Analytical design of multi-threshold and high fan-in DNA-based logical sensors to profile the pattern of MS microRNAs

Abstract

Early detection of diseases is very important to increase the life quality and reduce the treatment cost for the patient. MicroRNAs have been introduced in recent years as an efficient class of biomarkers for detecting the risky situation of many diseases such as cancers, Multiple sclerosis (MS), and heart attacks, and other diseases. Now, real-time PCR has been used to profile the microRNA expression, which is expensive, time-consuming, and has low accuracy. Most recently, DNA logic gates are used to detect the MicroRNA expression level that is more accurate and faster than previous methods. In this paper, we improved the design of multi-threshold and multi-input DNA-based logic gates in response to specific microRNA (miRNA) inputs. The proposed design style can simultaneously recognize multiple miRNAs with different rising and falling thresholds. The proposed structure in this paper is used to diagnose Multiple Sclerosis (MS) as a case study. We simulated this system to understand its performance and compare it with other existing methods. The simulation results show the efficiency of the proposed method in terms of accuracy, efficiency, and speed. In this analysis, unwanted reactions, fault positive, and the probability of generating the final output using the formal method are investigated in depth. Finally, the proposed solutions are improved based on the results of these analyses. The analytic approach of this paper helps to design the DNA-based logic gates for real diseases.

Introduction

Multiple sclerosis (MS) is a widespread disease that is caused by the destruction of the myelin cover (sheath). Due to the presence of a myelin sheath, the body will be able to create harmonious movements. In MS disease, this nerve sheath is destroyed and nerve signals transmitted from the brain are not well. Although MS disease is not a contagious or hereditary disease, a genetic role in its creation is approved [1]. Currently, MS disease has no promising treatment [2]. But, MS patients can receive more effective precautionary services to prevent the progression of the disease, if the disease diagnosed in the early stages [3]. Symptoms may appear very early in some patients. While the other patients do not have any symptoms for a longer period. The symptoms of MS disease vary greatly and the symptoms depend on the severity and location of the damage, which makes it difficult to diagnose correctly. Currently, the disease is usually diagnosed through clinical examination, electrophysiology, MRI and other tests [4].

Some biomarkers are common to most of the patients and can be detected from the very first stages To early detection of this disease. Finding a proper biomarker is a major challenge in the diagnosis and curing of illness [5] and [6]. A biomarker is defined as an indicator of objective measurement that indicates the presence or progress of a particular situation. It can also be used to monitor the efficiency of treatment. MicroRNA strands are a class of RNA molecules that have a length of 19 to 24 nucleotides. MicroRNAs (miRNAs) play an important role in regulating genes that involved in processes such as development, differentiation, and control of cell growth [7].

Recent studies have shown that miRNAs have distinguishable expression profiles in immune systems and play pivotal roles in the regulation of cell development and function [2, 5, 8–11] and [12]. Moreover, when miRNA expressions are changed, they can contribute to pathological conditions involving the immune system, such as cancer and autoimmunity. Authors of [8] analyzed the expression of 866 human miRNAs. They used microarray and the Genom Real-Time Analyzer (GRTA) platform and identified 165 miRNAs that were significantly up- or down-regulated in patients. Also, the authors of [9] assessed miRNA genome-wide expression profile by microarray on T cells. They found 23 human miRNAs differentially expressed. Expression analysis for miR-21, miR-146a and -b, miR-150 and miR-155 was done in [10]. A significant increase in miR-21, miR-146a, and –b expression was observed in [10]. The miRNA expression can be analyzed in whole blood samples. Authors of [11] and [12] used serum samples from MS patients. They targeted the miRNAs in the circulation. In [11], miRNAs expression was determined by qPCR. They found that 19 miRNAs were differentially expressed. Among them, 15 were up-regulated and 4 were down-regulated. In [12], some samples are analyzed by NGS, microarray analysis, and qRT-PCR.

A conventional method for detecting miRNA strands is Real-Time PCR (Polymerase Chain Reaction). This method uses colored molecules that released fluorescent light after miRNAs binding to a double-stranded structure of DNA. Therefore, the fluorescent concentration in the solution increases during the reaction of this PCR model. Finally, a curve is obtained by measuring the intensity of the fluorescent light at the end of each period. However, this method is quite a laboratory and special conditions are required for preserving primers and probes. Another disadvantage of this method is its inability to estimate the size of the reproduced product. Also, it is difficult to identify them with this method [13] because of the short length of miRNA strands and their similarity to the primer strands used in the PCR process.

DNA computation is a promising technique for monitoring cellular systems. Recently, DNA logic gates are proposed as a new method in numerous ways to detect the expression of microRNAs [13–19]. DNA logical gates are built from DNA strands comprised of multiple strands as inputs, a strand as an operator, and a strand as output. New researches show the efficiency and integrity of this approach. However, there is some serious face some serious challenges of this technology that has been focused on by many researchers in these years.

Recent contributions show that DNA logic gates are responsible for detecting the very low concentration of the microRNAs. Laboratory implementation of these systems such as [21, 17, 22], and [20] investigated and addressed this fact. This is because a fluorescent is bound to these gates that are released by detecting a negligible amount of the inputs. Therefore, the sensitivity of DNA-based logic gates is very high. On the other hand, the output fluorescent can be detected easier and cheaper than PCR operations.

Seesaw logic gates were proposed by Qian and Winfree to create a scalable DNA circuit architecture [14, 15] and [16]. This methodology is based on the principle of Toehold exchange and uses some strands to provide a higher level of scalability compared with the previous methods. Proposed gates in these papers apply to many uses, including medicine. However, the designed gate is general-purpose and the complexity of its design affects the speed and display of the result.

