1 Fluorescence Energy Transfer

Nanoscale fluorophores such as molecular fluorophores and quantum dots serve as interfaces between the nano- and macro-worlds using optical excitation and emission [1]. Fluorescence imaging provides information with nanoscale spatial resolution [2]. Molecular beacons, which modulate the fluorescence properties in response to input stimuli in a molecular environment, have been widely used in biomedical measurements [3]. Designing combinations of input stimuli and fluorescence modulation also enables the fabrication of nanoscale devices including photonic wires [4] logic gates [5], and memory [6]. The integration of these diverse nanoscale devices is expected to enable sophisticated information exchange between the nanoscale and macroscale [7]. In systems that use the propagation of light, the spatial resolution and processing density are often limited by the diffraction of light [8]. Nanoscale fluorophores are advantageous for optical systems with resolutions beyond the diffraction limit [9].

The excited state energy of nanoscale fluorophores can be relaxed through various processes (Fig. 1a) [1]. In addition to radiative processes such as fluorescence, non-radiative processes such as thermal dissipation can also be involved in relaxation. Another feature of the relaxation process is fluorescence energy transfer, which allows the excitation energy to move non-radiatively between nearby fluorophores (Fig. 1b). Förster resonance energy transfer (FRET) is a dipole-dipole interaction-based fluorescence energy transfer technique that has been widely applied in various bio-applications [10, 11].

Fig. 1
figure 1

Schematic illustration of energy diagram of a excitation of single fluorescent molecule and b FRET

Full size image

FRET is a phenomenon in which excitation energy is transferred from one molecular fluorophore or quantum dot to a nearby molecular fluorophore [12, 13] or quantum dot [14]. The energy transfer rate constant k is expressed as follows [1]:

$$\begin{aligned} k = \frac{9000 (\textrm{ln} 10)}{128 \pi ^5 \eta ^4 N_A \tau _{a}} \cdot \frac{\phi _a \kappa ^2}{R^6}\int f_a (\lambda ) \epsilon _b (\lambda ) \lambda ^4 d\lambda , \end{aligned}$$
(1)

where \(\eta \) is the refractive index of the medium, \(N_A\) is Avogadro’s number, \(\tau _a\) is the donor fluorescence lifetime, \(\phi _a\) is the donor fluorescence quantum yield, \(\kappa \) is the orientation factor, \(f_a(\lambda )\) is the normarized fluorescence spectrum of the donor, \(\epsilon _b(\lambda )\) is the absorption spectrum of the acceptor, R is the distance between the donor and acceptor, and \(\nu \) is the frequency. The distance R at which k becomes 0.5 is known as the Förster radius and can be expressed as [1]

$$\begin{aligned} R_0 = 0.211 [\kappa ^2 \phi _a \eta ^{-4} \int f_a (\lambda ) \epsilon _b (\lambda ) \lambda ^4 d \lambda ] ^{1/6}. \end{aligned}$$
(2)

\(R_0\) is typically between 5 and 10 nm [12, 15].

From Eq. (1), FRET occurs when the donor is in close proximity to the ground-state acceptor and the acceptor’s absorption spectrum significantly overlaps with the donor’s emission spectrum. Figure 2 shows an example of FRET. FRET serves as one of the relaxation pathways for the excited donor. The excitation energy transferred to the acceptor undergoes a relaxation process, including acceptor fluorescence, resulting in a signal with a wavelength different from that of the donor fluorescence. The FRET pathway competes with the natural fluorescence process, reducing the fluorophore’s excitation state lifetime and fluorescence probability. FRET modulates the fluorescence intensity and lifetime signals. The probability of FRET depends on the absorption and emission properties and the relative positions of the fluorescent molecules, indicating that fluorescence signals can be modulated by FRET.

