Introduction. Nucleic acid amplification is a valuable molecular tool not only in fundamental research, but also in applied areas, such as the diagnosis of infectious diseases, hereditary pathologies, establishing kinship, etc. Currently, amplification methods are intensively developing, and their application areas are expanding. The most popular and most frequently used amplification method is polymerase chain reaction (PCR) [1]. PCR is a reaction that takes place under three different temperature conditions: denaturation (95°C), annealing of primers (from 50° to 60°C), elongation (72°C). To quickly change these modes, a special device is needed — a DNA thermocycler [2]. At this, temperature variation in the amplifier does not occur instantly, but starts only when the desired temperature is reached, and this causes artificial containment of the reaction. As a rule, the duration of PCR is 1–1.5 hours.

The second most popular amplification method is loop-mediated isothermal amplification (LAMP) [3]. A water bath or thermostat is sufficient for LAMP, since the reaction takes place at one and the same temperature, and the first results can be seen in 15 minutes.

For both LAMP and any other type of amplification, the key component is primers, which are short sequences of nucleic acid. They serve as a starting point for increasing copies of a specific region of DNA. It is the primers that determine which DNA sequence will be copied.

The main difference of LAMP implementation is the number of primers. For a conventional LAMP, at least four primers are required (two external, two internal), while for a conventional PCR, two are sufficient (direct, reverse).

To increase the specificity and accuracy of the reaction, it is important to select the right primers. For the automatic selection of primers for PCR, more than 150 different computer programs have been developed that provide the selection of primers for any modifications of this reaction [4]. However, there are very few such programs for LAMP, no more than ten, and only two of them are available online. These programs also have a number of disadvantages, such as restrictions on the length of the analyzed sequence; they do not exclude the possibility of formation of homo- and heterodimers of primers, repeats of nucleotides in one primer. And none of the programs take into account the close arrangement of primers in one set, which, in turn, reduces the quality of primers and the accuracy of reaction results [5].

Thus, an urgent task is to develop a new computer program to select (model) high-quality sets of primers for LAMP with tougher conditions for choosing primers for nucleotide sequences of any length.

Materials and Methods. The authors of [3] proposed using two external, F3 (Forward), B3 (Backward), and two internal primers, FIP (Forward Inner Primer), BIP (Backward Inner Primer). It was assumed that the internal primers had double length (FIP: F1c/F2, BIP: B1c/B2) and were annealed at four regions of the nucleotide sequence. Schematically, the location of LAMP primers can be seen in Figure 1.

External primers are only needed at the initial stage. They are designed to limit the analyzed region of the nucleotide sequence and form a single-stranded structure of this region. A pair of internal primers, F1c and B1c, start their work already at the second stage, as they are annealed after the formation of new DNA chains.

Later, the same authors proposed a modified method offering the use of not four, but six primers, annealed already at eight regions of the target nucleotide sequence [7]. It was proposed to add two more loop primers (Loop B, Loop F), which should react at the third stage after the formation of a dumbbell-like DNA structure and anneal between regions F1/F2 and B1/B2, respectively. The use of additional primers implies an increase in sensitivity and reliability of the reaction.

Any amplification reaction has its own sensitivity threshold, and the spread of this indicator is very large due to the fact that numerous factors affect the course of both PCR and LAMP. Some papers have noted that LAMP is significantly more sensitive than PCR. The authors of [8], e.g., claim that LAMP is 10 times more sensitive than PCR. The authors of other studies have found that LAMP is 100 times more sensitive than PCR [9], and in some investigations, this indicator reaches 1,000 times [10].

In addition to sensitivity, any amplification reaction has another equally important indicator — its specificity. And here, questions have recently begun to arise about the LAMP method [11], including due to the emergence of the so-called primer homo- and heterodimers, which are more difficult to exclude in this reaction than in PCR, because of the larger number of primers used and their increased length [12].

For successful amplification, it is necessary to select the right primers. When using the LAMP method, the main difficulty is in modeling primers with account for all recommended conditions, namely:

Table 1 provides brief characteristics and features of the most popular LAMP primer design programs [5].

The design of primers for LAMP is a very difficult task and requires the development of a special computer program with proper functionality, taking into account all recommended conditions, and with the possibility of an extended selection of primers and a user-friendly interface.

The computer program for primer design is developed in the Python programming language. This language has the bioPython library, which allows working with nucleotide sequences, as well as the Qt framework for interface development.

Research Results. With account for the structural features of nucleotide sequences and the criteria for selecting LAMP primers, a modification of the direct sampling method using a stencil approach has been proposed. It considers the GC composition, the annealing temperature of the primers, and reducing the complexity of the sampling.

As is known, the GC composition of primers should be in the range from 40 to 60%. This is one of the important criteria for selecting LAMP primers, which depends on the sequence being analyzed, the length of the primer, and it partially affects the annealing temperature (Тm, °С).