Winfree et al. presented another kind of logical gate in [21]. Their AND gate was constructed based on dual-rail signal representation. They have some kinetic analysis of the module of this gate using reaction equations. The main approach of [21] is using formal CRNs (Chemical Reaction Network) for modeling chemical reaction kinetics. They provided a framework for successful generalization and unifying the existing experimental achievements in this direction.

The objective of [17] was designing the efficient DNA logic circuit. Authors of [17] succeed to detect the miRNA expression patterns of some diseases and proposed a diagnosis system with two inputs (miR-21 and miR-122) to detect these microRNA as the most critical biomarkers of Lung cancer. Any increase in the expression of miR-21 is common in most cancer while miR-122 is involved in hepatocellular carcinoma and hepatitis-C virus replication [17]. Authors of [18] designed some logic gates on DNA Origami for miRNA analysis. In [18], miR-21 and miR-195 were selected as the input strands to detect the heart failure.

Deiters et al. in their recent paper ( [22]) have used the introduced gate in [17]. They proposed AND/OR logic gates that detect miRNA strands. This circuit can be easily expanded into more complex systems through multiplexing.

A molecular robot is a biochemical machine that imitates the actions of microorganisms. It is made of biomaterials such as DNA strands. This paragraph focuses on a few recent researches on the molecular robot. In [23] reviewing recent research on synthetic ion channels and DNA computing technologies which they are potential candidate components of molecular robots. Also in reference [24], a DNA logic operation was proposed as a powerful tool for the recognition of microRNA patterns. This method recognized two microRNAs (miR-20a and miR-17-5p). The proposed method was based on DNA computing and Nano-pore technologies and could be integrated into the construction of a molecular robot.

As mentioned before, considerable contributions are reported on using the DNA-based logic systems in modern medical applications to profile the miRNA expression patterns. However, current DNA-based logic gates suffer from the complexity, especially for high fan-in gates. This complexity increases the cost and error rate of these systems such that they may not be feasible for real applications. Many successful experiences in computer science can be used to optimize the size/cost of these DNA logic gates.

We proposed a DNA-based logic design style to achieve low-complexity and extendable multi-input DNA logic gates with the multi-threshold capability to profile the expression pattern of different microRNAs [25]. This system provides the ability to detect large numbers of miRNAs at different levels (multi-threshold). Moreover, this logic system can simultaneously detect miRNAs that have been reduced due to illness and those whose expression levels have increased.

In this paper, we use the DNA-based logical system [25] to detect MS biomarkers as a real case study to evaluate it for a real disease. Many diseases are detectable by blood biomarkers. The system presented in [25] can diagnose these diseases in the early stages. The expansion and cascading of the proposed gates can be easily automated because of the low complexity and the error rate of the proposed method [25]. However, this method has not yet been investigated in the vitro and only has been used simulation results is not reliable. So, we used probabilistic model-checking (PRISM) to increase the reliability of the system. The results of these analyzes will help us to improve the proposed system.

We have presented a DNA-based logic gate in [25] to detect cancer biomarkers. The proposed method in [25] is simulated and verified using the VisualDSD, a well-known DNA reaction simulation tool. However, an analytical investigation is required to validate the unwanted reactions, the correctness of the responses, and the robustness of the system that is proposed in this manuscript. Moreover, considerable improvements are made on the gate in this paper and also it is applied to the biomarkers of other types of disease to analyze the coverage and scalability of the proposed gate. Therefore, This paper improves the quality of the proposed gate in [25] with an analytical approach to verify and prove the properties of the proposed system.

The organization of the paper is as follows. In Section two, explanations are given on DNA logic gates in medical applications. Section three presented a proposed logical system for diagnosing MS disease. The fourth section compares the proposed design method with existing methods. The fifth chapter shows the results and eventually leads to the sixth chapter of the paper.

Applications of DNA-based logic gates in medicine

Recently, many miRNAs have been introduced as the biomarkers of the wide range of diseases. In other words, research shows that the occurrence or progression of the disease is related to the expression pattern of these miRNAs. On the other hand, recent research has shown that DNA-based logic gates can detect miRNA patterns with high accuracy and low-cost [6].

Authors of [21] have designed a two-input AND gate as shown in Fig. 1. In this gate, all the inputs must be simultaneously existed to generate the output strand. Accordingly, the ideal state in the absence of one of the inputs is that the other inputs don’t react with the gate strand. This is an important challenge in the design of a DNA-based AND gate. The authors of this paper [21] indicated the reversible reactions is the answer to this challenge. In this structure, the first strand has a reversible reaction with the gate. If the second input is present in the environment, the reaction is continued and released the output strand. Otherwise, the inverse of the first reaction releases the first input and returns to the environment.

Fig. 1.

A schematic representation of the proposed AND gate in [21]

Schematic representation of input and gate strands presented in Fig. 1. The chain of reactions begins with the first input strand (i.e. $i^{\ast }{a}^{\ast }{b}^{\ast }{c}^{\ast }$). Each letter of this DNA strand means a part of its sequence (sub-strand), and the star sign means that this sub-strand is a complementary part. The colored sub-strands in Fig. 1 are toeholds. Toeholds are small sub-strands with a high desire to react. It reacts more quickly such that it can start or direct other reactions. Firstly, sub-strands a and $a^{\ast }$ are paired together and separate the $b^{\ast }{c}^{\ast }{d}^{\ast }$ and then $i^{\ast }{a}^{\ast }{b}^{\ast }{c}^{\ast }$ completely attaches to the gate. After that, the second input $j^{\ast }{d}^{\ast }{e}^{\ast }{f}^{\ast }$ reacts with the gate and finally, the output strand $e^{\ast }{f}^{\ast }{g}^{\ast }{h}^{\ast }$ will be released and will be visible and detectable in the environment.