Fig. 2
figure 2

FRET between Alexa 488 and Alexa 568. a Molecular fluorophores. b Absorption and fluorescence spectra of Alexa 488 and Alexa 568. c Fluorescence with and without FRET

Full size image

Fluorescence signal modulation through FRET using the relative positions of fluorescent molecules is widely used in biomolecular sensing and measurement [16, 17] (Fig. 3a). The FRET technique has been applied to molecular beacons by linking binding reactions in molecular sensing to changes in the positions of donor acceptors [18]. Molecular rulers have been proposed based on the fact that the donor–acceptor distance affects the FRET efficiency [19]. This allows nanometer-scale information to be read as a fluorescence signal. In addition, by using fast FRET measurements, molecular conformational changes can be monitored [20].

Fig. 3
figure 3

Fluorescence signal modulation. FRET control using a relative positions of fluorescence molecules, b photoswitchable fluorescent molecules, and c multi-step transfers

Full size image

Another technique, fluorescence modulation based on FRET, can be achieved by changing the absorption of an acceptor molecule through light irradiation [21, 22] (Fig. 3b). According to Eq. (1), the efficiency of energy transfer in FRET is also determined by the degree of overlap between the fluorescence spectrum of the donor molecule and the absorption spectrum of the acceptor molecule. Photoresponsive proteins and photoswitchable fluorescent molecules can change their absorption spectra upon light irradiation through induced changes in their molecular structures or binding to functional groups. These molecules allow on/off switching of signal transmission through FRET in response to optical signals. Another method involves inhibiting the excitation transition from the donor by optically exciting the acceptor to an excited state [23]. This technique usually requires high-power irradiation to saturate the acceptor.

FRET occurs in multiple steps between multiple phosphors [1, 24] (Fig.3c). Multi-step FRET (cascade of FRET) can also be understood in principle using Förster theory. Multi-step FRET has been experimentally demonstrated between fluorescent molecules [4] arranged in one dimension and between quantum dots [25]. Compared to simple single-step FRET, energy can be transferred across longer ranges and more diverse fluorescence signal generation is possible [26]. Furthermore, FRET can also occur when quantum dots of the same or multiple species are arranged in two dimensions [27]. Theoretical analyses are underway, and diverse fluorescence signal modulations have been experimentally verified [28, 29] and theoretically [30]. Applications of computing utilizing this fluorescence signal modulation are also being studied [31].

2 FRET-Based Device

Controlling energy flow through FRET enables the implementation of nanoscale signal processing devices. In FRET control, the distance between the fluorescent molecules is a key parameter. DNA self-assembly is a useful method for positioning fluorescent molecules to achieve FRET control. This method has been used to align multiple fluorescent molecules and quantum dots and to design FRET pathways between them. Dynamic FRET pathways can be established based on the binding/dissociation switches of fluorescent molecules using DNA reactions. Other important factors that may influence FRET-based devices include overlap and excitation states. This section reviews FRET-based devices that use DNA self-assembly.

Fig. 4
figure 4

a Adenine (A), Thymine (T), Guanine (G), Cytosine (C). b Complementary binding. c Structure and size. d DNA hybridization reaction

Full size image

2.1 DNA for FRET Devices

DNA is a polymer molecule composed of four types of nucleotides: adenine (A), guanine (G), cytosine (C), and thymine (T), which are linked together (Fig. 4a). Based on the Watson–Crick complementarity, as shown in Fig. 4b, A pairs specifically with T and G pairs specifically with C through hydrogen bonding. Single-stranded DNA with complementary sequences can selectively bind together to form a double-helix structure, as shown in Fig. 4c. Typically, double-stranded DNA has a diameter of 2 nm and contains 10.5 base pairs (bp) per helical turn, corresponding to a length of 3.4 nm [32]. By using appropriate sequence design, double-stranded DNA structures can be programmed. Various two- and three-dimensional nanostructures have been created using this approach [33]. Additionally, other functional molecules can be conjugated to DNA to introduce new functions. Fluorescent molecules and quantum dots can be attached to the ends of DNA to control the nanoscale arrangement, enabling the implementation of fluorescent configurations to control FRET efficiency [20].

