dots in the system many progress can be made.
While the goal is small sensors, this still seem far away. Larger devices for company or laboratory use can
probably be made but still specificity is not always as good as desired and needs to be worked on.
Therefore, much research is yet focussed on sensors for specific targets for laboratory use. The research is
not yet so far to launch a small sensor device for commercial or practical use. However, FRET is used
extensively in laboratories all over the world.
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6. References
(1) Medintz, I.L. ,Clapp, A.R.,Mattoussi, H.,Goldman, E.R.,Fisher, B., Mauro, J.M., Nature Mater. 2, 630-638 (2003)
(2) O’Connel, P.J. and Guilbault, G.G. , Anal. Lett. 34, 1063-1078 (2001)
(3) van Hal, P. , Photophysics of Molecules and Materials for Polymer Solar Cells, Thesis Technische Universiteit
Eindhoven, (2003)
(4) Förster, Th. , Ann. Phys. 2, 55 (1948)
(5) Frenkel, J. , Physik. Z. Sowjetunion 9, 158 (1936)
(6) Davydov, A. S. , Zh. Eksperim. i Teor. Fiz. 19, 210 (1948)
(7) Förster, Th. in Modern Quantum Chemistry, Part III Action of Light and Organic Crystals, Academic Press, New
York and London, 1965
(8) Förster, Th. , Fluoreszenz Organischer Verbindungen, Vandenhoek & Ruprecht, Gottingen, 1951
(9) Okuno,Y and Mashiko, S, Int. Jour. Quant. Chem. 90, 772-777 (2002)
(10) Dexter, D.L. , J. Chem. Phys. 21, 836 (1953)
(11) Atkins, P.W. and Friedman, R.S. , Molecular Quantum Mechanics, Third Edition, Oxford University Press,
Oxford, 1997
(12) Gu, Y. ,Di, W.L. , Kelsell, D. P. and Zicha, D., J. Microscopy 215, 162-173 (2004)
(13) Eidne, K.A. , Kroeger, K.M. , Hanyaloglu, A.C. , Tr. Endocrinol. Metabol. 13, 415-421 (2002)
(14) Harpur, A.G. , Wouters, F.S. , Bastiaens, P.I.H. , Nat. Biotechnol. 19, 167-169 (2001)
(15) Berney, C. , Danuser, G. , Biophys. Journal 84, 3992-4010 (2003)
(16) Bruchez, M. , Moronne, M. , Gin, P. ,Weiss, S. , Alivastos, A.P. , Science 281, 2013-2016 (1998)
(17) Neher, R.A. and Neher, E. , Microscopy Research and Technique 64, 185-195 (2004)
(18) Grant, S.A. , Xu, J. , Bergeron, E.J. , Mroz, J. , Biosensors & Bioelectronics 16, 231-237 (2001)
(19) Fox, M. , Optical Properties of Solids, Oxford University Press, Oxford, 2001
(20) Alivisatos, A.P. , J. Phys. Chem. 100, 13226-13239 (1996)
(21) Peng, Z.A. , Peng, X. , J. Am. Chem. Soc. 123, 183-184 (2001)
(22) Murray, C.B. , Norris, D.J. , Bawendi, M.G. , J. Am. Chem. Soc. 115, 8706-8714 (1993)
(23) Dabbousi, B. O. ,Rodriguez-Viejo, J. ,Mikulec, F. V. ,Heine, J. R. ,Mattoussi, H. ,Ober, R. , Jensen, K. F.
,Bawendi, M. G. , J. Phys. Chem. B 101, 9463-9475 (1997)
(24) Mattoussi, H. , Mauro, J.M. , Goldman, E.R. , Anderson, G.P. , Sundar, V.C. , Mikulec, F.V. , Bawendi, M.G. , J.
Am. Chem. Soc. 122, 12142-12150 (2000)
(25) Hines, M.A. , Guyot-Sionnest, P. , J. Phys. Chem. 100, 468-471 (1996)
(26) Chan, W.C.W. , Maxwell, D.J., Gao, X. , Bailey, R.E. , Han, M. , Nie, S. , Curr. Op. Biotechnol. 13, 40-46 (2002)
(27) Chan, W.C.W. , Nie, S. , Science 281, 2016-2018 (1998)
(28) Jin, Z. , Wang, B. , Peng, Y. , Zhao, F. ,Chen, W. , Liu, S. , Gao, C. , Surface Sciece 423, L211-L215 (1999)
(29) Raab, A. , Springholz, G. , Appl. Phys. Lett. 81, 2457-2459 (2002)
(30) Ohshima, T. , Song, H.Z. , Okada,Y. , Akahane, K. , Miyazawa, T. , Kawabe, M. , Yokoyama, N.,
Phys. Stat. Sol. 0, 1364-1367 (2003)
(31) Floro, J.A. , Chason, E. , Twesten, R.D. , Phys. Rev. Lett. 79, 3946-3949 (1997)
(32) Zlokarnik, G. , Negulescu, P.A. , Knapp, T.E. , Mere, L. , Burres, N. , Feng, L. , Whitney, M. , Roemer, K. ,
Tsien, R.Y. , Science 279, 84-88 (1998)
(33) Kikuchi, K. , Takakusa, H. , Nagano, T. , Trends Anal. Chem. 23, 407-415 (2004)
(34) Hamner, M. , Fontaine, A. , Atsavapranee, P. , ´Development of a New Pressure Sensitive Luminescent Coating´ ,
41st Aerospace Sciences Meeting & Exhibit, 6-9 January 2003, Reno, Nevada.
(http://www.leatechllc.com/Pubs/AIAA%202003-0091.pdf )
(35) Giordano, L. , Jovin, T.M. , Irie, M. , Jares-Erijman, E.A. , J. Am. Chem. Soc. 124, 7481-7489 (2002)
(36) Song, L. , Jares-Erijman, E.A. , Jovin, T.M. , J. Photochem. PhotoBiol. A 150, 177-185 (2002)
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