As previously mentioned, in [17] a DNA-based gate is designed to detect patterns of miR-21 and miR-122 in living mammalian cells. Figure 2 shows the logic view of this gate.

Fig. 2.

An overview of the two-input AND gate [17]

The design of the gate of [17] has a considerable limitation. In this gate, all the inputs must have the same toehold that is not an acceptable condition in real diseases as shown in Fig. 3. This ensures that the output is ‘1’ if and only if both inputs are present at the same time. This same toehold determines the order of the reactions. However, the structure of gate inputs (miRNA strands) does not have the same toehold and cannot react with the gate designed in [17]. Therefore, the problem arises in reacting and producing output. Designers need to produce intermediate strands to solve this problem (M122 for miR-122 and J21 for miR-21). In this way, if any input string (miR-122 and miR-21) are available (input = 1), an intermediate strand will be released. Otherwise (at least one input = 0), this middle strand will not be released. Therefore, the AND gate does not enter any reaction and the output of the circuit remains zero. This will increase the complexity of the system because it needs to design a 2-input gate on the 2-floor, increasing the number of strands and carrying out additional reactions.

Fig. 3.

Implementation detail of 2-input gate [17]

Figure 3 illustrates the implementation of this two-input gate. In this figure, colored parts are considered as Toehold. The Toehold sections are blue and green for miR-21, and orange and red colors for miR-122. The complementary parts (shown with the same color) connect. In this design, the same toehold is the red part that must be present at 2 main gate inputs to react to the gate strand. Because naturally there is no such part, so, this part is released through the extra level. The extra level is defined as J21 and M122, respectively, for miR-21 and miR-122. In the main AND gate, the blue circle Q represents the BlackHoleQuencher2 and the TAMRA Fluorophore is seen in red and F. The reactions and output strands are shown in Fig. 3. Finally, the release of the strand containing F activates fluorescence and produces light.

As it can be seen in Figs. 2 and 3, the design of [17] requires auxiliary inputs (J21 and M122) and additional gate levels that increase the number of strands and reactions, which leads to more complexity and excessive overhead. This is one of the disadvantages of the design method of [17]. Another problem is that this logic gate cannot be easily extended and the number of inputs cannot be increased.

The most important limitation of this gate is that extending it is not straightforward. The number of miRNAs is important to diagnose the disease and the expression pattern of some miRNAs are common to many illnesses and may even occur in a healthy person. Therefore, a specific pattern of each disease including a cluster of miRNAs should be provided and examined. By increasing the number of miRNAs, the gate can have a reliable diagnosis, and the probability of error decreases. Two different strategies can be used to expand the proposed gate of [17].

The first method for extending the gate of [14] is using multiple two-input gates and make larger gates with them. In this method, we assign each 2 arbitrary inputs are assigned to a gate [17] and the results of these gates are sent to another gate. For example, a three-input AND gate are shown in Fig. 4. That made of 2 gates of [17]. Increasing the complexity of the gate is well seen in Fig. 4.

Fig. 4.

Extended three-input “AND” gate in 3 levels a an electronic representation of 3-input gate. b a schematic representation of 3-input gate [17]

As it can be seen in Fig. 4a, 5 gates are required in 3 levels to realize a 3-input AND gate. Moreover, 3 auxiliary strands are required corresponding to each input (i.e. M122 with miR-122, J21 with miR-21, and F210 with miR-210). Figure 4b shows the order of the reactions required for producing the final output. As can be seen in this figure, the output strand will be generated only when all of the 4-input strands (i.e. miR-21, J21, miR-122, M122) are present in the system.

As shown in Fig. 4, more than 14 unique sub-strands are required for the implementation of this gate and the gate is too complex for three inputs. In real cancers, more than a dozen of microRNAs should be profiled. In this situation, this complex AND gate will be inefficient or even infeasible.

The second method is to use the logic of constructing a two-input gate [17] and construct larger gates. A larger gate with the experience of the Gate [17] is suggested in this paper. In this way, the main gate and some auxiliary gates for the input stand are needed. For example, a 3-input AND gate are given in Fig. 5. Increasing the complexity of the gate is much less than Fig. 5 and this gate is simpler than the first method considerably.

Fig. 5.

Extended three-input “AND” gate in 2 levels a an electronic representation of 3-input gates. b a schematic representation of 3-input gate [17]

The number of sub-strands is reduced by substituting them with a 3-input gate to 11 sub-strands in Fig. 5. This trend will be continued by increasing the number of inputs. Because by using the 2-input gate for each input, more than 7 sub-strings will be added, but in the expanded method, adding 4 sub-strands is sufficient.

One of the latest reported works on diagnosing the microRNA using DNA computation is [22]. This research is a continuation of the previous work of this group in [17]. These systems are functional in the context of a small DNA-based circuit (3-input) and were quickly expanded into more complex systems through multiplexing (6-input). Dieters in this article modified the structure and some parts of the chemical formula to slightly achieve. In this new structure (Fig. 6) one of the additional gates has been removed. Removing this part is done to connect the gate to the make an OR gate. Figure 6a shows the electronic structure of the new gate. As you can see, the MIR-21 is used directly as a gate input. A simple schematic representation of input strands and how they react with the gate is provided in Fig. 6b. Reducing additional gate (J21) reduces the number of strands, system responses, and the complexity of the design.