2.2 FRET-Based Photonic Wire

Nanoscale photonic wires are of particular interest for nanoscale information devices because of their ability to control energy transfer via FRET and deliver light energy. The simplest and most common photonic wire design is multi-step FRET with a linear array of phosphors [26]. Such wires exhibit a linear array of dye absorption and emission that changes from blue to red, creating an energy landscape of downward energy transfer within the structure [34]. Photonic wires have been constructed using up to seven dye molecules sequentially arranged on DNA scaffolds [34]. Nanoscale photonic wires have also been realized using FRET between quantum dots and between QD-dye [35].

2.3 FRET-Based Photonic Switch

The FRET optical switch enables on/off control of the energy transfer along the FRET pathway and selection of the pathway. Control of the FRET pathway via light irradiation can be utilized for light access from macro- to nanoscale information devices. An optical switching technique using energy transfer between quantum dots and the saturation of the excitation level has been proposed [36]. Similar approaches have been employed for FRET pathway manipulation using fluorescent molecules [23]. In these techniques, the excitation levels of the acceptors are exclusively occupied to inhibit FRET and adopt a different FRET pathway from that in the non-excited state. Other techniques use the optical control of molecular separation or cleavage to regulate the distance between fluorescent molecules [37]. Although most of these methods are based on permanent changes, their application to high-density optical storage has been proposed [38].

2.4 FRET-Based Logic Gate

Logic gates based on FRET are interesting not only in terms of expanding the applications of information processing technology, but also for achieving on-site information processing in the nano-world. Several approaches have been proposed for logic gates based on FRET [39,40,41]. The inputs are represented by pH, molecules, and light stimulation, whereas the outputs are represented by the responsible fluorescent signals [42].

3 Scaffold DNA Logic

Scaffold DNA logic has been proposed as a method for systematically constructing information systems using FRET [43]. This is a molecular computing system that accepts molecules, such as nucleic acids, as inputs and processes them using signal processing based on FRET in an intra-single DNA structure. Molecular circuits design and implement complex molecular reaction systems to construct molecular signal systems, so that the desired processing is executed against the inputs. This section presents the scaffold DNA logic.

3.1 Basic Concept

The energy transfer efficiency of FRET depends on the type and spatial arrangement of the fluorescent molecules, and FRET transfer can be controlled by selecting and manipulating them. As shown in Fig. 5, by arranging or removing fluorescent molecules on scaffold DNA in response to the input, on/off switching of signal transmission via FRET can be achieved. When fluorescent molecules of FRET pairs are arranged on the scaffold DNA within the FRET-allowable distance, FRET occurs, and the signal transmission is turned on. On the other hand, when they are removed from the scaffold DNA, FRET does not occur, and the signal is not transmitted.

Fig. 5
figure 5

FRET signal control through positional control of fluorophores

Full size image

Because input signals are assumed to be molecular inputs, it is necessary to control the arrangement of fluorescent molecules on the scaffold DNA in response to the input molecule and to obtain the calculation results through signal processing based on FRET-based signal processing constructed on the scaffold DNA. An overview of this process is shown in Fig. 6. When the fluorescent molecule is excited, the output is represented by 1 or 0, depending on whether the output fluorescent molecule is excited via FRET. If the input signal meets these conditions, the FRET circuit is complete, the output fluorescent molecule is excited, and the fluorescent signal is the output. This state is defined as an output of 1. If the given logical conditions are not satisfied, the FRET pathway is not completely constructed, and the output fluorescent molecule is not excited. This state is defined as an output of 0. Local FRET phenomena on the scaffold DNA allow the necessary signal processing for the execution of logical operations.