In this paper, the following formula is used to calculate the annealing temperature of primers:

(1)

where [Na+] — molar concentration of sodium ions; (%G + %C) — GC composition in the analyzed sequence, expressed as a percentage; L — length of the primer. It was based on a well-known dependence:

(2)1

Formula (1) was selected empirically, the calculated values were compared to the values obtained through the convenient OligoAnalyzer2 utility, which provided a high-quality selection of primers for all types of nucleotide acid amplification. Through determining the length of the primers, GC composition and annealing temperature, all possible primers can be found in a nucleotide sequence of any length that will meet the specified criteria.

If we imagine the primer as a substring, and the analyzed nucleotide sequence as a longer string, this task can be represented as a search of all possible options (direct search), but complicating it through calculating the GC composition and annealing temperature of the primers.

Figure 2 shows a complete block diagram of the direct search algorithm, taking into account:

The total complexity of the modified algorithm in the worst case is O(m×n), where n — length of the primer, m — length of the nucleotide sequence. It should be understood that the running time of the algorithm directly depends on how often the nucleotide fragments that meet the requirements are found.

Table 2 shows the search data for all possible primers in nucleotide sequences of different structures over time.

Further, it is necessary to form sets from all the primers found, taking into account the close distance between the primers, the heterodimeric properties in one set, as well as the minimum temperature difference between the annealing of the primers.

The design scheme for forming primers into the LAMP sets is shown in Figure 3.

At the input, the program reads the nucleotide sequence, either the desired file is loaded, or a fragment is inserted through the clipboard. Next, configurations are set, such as primer length, GC composition, primer annealing temperature, and temperature difference in one set. Then, all possible parameters satisfying the set configurations are searched, the selected primers are sorted into sets and displayed to the user.

The operation of the computer program:

If all of the above conditions are met, the set is considered to be working.

The LAMP program is registered in the Register of Computer Programs under the name LAMPrimers iQ, No. 2022617417 on April 20, 2022, and LAMPrimers iQ-loop, No. 2023662840 on June 14, 2023. The program code is publicly available3.

The developed software product has a user-friendly and intuitive interface, which can be used directly by end users — experimenters engaged in LAMP.

Discussion and Conclusion. The number of primer sets issued depends on the specified search parameters. The stricter the parameters, the fewer sets will be found. In case of hard restrictions, the program may not output a single set. The number of primer sets with different selection parameters for the genome of the bacteriophage lambda [13], whose length is ~48,500 nucleotides, is shown in Table 3.

For relatively short nucleotide sequences (up to 2,000 nucleotides), the selection of primers takes less than a second. With increasing sequence length, the duration of the primer search grows exponentially.

Figure 4 shows the effect of the length of the nucleotide sequence on the duration of the selection of primer sets. The data for the nucleotide sequence of the bacteriophage lambda on a laptop with the parameters are as follows: Intel(R) Core(TM) i7-10750H CPU, 2.60GHz, 6 cores. 16 GB RAM. The parameters of the soft selection of primers are indicated (40–60 % GC, ΔTm = 5, length of the analyzed region is up to 300 bp).

It should be noted that the duration of the search for primers depends on the power of the computer.

To compare and determine the quality of the simulated primer sets, a number of field experiments were conducted to detect the RNA of the SARS-CoV-2 coronavirus, whose length was ~ 30,000 nucleotides. To do this, sets of LAMP primers were selected for the same region of the nucleotide sequence of the coronavirus using the LAMPrimers iQ program and two popular and accessible online utilities from New England Biolabs (NEB LAMP)4 and PrimerExplorer5. The designations L, N and P correspond to the sets of primers LAMPrimers iQ, NEB LAMP Primer Design and PrimerExplorer; “+” — samples contained RNA of SARS-CoV-2 coronavirus, “–” — samples did not contain nucleic acids. Figure 5 shows the curves of this experiment.

The primers obtained through PrimerExplorer, showed the latest rise in amplification curves (P+) compared to NEB LAMP (N+) and LAMPrimers iQ (L+). The primers obtained through LAMPrimers iQ, provided a later rise in the amplification curves (L+) compared to (N+). However, samples that did not contain virus RNA (P–), showed a later rise compared to the set (N–), while (L–) showed no rises even after 50 minutes, thereby providing the highest reliability of viral RNA detection.

The performed experiments showed a higher accuracy and specificity of the primer sets selected through LAMPrimers iQ computer program, caused by a decrease in the reaction rate with negative control samples. The amplification curves had later rises, or did not have them at all, even after 50 minutes of reaction time.

1. Oligo Calc: Oligonucleotide Properties Calculator. URL: http://biotools.nubic.northwestern.edu/OligoCalc.html (accessed: 10.12.2023). 2. OligoAnalyzer™ Tool. URL: https://eu.idtdna.com/pages/tools/oligoanalyzer?returnurl=%2Fcalc%2Fanalyzer (accessed: 10.12.2023). 3. LAMPrimers-IQ. URL: https://github.com/Restily/LAMPrimers-iQ/blob/main/lamp/start_lamp.py (accessed: 10.12.2023). 4. NEB LAMP Primer Design Tool. URL: https://lamp.neb.com/#!/ (accessed: 24.11.2023). 5. LAMP primer designing software Primer Explorer. URL: http://primerexplorer.jp/e (accessed: 25.11.2023).