Fig. 6.

The “AND” gate a an electronic representation of the gate. b a schematic representation of the DNA implementations [22]

Moreover, the fluorescent output was calculated using standard curves of AMC- or ABNI-azido-modified DNA and free fluorophore. The mixture of TG122 and AND-G21 was incubated at 37 °C, and the fluorescence intensity of AMC was measured after 1h. Three independent experiments were averaged, and the error bars were represented as standard deviations. This gate will be examined in depth in the experimental section.

Besides, they designed a DNA logic gate to detect iR-122 OR miR-125b (Fig. 7) that provides an output in the presence of either or both of the two miRNA inputs. Figure 7a shows an electronic representation of the gates structure. The miR-21 is one of the inputs of the AND gate and the other input of the gate is the output strand of the OR gate. In Fig. 7b, a simple schematic of input strands and how they react with the gates is provided.

Fig. 7.

The “AND/OR” gate. a Electronic representation of the gates. b Schematic representation of the DNA implementations [22]

This gate is made of two 2DPBM-modified translator gates (TG122 and TG125b) (Fig. 7b). The outputs of TG122 and TG125b both have the same toehold which can react with AND gate. In AND gate, as previously noted, the 2DPBM-modified strand can only hybridize to the gate after miR-21 displaces the top strand leading to exposure of a new toe-hold.

Since a dozen of miRNAs are normally associated with recognizing diseases such as cancer, MS, viral infection, etc., high fan-in logic gates are needed. Most existing methods cannot be extended to identify a large number of inputs for Accurate diagnosis of diseases. Moreover, the proposed styles can design the gate with different thresholds for inputs. In the next section, the proposed system will be investigated.

The proposed DNA-based diagnosis system

As mentioned before, a DNA-based logical system is presented in this manuscript to detect the biomarker expression pattern of MS. The main objective for this gate is providing a reasonable trade-off between scalability for a large number of inputs, the correctness of the gate, the speed of the response generation, and cots of the detection system. We proposed the concept and structure of the proposed gate in this 3ion and MS disease is selected as a case study for evaluating the proposed gate. We selected MS disease because of this illness the center of enormous studies now. There are considerable published researches on the list of effective MicroRNA biomarkers [8–12] for this disease that can be used as a case study for the proposed gates.

The suggested DNA gate system consists of four important components:

• The first section is the input strands of the system. These strands are chosen based on the highly-cited published papers on MS diagnosis that presented a suite of MicroRNAs that their expression pattern has a great impact on this disease [8–12]. Table 1 shows the list of identified miRNAs for MS disease that are addressed in many related papers [8–12]. Table 1 lists the 22 miRNAs found to be expressed at higher or lower levels. Column miRNA in this table shows the name of the microRNA and column expression change represents the risky range of the microRNAs for detecting the MS. Some microRNAs have up-expression in a risky situation while others have down-expression.

• The next important part of the proposed system is the gate strand that is the computation engine of the system. The gate must be designed in such a way that it can identify a large number of inputs consists of up and down-regulated strands with various thresholds. In our design, the miRNAs that are up-expression react directly to the gate while the down-expression miRNAs are reactive with auxiliary strands (the third part of the system) at first the result of this step reacts to the gate. Eventually, the main gate releases a fluorescent strand at the output, if all conditions were provided.

• The other part of the system is an auxiliary strand for detecting the changes in the down-expression miRNAs.

• Finally, the fourth part is output strands. A photo-chemically activated fluorescence strand is used to display the output of the DNA logic gate. The main advantage of using fluorescence in the output is that its detection is simple, low cost, and high sensitivity.

Table 1.

Details of identified miRNAs for MS disease [8] to [12]

miRNA	Expression change	miRNA	Expression change
Hsa-let-7a-5p	UP	Hsa-miR-7-1-3p	DOWN
Hsa-let-7b-5p	UP	Hsa-miR-27a-5p	DOWN
Hsa-miR-16-5p	UP	Hsa-miR-29a-3p	DOWN
Hsa-miR-16-2-3p	UP	Hsa-miR-29c-3p	DOWN
Hsa-miR-342-5p	UP	Hsa-miR-95	DOWN
Hsa-miR-346	UP	Hsa-miR-149-5p	DOWN
Hsa-miR-518b	UP	Hsa-miR-423-5p	DOWN
Hsa-miR-760	UP	Hsa-miR-874	DOWN
Hsa-miR-22-5p	UP	Hsa-miR-20a-5p	DOWN
Hsa-miR-125b-5p	UP	Hsa-miR-151a-3p	DOWN
Hsa-miR-629-5p	UP	Hsa-miR-100-5p	UP

The details of the gate and its internal operation will be explained in the following subsections.

Structure of the proposed gate

In this subsection, the logical DNA-based gate is proposed without the need for auxiliary inputs [25]. In this gate, the reaction is performed directly between the input strands and the gate strand. It should be noted that the design of this gate does not depend on the structure of the input strand and it can use any miRNA as an input. Therefore, detecting microRNA types have not any impact on the gate structure. Moreover, the mentioned gate design method can be easily extended to design multi-input gates because its operation does not force any limitation on input miRNAs. Figure 8 shows the 2-input gate and the process of its reactions. In this gate, our inputs are miR-1 and miR-2. First, the miR-1 reacts with the isolated strand from the gate (in the next section, this reaction is more accurately investigated). Then, miR-2 reacts with the lower strand of the gate and releases the upper strand. This released sub-strand is the final output. This sub-strand is attached to fluorescent, which is activated by separating from the lower string. Therefore, the fluorescent is generated when the output strand is generated. Figure 8 sows a 2-input AND gate in the proposed structure.