Fig. 6
figure 6

FRET cascade control through positional control of fluorescent molecules

Full size image

3.2 Arrangement Control of Fluorescent Molecules

The positioning of the fluorescent molecules on the scaffold DNA is controlled using connecting DNA (Fig. 7a) and disconnecting DNA (Fig. 7b). The connecting and disconnecting DNA are modified with fluorescent molecules and are composed of recognition and address regions. The recognition region recognizes the input molecule, and the address region specifies binding to the prepared sites on the scaffold DNA. In the absence of an input molecule, the connecting DNA forms a closed hairpin structure. In this state, the address region is covered and the connecting DNA maintains a dissociated state from the scaffold DNA. Therefore, fluorescent molecules were not positioned on the scaffold DNA. In the presence of an input molecule, the connecting DNA (Fig. 7a) binds to the input molecule, and the hairpin structure opens. In this state, the address region is in a single-stranded state and binds to the scaffold DNA. As a result, the fluorescent molecules are positioned at the site specified on the scaffold DNA. The disconnecting DNA (Fig. 7b) binds to the specified site within the scaffold DNA when the input molecule is absent. In the presence of the input molecule, it forms a linear structure by binding to the recognition region, resulting in its dissociation from the scaffold DNA. Using these configurations, the positioning/removal of fluorescent molecules can be controlled depending on the presence or absence of the input molecule.

Fig. 7
figure 7

Reproduced with permission from Appl. Phys. Lett. 101, 233703 (2012). Copyright 2012, AIP Publishing LLC

Fluorescent molecule control on DNA scaffold using a connecting DNA and b disconnecting DNA.

Full size image

3.3 Design of Logic Operations

By constructing connecting or disconnecting DNA, it is possible to pre-specify the input molecule species, placement of fluorescent molecules, and placement sites on the scaffold DNA. Through these combinations, it is possible to establish FRET pathways on the scaffold DNA for the input molecules. Placing FRET pair molecules on adjacent sites corresponds to connecting the FRET pathways in series, enabling the implementation of the AND operation (Fig. 8a). In contrast, placing the same type of fluorescent molecule at the same site for multiple inputs represented by different molecular species corresponds to connecting the FRET transmission pathways in parallel. This enables the implementation of the OR operation (Fig. 8b). In addition, the NOT operation can be implemented by utilizing the relationship between the input and signal transmission through the disconnecting DNA (Fig. 7b). Because any logical expression represented in a conjunctive normal form can be implemented, any logical operation can theoretically be performed. The following sections provide an overview of each operational experiment. For details on the experiments, including the DNA sequences, please refer to [43].

Fig. 8
figure 8

Reproduced with permission from Appl. Phys. Lett. 101, 233703 (2012). Copyright 2012, AIP Publishing LLC

Implementation of a AND and b OR operations.

Full size image

3.4 AND Operation

To confirm the AND operation, \(I1 \wedge I2\) operation was performed using two types of single-stranded DNA, strands I1 and I2, as input molecules. Figure 9 shows the reaction scheme. FAM and Alexa 546 were used as FRET pairs. Strand C1 detects strand I1 and positions FAM at site 1. Strand C2 recognizes strand I2 and positions Alexa 546 at site 2. When the input (1, 1) is present, FAM and Alexa 546 bind to the DNA scaffold. The distance between the modification positions of FAM and Alexa 546 is 13 bp, which is calculated to be 4.6 nm. Because the Förster radius of FAM and Alexa 546 is 6.4 nm, they are sufficiently close for FRET to occur. At this point, the excitation energy is transferred from FAM to Alexa 546 via FRET, resulting in an output of 1. In other cases, at least one of FAM and Alexa 546 is not bound to the scaffold DNA, and FRET does not occur, resulting in Alexa 546 not being excited. This state results in an output of 0.

Fig. 9
figure 9

Reproduced with permission from Appl. Phys. Lett. 101, 233703 (2012). Copyright 2012, AIP Publishing LLC

a Design and b results for \(I1 \wedge I2\) operation.

Full size image

Figure 9a shows the reaction scheme for \(I1 \wedge I2\) operation. The fluorescence intensity of FAM decreased only in the case of (1, 1), and that of Alexa 546 increased. The decrease in FAM fluorescence intensity in the case of (1, 0) may be attributed to the quenching effect of the DNA bases. The fluorescence output was evaluated as the change in intensity before and after the input at the fluorescence peak wavelength of the output molecule. The results are shown in Fig. 9b. The fluorescence output significantly increased in the case of (1, 1). The reason for the negative values could be the decrease in concentration due to the sample volume increase caused by the input. These results demonstrate that an appropriate AND operation can be achieved by positioning the FRET pair of fluorescent molecules at adjacent sites using different input molecules.