Fig. 8.

The 2-input gate and its reactions. a The gate strand. b Reaction between miR-1 and the gate strand. c Reaction between miR-2 and strand of previous reaction output

In this system, when miR-1 entered the system, it joins to the upper part of the gate strand (i.e. $\sim M1T.\sim M1B1.\sim M1B2$) and separates the double-strand M1 from the gate strand. The main point is that the sub-strand M2T is also separated from the gate by splitting the M1 from it because it does not connect to the rest of the gate. These reactions are shown in Fig. 8b. By adding the second input (e.g. M2), it joined with $\sim M2T$ and generated the double-strand M2 that results in the output strands (Fig. 8c). Consequently, the output strand is generated when both inputs (M1 and M2) exist in the system.

Figure 9 shows the generalized structure of k-input gate. Figure 9 represents a gate with the k-input of miRNAs (e.g. MIR1 to MIRK).

Fig. 9.

The structure of proposed gate [25]

In Fig. 9, each input strand consists of 3 parts. The beginning and ending segments ($MIRi-A$ and $MIRi-C$; $1\le i\le k$) each have 6 nucleotides that are the toeholds of the input. The reaction always starts with the left side toehold ($MIRi-A$) of the input strand. Then it goes through the middle sub-strand ($MIRi-B$) and ends with the right side toehold ($MIRi-C$).

When $miR-1$ entered into the system, it joins to the upper part of the gate strand (i.e. $\sim MIR1A.\sim MIR1B.\sim MIR1C$) and separates the double-strand MIR1 from the gate strand. Figure 10 shows the process of this reaction. In this figure, the K-input gate and the first input (i.e. $miR-1$) are displayed. At the beginning of the reaction, the sub-strand MIR1A and $\sim MIR1A$ join together. Then MIR1B and MIR1C are matched with $\sim MIR1B$ and $\sim MIR1C$, respectively. In the end, the first input separates the upper sub-strand from the gate. As mentioned before, sub-strand MIR2A is also separated from the gate by splitting the MIR1 from it. In the existence of the second input (e.g. MIR2), it joined with $\sim MIR2B$ and $\sim MIR2C$ and generates the double-strand MIR2. Moreover, splitting the double-strand MIR2 from the gate strand also separates the sub-strand MIR3A. This process is performed when all inputs exist in the environment. Consequently, the output strand is generated when all k inputs (i.e. $MIR1,MIR2,\cdots ,MIRK$) exist in the system.

Fig. 10.

Steps of reacting miR-1 and the proposed K-input gate

In the proposed gate design, the auxiliary inputs and corresponding gates are removed. Therefore, this design style reduces the gate complexity and strands significantly. Moreover, this gate can be easily extended to larger input gates for real applications.

Multi-threshold microRNA detection

As mentioned before, we proposed a design methodology for multi-threshold and multi-input DNA-based logic gates in live mammalian cells [25]. This design style simultaneously recognizes multiple miRNAs with different rising and falling thresholds. It is noting that the inputs have different thresholds to detect the risky pattern of renal disease and the safe expression levels of the various miRNAs are very different. Even, this level on a specific miRNA may be different for each person. Therefore, considering the existence or absence of a miRNA (binary logic) and ignoring them would be misleading. The threshold should be considered for various diseases or patients. In the paper, [25] an example of the required gates in cancer detection is explained. Each miRNA may have a different maximum and minimum threshold value. It uses High Risky Range and Low Risky range for the situations that high-expression and low-expression of microRNA show the risky condition, respectively. High risky ranges (HRR) are shown in red color and low risky ranges (LRR).

MicroRNA biomarkers may have a down threshold were decreasing the expression means potentiality of disease. Therefore, we suggested a mechanism to detect the down-regulated MicroRNA biomarkers. We called this mechanism a two-step detection in this paper. The main concept of this method has been used in other research too [18]. Figure 11 shows this detection method. In this figure, a down-regulated strand is shown as an inhibitor of a reaction. When the concentration of this strand is in the normal range (NR), it reacts with the complementary strand. Otherwise, in the first step, the complement strand of input miRNA reacts with the input sample. After a while, if this strand (complement of input strand) is still presented with a certain concentration in the environment, it means that the value of the input strand has been low. Therefore, in the next step, we recognize the complementary strand with our gate.

Fig. 11.

The “two-step detection” method

The proposed system for MS

We selected the most effective 6 miRNA strands from Table 1 that are highly are cited as the biomarker of MS disease. They are Let-7a, miR-22, miR-125b, miR-629, miR-16-2, miR-100, miR-342, miR-346, miR-518b, miR-760, miR-16, miR-27a, miR-29, miR-95, miR-149, and miR-20a. These strands are mostly-mentioned biomarkers of MS disease which the last five strands are down that decrease in the event of MS disease and the rest are up. These DNA/RNA strands are our system inputs. The up-expression strands react directly to the gate to generate the output strands. However, the down-expression strands react during the “two-step detection” process and the result of this step reacts to the main gate. Finally, if all of the above conditions are met, the main gate output will indicate the pattern of the projected biomarkers of the MS disease.

Analytical discussion

In this section, we want to evaluate the proposed method and compare it with the methods in [17, 21, 25] and [22] to determine the difference between these methods and express the advantages of the proposed method. Moreover, this section will analyze why the proposed method is better than other methods. it is explained why the results of our experiments are better than other methods.

The designed gate of [21] has been described in Section II of this article. In both methods ( [25] and [21]), the first reaction begins with the first toehold of the left side of the first input with the free toehold of the gate strand. This reaction is started by pairing the first input and its complement in the up-strand of the gate. Figure 12 shows this reaction in both gates. The first difference between the proposed gate and the gate [21] is This reaction. The reaction of the proposed gate causes the sub-strand to be split up and paired with the input strand (The reaction output is a double strand). But the gate reaction [21] causes the input strand to be connected to the gate (The reaction output is a single strand). Therefore, in the proposed gate, the interest (e.g. probability) of backward reactions is diminished considerably. The second reaction is the same for both gates. In this way, the compliment toehold of the second input will be released. Then the second input strand reacts with the gate and the result of this reaction will release the output strand.

Fig. 12.

The first reaction steps of AND gates [25] and [21]. a The reaction process of proposed gate [25] . b The reaction process of gate [21]

The final output of the reaction (Fig. 12a) tends to separate and reacts with the gate due to having a free toehold. Figure 12b is more reversible because the released strand is single. Therefore, this strand tends to react again with the gate strand more than the double-strand (the reaction output of the proposed gate). The authors of the paper [21] have noted that this reversibility is a gate advantage. In the absence of a second input in the environment, the reversible reaction prevents consuming the first input. However, in the presence of the second input, this reversibility will also cause an obstacle in the release of the output. In this research, a solution has been considered to reduce the negative effect of this reaction (unwanted reaction). In the proposed system, the sink strand reacts to the upper strand after separating the paired strand. This reaction is shown in Fig. 13. The sink strand is defined in a way that does not react to the gate. By reducing the rate of reversibility, the speed and accuracy of the proposed gate reaction are far better than [21].

Fig. 13.

How the sink strand reacts to intermediate strands

As mentioned before, the gates of [17] and [22] have the same structure with a slight difference. There is a common toehold between the first and second part of the structure of these gates. This common toehold ensures that if both inputs are present, the gate will be released the output. There is not the same toehold in the input strands. So there should be an extra step to produce the same toehold. The proposed structure does not need the same toehold. As a result, our design will be simpler, more expandable, faster, and more accurate.

In addition to all of these advantages, the proposed system provides a solution for detecting miRNAs with different thresholds. These miRNAs may have up-expression or down-expression (i.e. in illnesses the expression level is an increase or decrease). This mode brings us closer to the concept of personalized medicine. In the next section, simulation results and probabilistic analysis of all these schemes are presented. The results show that the proposed method [21] is the best among the existing methods.

Experimental results

In this section, the suggested gate design model is implemented and compared with the recent samples ( [17, 21, 22] and [25]). We modeled these in DSD language and simulated them with Microsoft Visual-DSD tool that is a well-known academic simulator for DNA strand displacement simulation [26, 27]. Visual-DSD is responsible for simulating the reactions that occurred between the DNA strands and generates suitable results such as reaction time and concentration of output strands. It is worth noting that Visual-DSD can be used to simulate DNA and RNA strands because the laws of the reaction of DNA and RNA strands are the same and their structure is different in only one nucleotide.

In all simulations, the concentration of 70nM is considered as the minimum permissible concentration for logic ‘1’ of input, and the concentration of 30nM is assumed as the maximum allowed concentration for logic ‘0’. In the following subsections, the reaction time of the implemented gates with the proposed method will be compared and analyzed with other gates. Also, the probability of reversibility of the reactions will be investigated. Reversibility, in addition to decreasing speed, affects the accuracy of output measurement (final concentration of output). Because it does not allow the whole input concentration to react with the gate and release the output strand. This will increase the output error rate.

PRISM (probabilistic model checker) [28] is a tool developed at the Universities of Birmingham and Oxford. It can be used to evaluate the merits of contrasting design decisions. Checking a probabilistic model is a verification technique. The Prism tool supports various types of probabilistic models. We use the PRISM, attendant the DSD language, to design and analyze DNA strand displacement and to investigate their kinetics [29].

Visual-DSD can export the reaction network to be sent out as a model that can be loaded into the PRISM for verification. All of the models discussed in this paper were analyzed using PRISM. For a better comparison and review of these methods, the continuation of the section is divided into two sub-sections. The first sub-section examines the timing of the reactions in the simulator with the probabilistic analysis of the production output of each method. In the next sub-section, we will see the probability analysis of the reverse reactions.

Response time

Response time of a logic gate can be defined as the time that is required to reach the output concentration over/under the threshold value corresponding with the final logic. As described before, we defined the 70nM in this paper as the concentration level for logic ‘1’.

2-input gates

In this sub-section, we want to compare the introduced gates in 2-input mode. The reason is that the previously presented structures have been two inputs. Therefore, the most accurate comparison is for their original state. In this study, we simulated the proposed 2-input gate, the gate [17], the gate [21], and [22] in the Visual-DSD tool. In these simulations, we assume maximum concentrations for inputs of 100nM and 1000nM for gates. Figure 14 shows the code of these gates in visual-DSD.

Fig. 14.