3.5 OR Operation

To confirm the OR operation, three types of strands, I1, I2, and I3, were used as inputs to perform \(I1 \wedge (I2 \vee I3)\). The reaction scheme is shown in Fig. 10a. Strand C3, which recognizes strand I3 and places Alexa 546 at site 2, was added to the reaction system used for \(I1 \wedge I2\). When strands I2 or I3 are present, Alexa 546 is placed at site 2. This allows OR operations on I2 and I3. When (1, 1, 0), (1, 0, 1), or (1, 1, 1) are input, FAM and Alexa 546 bind to the scaffold DNA. Only in this case does the excited energy transfer from FAM to Alexa 546 through FRET, resulting in the excitation of Alexa 546, which is defined as an output of 1. In other cases, because neither FAM nor Alexa 546 binds to the scaffold DNA, FRET does not occur, and Alexa 546 is not excited, which is defined as an output of 0.

The fluorescence outputs of each input are shown in Fig. 10b. The fluorescence output increases significantly for the (1, 1, 0), (1, 0, 1), and (1, 1, 1) cases. However, in the other cases, the fluorescence output is almost zero, indicating that \(I1 \wedge (I2 \vee I3)\) is accurately performed.

Fig. 10
figure 10

Reproduced with permission from Appl. Phys. Lett. 101, 233703 (2012). Copyright 2012, AIP Publishing LLC

a Design and b results for \(I1 \wedge (I2 \vee I3)\) operation.

Full size image

3.6 NOT Operation

The NOT operation was implemented using disconnecting DNA. The system for \(\lnot I1 \wedge I2\) is illustrated in Fig. 11a. Strand C1 used in the reaction system for \(I1 \wedge I2\) is replaced with strand D1. Strand D1 releases FAM from site 1 when it recognizes strand I1, enabling the execution of the NOT operation. In this case, the fluorescence output increases significantly via FRET for the (0, 1) case. The fluorescence outputs for each input are shown in Fig. 11b. The fluorescence output increases significantly in the (0, 1) case, whereas it is almost zero in the other cases. Thus, logic operations, including NOT operations, can be performed accurately using disconnecting DNA.

Fig. 11
figure 11

Reproduced with permission from Appl. Phys. Lett. 101, 233703 (2012). Copyright 2012, AIP Publishing LLC

a Design and b results for \(\lnot I1 \wedge I2\).

Full size image

3.7 Extended FRET Connection

To confirm that the FRET connections could be extended, \(I1 \wedge I2 \wedge I3\) was implemented using multi-stage FRET. The reaction system used for this operation is shown in Fig. 12a. The fluorescent molecules used were FAM, Alexa 546, and Alexa 594. For the reaction system used in \(I1 \wedge I2\), we changed strand S1 to strand S2, which has three sites. We also introduced strand C4, which places Alexa 594 at site 3 when recognizing strand I1. As shown in Fig. 12b, the output intensity increases for the input (1, 1, 1). It was demonstrated that circuit expansion is possible by utilizing multi-stage FRET. The slight increase in the output intensity in the cases of (0, 1, 1) and (1, 0, 1) may be due to the excitation of Alexa 546 and the FRET between FAM and Alexa 594, which can be improved by adjusting the fluorescent molecule composition and excitation wavelength.

Fig. 12
figure 12

Reproduced with permission from Appl. Phys. Lett. 101, 233703 (2012). Copyright 2012, AIP Publishing LLC

a Design and b results for \(I1 \wedge I2 \wedge I3\).

Full size image

4 Optical Program of DNA Scaffold Logic

Optical input can be incorporated into the framework of the DNA scaffold logic. The use of fluorescent molecules that can reversibly change their fluorescence properties upon light irradiation is effective. In this subsection, we introduce light control using cyanine-based fluorescent molecules, as well as their applications in the optical control of the FRET pathway and optically programmable DNA scaffold logic.