The Visual-DSD codes of 2-input gates. a 2-input AND gate [25]. b 2-input AND gate [17]. c 2-input AND gate [22]. d 2-input AND gate [21]

Figure 14 shows one of the 2-input gates of [25, 17, 22] and [21]. Each of these codes has three parts. In the first section, concentrations and reaction speed are defined. The inputs, the extra strands, and gate strand are defined in the ‘definition of variables and strands’ parts of each code. The second part is the code variables (format of strands) and the last part of the code is the definition of the strands. Also, the output of the gate has been selected for building the concentration graph. The simulation result of these gates is presented in Fig. 15. In this figure, the red graph is a result of the proposed gate in [25]. The gate diagram of [21] is displayed in green and it is the best answer after the proposed gate. The next two graphs (blue and yellow) are related to the gates [17] and [22]. These gates have lower speed and accuracy (output concentration) than the [17] and [22] due to more complexity.

Fig. 15.

Output concentration of attempted 2-input AND gates. a The simulation result of proposed gate in [25]. b The gate diagram of [21]. c the simulation of gate [17]. d the gates [22]

Figure 15 shows that the delay in the proposed model is better than the others. The reason is that our gate is the simplest and the minimum number of reactions is required to generate the output strand. Also, we have taken another output of the Visual-DSD. This output is a code that can be used in PRISM. The goal is to obtain the probability of generating the output of each gate during the reaction time. This probability chart can confirm the results of the Visual-DSD. A high probability indicates a greater willingness to react and more quickly. Figure 16 shows the probability of output generation over time.

Fig. 16.

Probabilistic diagrams for outputting two-input gate. a 2-input AND gate [25]. b 2-input AND gate [21]. c 2-input AND gate [22]

The probability diagram of the proposed gate is in Fig. 16a and the gate diagram of [21] are in Fig. 16b. The graph of Fig. 16c shows the probability of the reaction of the gate [22]. Gate [22] is the latest version of the gate [17], so the probabilistic investigation of one of them is enough.

These graphs start at zero and quickly reach the maximum possible value. The reason for this incident is that at the beginning of the reactions, the concentrations of inputs are high and the probability of the reaction will be maximized. Over time, the concentration of inputs will be reduced. As a result, the probability of reactions is reduced until it reaches its minimum.

As shown in the diagram, the probability of reaction [22] is less than the other two gates. The proposed gates of [21] and [25] have the most probable response. The probability of a reaction in these gates (in the case of high input concentrations) is approximately equal to 1. While the most probability of [22] is a bit more than 0.75. Even if the concentrations of inputs are low, the conditions of [21] and [25] are better than the [22]. That’s why their simulation results are better than [22].

The graphs of [21] and [25] are similar. The reason for this similarity is discussed in Section IV. The structures of these two gates are similar; Both models use a similar way to solve the problem of the absence of the same toehold in the inputs (miRNAs). The same toehold ensures that the output is generated only if all inputs are present. In the two models ([21] and [25]), the structure of the gate has changed instead of using the additional gates of [22] (The production of the middle-strand with the same toehold). In these structures, an additional toehold is connected to each upper sub-strand of the gate that does the same (refer to section IV). However, there are differences in these two models ([21] and [25]) that affect the reverse reactions and simulation results. Then it is better to check the probability of reverse reactions to compare these two models (in the next sub-section).

Multi-input gates

In this sub-section, we will examine which method is better in terms of expanding the number of inputs. As mentioned in section II, there are two methods for extending the Deiters’ gate [17]. The two-input gates are used to construct a larger gate (Fig. 4) as the first method. In the second method, the gate structure of the two-input is taken and the larger gates are constructed (Fig. 5). We can also use the same two methods on the proposed structure [25]. In this sub-section, four three-input gates are designed with these methods. These four gates are constructed according to the first and second methods for the gate [17] and for the gate, [25]. These gates are simulated in the Visual-DSD tool. Figure 17 shows concentration graphs on the time of these gates. In these graphs, one can compare the speed (when the output concentration reaches ‘1’) and the accuracy (final gate concentration) of the gate.

Fig. 17.

Output concentration of 3-input AND gates. a The simulation result of three-input gate in [25] made by two-input gates. b The three-input gate diagram of [25]. c the simulation of three-input gate [17] constructed with two-input gates. d the three-input gates [17]

In Fig. 17, the 3-input gate [17] constructed with two-input gates is red-dot, yellow is the three-input gate [17], the three-input gate [25] is blue, and green graph is the 3-input gate [25] made by two-input gates. The green graph has a less reversible reaction than the blue diagram gate. That’s why it has the best result in the three-input gates. In total, the three-input gates [25] are better than the gates [17]. As a result, this method is suitable for the construction of the larger gates.

High fan-in gats (16-input as a case study)

We implemented a logical 16-input system with both method [17] and [25] to detect these inputs: Let-7a, miR-22, miR-125b, miR-629, miR-16-2, miR-100, miR-342, miR-346, miR-518b, miR-760, miR-16, miR-27a, miR-29, miR-95, miR-149, and miR-20. These miRNAs are selected from Table 1. This gate is designed to diagnose MS. However, all the 2, 4, 8, and 16-input gates are simulated to make a better comparison. The detailed value of delays is shown in Tables 2, 3, 4 and 5 for clear comparison and understanding of speed. Row T70% shows the required time to reach the concentration of the output strand to 70% of the final concentration level. This parameter is compared among other gates.

Table 2.

Quantitative comparison in terms of response time between the 2-input gates

Delay	2-input dieters gate	2-input proposed gate
$T_{70\%}$	105.9	54.98
Improvnents	48.6%

Table 3.

Quantitative comparison in terms of response time between the 4-input gates

Delay	4-input dieters gate	4-input proposed gate
$T_{70\%}$	225.9	102.99
Improvnents	55.07%

Table 4.