4.1 Optical Control of FRET

According to Eq. (1), the energy transfer efficiency in FRET depends on the overlap between the fluorescence spectrum of the donor molecule and the absorption spectrum of the acceptor molecule. Photoresponsive proteins and fluorescent molecules are molecules whose absorption spectra change because of changes in their molecular structure induced by light irradiation or binding with functional groups [44]. Using these molecules, it is possible to switch the on/off state of signal transmission via FRET in response to light signals [45]. Here, we utilize optical control based on cyanine-based fluorescent molecules as an example of absorption spectrum modulation. Cyanine-based fluorescent molecules are light-controllable molecules that can control their fluorescent or bleached state through light irradiation [44]. This mechanism is based on a photochemical reaction that induces the binding and dissociation of the thiols of the cyanine dye [44]. Additionally, when other fluorescent molecules (activators) are present near the cyanine-based molecules, the dissociation of the cyanine-based molecules and thiols can be controlled by their excitation [46, 47]. This means that the wavelength of the activated light can be set by selecting the fluorescent molecules to be placed nearby. Without synthesizing special fluorescent molecules or fluorescent proteins, it is possible to control the fluorescence properties using light at various wavelengths by selecting fluorescent molecules to be placed nearby.

Figure 13 shows an overview of the optical control of FRET. Fluorescent molecules with three different functions (donors, acceptors, and activators) are prepared. Cyanine-based fluorescent molecules are used as acceptors, and activators are placed near the cyanine molecules. When the acceptor is strongly excited, it changes to a dark state. In this state, the excitation of the donor does not cause FRET to the acceptor. When the activator is excited, the acceptor recovers its fluorescent state, enabling FRET from the donor to the acceptor. Thus, FRET can be switched on and off using light irradiation.

Fig. 13
figure 13

Schematic illustration of optical control of FRET

Full size image

4.2 Optical Control of FRET Pathway

FRET pathways are controlled by using cyanine-based fluorescent molecules, as shown in Fig. 14 [48]. Two sets of acceptor and activator molecules are arranged on the DNA scaffold. Because the absorption peak wavelengths of acceptors 1 and 2 are different, photoactivatable fluorescent molecules in these systems can be independently controlled using external light of different wavelengths. When only acceptor 1 is activated, FRET occurs only in pathway 1. Conversely, when only acceptor 2 is activated, FRET occurs only in pathway 2. Therefore, by independently switching each system, it is possible to change the energy transfer pathway. When the activation light for pathway 1 is irradiated, the fluorescence intensity of pathway 1 mainly increases, while that of pathway 2 decreases. This indicates that FRET occurs more frequently in pathway 1 than in pathway 2. In contrast, when applying the activation light for pathway 2, more FRET occurs in pathway 2 than in pathway 1. These results demonstrate that systems using different activators can be independently activated at the corresponding wavelengths and that FRET efficiency can be controlled.

Fig. 14
figure 14

Optical control of FRET pathway

Full size image

4.3 Optically Programmable DNA Scaffold Logic

The optical control of a FRET molecular logic circuit has been demonstrated using a FRET pathway optical selection technique [49]. This enables the execution and timing of molecular logic operations to be controlled solely by light irradiation, without altering the solution environment. This approach is expected to enable the processing of spatiotemporal information from dynamically changing molecular information, which is difficult to implement in conventional DNA logic circuits that execute operations based solely on molecular reactions.

Molecular logic operations are executed by controlling the arrangement of fluorescent molecules using changes in the DNA structure in response to molecular inputs and utilizing the formation of the FRET pathway, as shown in Fig. 15. Fluorescent molecules are attached to the scaffold DNA based on self-organizing reactions using DNA complementarity. FRET pathways are designed to extend from the initiating dye to the reporting dye when the given logical conditions are satisfied. Multiple FRET pathways with different programming operations are prepared on the scaffold DNA. The selected pathway is then controlled by manipulating the activation or deactivation of the light-sensitive fluorescent molecules using light irradiation. Molecular logic operations are executed based on the selected pathway and its timing.

Fig. 15
figure 15

Reproduced with permission from Appl. Phys. Lett. 107, 013701 (2015). Copyright 2015, AIP Publishing LLC

Schematic illustration of optically programmable DNA scaffold logic.

Full size image

To demonstrate time control of molecular information processing, we designed a FRET molecular logic circuit with light-controlled execution timing for I1\(\wedge \)I2 and I1\(\wedge \)I3 (Fig. 16). Functional DNA regulates the binding of fluorescent molecules to scaffold DNA according to the input molecular information. I1\(\wedge \)I2 and I1\(\wedge \)I3 are assigned to FRET pathways 1 and 2, respectively. To selectively induce FRET in each pathway, activator molecules (pathway 1: Alexa 405, pathway 2: Cy3) with different absorption spectra are pre-arranged on the scaffold DNA. By irradiating light at wavelengths corresponding to each activator molecule (pathway 1: 405 nm, pathway 2: 450 nm), the FRET pathway is selected, and the assigned operation is executed.

In the experiment, reporter molecules with different fluorescence spectra (pathway 1: Cy5, pathway 2: Cy5.5) were used to distinguish outputs. Input molecules I1, I2, and I3 were sequentially added to represent the time variation of the molecular information in the solution. The fluorescence intensity significantly increased only when the input molecular information satisfied the logical condition assigned to the light-selected pathway (Fig. 17). This result demonstrates that the timing of molecular logical operations can be controlled by light signals.

Fig. 16
figure 16

Schematic illustration for optical switch I1\(\wedge \)I2 and I1\(\wedge \)I3 executions

Full size image
Fig. 17
figure 17

Time courses of light irradiation signals and fluorescence output of I1\(\wedge \)I2 and I1\(\wedge \)I3, in response of inputs

Full size image

5 FRET Network-Based Computation

Sections 3.3 and 3.4 described a FRET device capable of performing simple logic operations at the molecular level (below 10 nm). FRET pathways are controlled by the placement of particles and molecules, energy level saturation control, and molecular property changes, implemented by a pre-designed FRET computational device. Although scaling up FRET computing devices that apply microfabrication technologies, such as DNA nanotechnology, has been anticipated, the number of FRET cascades is limited owing to the red-shifted FRET. Large-scale computation using FRET devices has not yet been implemented.

As a potential solution to this issue, a signal processing device employing FRET networks has been proposed [30]. This device operates by learning the input/output characteristics of FRET network devices, which comprise a variety of quantum dots randomly arranged at a high density [28, 50]. The input signals are encoded as light signals using time and wavelength. Utilizing a high-density random FRET network device alone does not achieve efficient signal processing to provide the desired output. However, recent breakthroughs in machine learning have facilitated the estimation of object information and the attainment of desired optical responses from input/output data, even for cases in which optical modeling is challenging. By adopting this approach, the input–output characteristics of a densely aggregated FRET network device with the disorder can be learned, allowing for the implementation of the desired optical transformation, and thereby enabling micro-scale and large-scale optical signal processing, which was previously hindered by physical constraints in using the designed FRET pathways.

By using machine learning techniques to impart the desired function to the FRET network device, a wide range of signal processing techniques, including input light signal distribution, product operation, and amplification, can be implemented through the control of single-step FRET with light. Despite the random distribution of quantum dots within the FRET network device, they respond to light control and modulate the fluorescence signals [51]. Applying machine learning algorithms to the input/output response of the FRET network device allows programming of the FRET network device using a control light, enabling the desired signal modulation of input/output signals, such as processing for neural networks or reservoir computing.

The FRET network-based approach holds the potential to enable a fast and efficient optical implementation for predicting and recognizing spatiotemporal data using reservoir computing. This technology has wide-ranging applicability to various types of spatiotemporal data, including images, sounds, and videos, and is poised to contribute significantly to the development of new computing devices.