Quantitative comparison in terms of response time between the 8-input gates

Delay	8-input dieters gate	8-input proposed gate
$T_{70\%}$	4999	1299
Improvnents	57.6%

Table 5.

Quantitative comparison in terms of response time between the 16-input gates

Delay	2-input dieters gate	2-input proposed gate
$T_{70\%}$	31368	18999
Improvnents	39.43%

The results show that the delay of the proposed model is the smallest. The reason is that our gate is the simplest and the minimum number of reactions is required to generate the output strand.

Noise margin analysis

In a digital circuit, noise margin is defined as the amount of change in the absolute value of signals that can be tolerated for logic ‘0’ or ‘1’. This parameter shows the robustness of the output logic values against environmental noises. We evaluated the noise margin of the proposed method in this subsection.

Figure 16 compares the output concentration of 16-input AND gate of Hemphil & Deiters with the proposed method for Input = “11”. In Fig. 18, Red curve represents the proposed system and the green curve represents the concentration of the output strand of [17]. The concentration level of the proposed method almost is higher than the Deiters method. The threshold concentration of logic ‘1’ is 700nM and the concentration corresponding with the logic ‘0’ is less than 300nM.

Fig. 18.

The logical 16-input DNA gate. a The diagram of output concentration of [25]. B The concentration of the output strand of [17]

Sensitivity and Specificity are among the most important criteria for testing diagnostic procedures. Sensitivity means the true positive rate or probability of detection. For example, it is the percentage of sick people who are correctly identified. Specificity also means the true negative rate. For example, it is the percentage of healthy people who are correctly identified. Noise margin determines how reliable the output is produced (Even if an error has occurred). If the range of zero and one are close together, the noise margin will be reduced and the sensor may easily detect the false signal. Our sensors have a good noise margin. So they have a high sensitivity and specificity.

Analyze the reversible reactions

A reverse reaction is an unwanted reaction that occurs during DNA computation. This reaction prevents the process of progress and diminishes the concentration of released output strands. Therefore, reverse reactions increase delay and affect the accuracy of the output. The probability of reverse reaction is evaluated in this paper to analyze the correctness and speed of the proposed gate in a deep biochemical view. This analysis is done with the PRISM tool. The probability diagram of the reverse reaction along with the probability diagram of output release confirms the results of the Visual-DSD tool.

The graphs of Fig. 19 provide the probability of reverse reactions of gates [21, 22] and [25]. These graphs start at zero and climb quickly. The climb speed indicates which reverse reactions are made earlier ( the reactions of this gate are more likely to return). With the passage of time and decreasing the number of reactions, the probability of the reverse reaction is also reduced to the minimum. Lower minimum probability means the gate is better.

Fig. 19.

The reverse reaction probabilistic diagram of 2-input gates. a 2-input AND gate [22]. b 2-input AND gate [25]. C 2-input AND gate [21]

The reactions of the two-input Deiters’ gate ( [17] and [22]) are not reversible. The Visual-DSD tool shows it well. The PRISM diagram also confirms this. Figure 19a shows the diagram of Deiters’ reverse reaction. The graph of this gate shows that the probability of a reverse reaction is very low. This probability at the highest point is less than 0.1. It can be said that the reactions of this gate are one-sided. However, the output release probability of this gate is low (it comes in the previous sub-section). So, Deiters’ gate [22] has slower than the others.

The reverse reaction probabilistic diagrams of [25] and [21] are shown in Fig. 19b, c. As seen in the previous section, the output release probability of the gate [21] and [25] is similar. However, the first reaction to these gates is different (Section IV). The reaction type of the proposed gate reduces the tendency to return the reaction. Also, in the proposed gate, the sink strands prevent the return of the reactions. These differences affect the probability of the reverse reactions. The probability of the reverse reaction [25] is less than [21]. The reverse reaction probability of the proposed gate [25] is less than 0.6, but this probability of [21] is greater than 0.6. Also, the climb speed on Fig. 19b is more than the Fig. 19c. This indicates a greater tendency to return the reaction. This tendency affects the speed of output generation and the accuracy of the final diagnosis. This is why the simulation results of the proposed gate [25] is better than [21].

Conclusion

Early detection of MS disease is very impacting on the life quality and cost of treatment. Recent studies have shown that microRNAs can be used as promising biomarkers to detect many diseases at the early stages. DNA logic gates are used to detect the MicroRNA expression level that is more accurate and faster than previous methods but the addressed methods face serious challenges such as the complexity and cost of the DNA gates. These current methods mostly were general-purpose and cannot be extended to identify a large number of inputs for diagnosing various diseases. We proposed the DNA-based diagnosis system in response to specific microRNA (miRNA) inputs [25]. We suggest a new design style to resolve the problems of the current method. We used the experiences of the logic design in the computer science area to develop a scalable method for early detection. Due to the simplicity and reduction of the number of strands, this design model has reduced the complexity and cost of designing and manufacturing the diagnostic system. In this paper, we used the structure presented in [25]. Our goal was to test the proposed method for MS disease and mathematical analysis of the proposed method. The simulation results demonstrate the efficiency and speed of our proposed method. Results of mathematical analysis verify the results of the Visual-DSD tool and it assures us that the conclusions made in the article are correct [25].

Conflict of interest

The authors declares that they have no conflict of interest.

Ethical approval

All applicable international, national, and/or institutional guidelines for the care and use of animals were followed.

Human and animal rights

This article does not contain any studies with human participants performed by any of the authors.