Team:Moscow/Model

Team:Moscow/Model - 2020.igem.org

Modeling

Overview

We started our project by inventing the detection system for viruses’ genotypes that have medical significance, thus, we needed to choose a target sequence. Firstly, we chose SARS-CoV-2 and started a list of SNPs for it. We worked through the literature about SARS-CoV-2 mutations and the division of the virus into clades. Based on the literature, we have compiled a table of SNPs. We used Benchling to map SNPs to sequences and find potential PAMs. Then, taking into consideration the experts' feedback that we got during the Human Practices work, our project switched to HCV. So, we made our own alignment of 17 genomes belonging to the most common genetic variants of HCV and selected SNPs. Finally, we created a detailed kinetic model to ensure system performance, optimal conditions, reaction time, and potential sensitivity.

SNPs research

Sars-CoV-2

In the spring of 2020, against the background of a general pandemic, we noticed that the virus is separeted into several genetic variants and its mutations can affect the severity of the disease, the development of drug resistance or the likelihood of re-infection. Different sources[1]-[4] represent slightly different trees of genetic variants. We relied on the clades presented on GISAID[5][6] . Clustering all genomes clearly highlights the five major phylogenetic groups G, GH, GR, S, and V and their characterizing mutations. Lineage “L” is corresponding to the reference genome. A general group for other sequences not matching any of criteria (e.g., other alleles or combinations) is defined as “O” clade[7].

From the very beginning, some mutations seemed suspicious. The mutation D614G of the Spike protein (a G-to-A base change at position 23,403 in the Wuhan reference strain.It was referred to as the “G” clade ), is suspected in increasing of the SARS-Cov-2 spread [8][9]. The teams of scientists from over the world used different pseudovirus systems and tested them on various kinds of cell, but the experiments pointed to the same conclusion: viruses carrying the G mutation infected cells much more ably than did D viruses — up to ten times more efficiently, in some cases [10].

There is a lot of discussion around another mutation - C14408T (results in an RNA-dependent RNA polymerase “RdRp”). Some authors suspect it as a possible drug-resistance mutation [11][12].

Also, there is a case of re-infection [13].

But, these studies come with many caveats — and their relevance to human infections is unclear. We want to repeat the words of one of the Nathan Grubaugh, a viral epidemiologist at the Yale School of Public Health in New Haven, Connecticut: “What’s irritating are people taking their results in very controlled settings, and saying this means something for the pandemic. That, we are so far away from knowing”[14].

Table1. The SNPs of Sars-CoV-2 virus
Position Nucleotide Haplotype
8782 C L
8782 T S
28144 T L
28144 C S
3037 T G
3037 T GH
3037 T GR
14408 T G
14408 T GH
14408 T GR
23403 G G
23403 G GH
23403 G GR
25563 T GH
28881 AAC GR
11083 T V
26144 T V
3037 C L
14408 C L
23403 A L
25563 G L
28881 GGG L
11083 G L
26144 G L

HCV

Based on sequence divergence hepatitis C virus (HCV) is currently classified into 8 major genotypes or clades (from 1 to 8) with more than 70 confirmed or presumed subtypes identified. HCV genotype determination is important for clinical management of chronic HCV infection. It is known that depending on genotype treatment response and optimal duration of treatment with existing anti-HCV combination therapy (pegylated alpha interferon and ribavirin) differ significantly. In general, HCV genotypes 1 and 4 are less likely to respond to current anti-HCV therapy and typically require a longer treatment than genotypes 2 and 3[15][16].

In Russia four genetic variants of HCV are common[17][18][19]:

  • 1b - tendency to chronicity of the process in 90% of cases, severe course;
  • 3 - the transition to the chronic form occurs in 33-50% of cases;
  • 1a - chronization of the process occurs in 33–50% of cases;
  • 2 - chronic infection in 33-50% of cases.

Some of the mutations may have clinical significance. Amino acid substitution C316N in the NS5B region is associated with direct anti-viral agents resistance[20]. Mutations in the V3 domain of a NS5A protein can have a contribution to Interferon resistance[21][22]. NS3 polymorphism also impacts response to antiviral specific treatment[23]. Polymorphisms in E2 protein may also play a role[24]. Sequencing of the hepatitis C virus genome showed that a recombinant HCV variant RF2k/1b circulates in Russia. RF2k/1b genotupe’s genome contains some genes inherent in HCV genotype 2 and part of genes from subtype 1b[25].

Description of how the alignment was done:

To determine the single nucleotide mismatches for the hepatitis C virus (HCV) genotypes in a representative way, we built an alignment of different genotypes.

Sequences for each major subtype were selected from the GenBank database for analysis. Altogether we analyzed sequences for 17 different hepatitis C virus genotypes that were downloaded from the GenBank database. Only the subtypes with the whole genome sequenced were used for the alignment. Interestingly, the genotype 2c stands out from other representatives.

Here are the links to the sequences used for the alignment: Genotype 1b EF032892
Genotype 1aM67463
Genotype 2m JX227968.1
Genotype 2c JX227966.1
Genotype 2k JX227953.1
Genotype 2b AF238486.1
Genotype 2a KF676351.1
Genotype 3 D49374
Genotype 4 FJ839870.1
Genotype 5 NC_009826.1
Genotype 6i DQ835770
Genotype 6v EU798760
Genotype 6k DQ278891
Genotype 6c EF424629
Genotype 6j DQ835769
Genotype 6p EF424626
Genotype 6f DQ835764

To build an alignment we used the MUSCLE (MUltiple Sequence Comparison by Log-Expectation) command using the EMBOSS package. The obtained alignment in a FASTA format was then opened as a Jalview project for the analysis.

By comparing non-conservative regions in sequences of different genotypes we found SNPs (single nucleotide polymorphisms) that potentially can become target sites for the CRISPR/Cas system.

Table 2. The SNPs for the hepatitis C virus (HCV) genotypes
HCV genotypes Subsets SNPs

Genotype 1

1a

A518, T548, T930, G975, C1098, A1143, T1214, A1302, A1419, A1420, T1435, A1460, C1548, A1634, G1673, A1704, G1771, T1780, C1790, T1940, G1953, A2012, G920289T, T2062, T2106, T2124, A2145, T2201, A2205, T2538, A2600, C2616, C2673, A2768, T2888, G3040, T3085, A3123, T3162, G3184, G3211, T3414, A3530, A(3614)TCA, C3640, A3685, T3849, A3878, G4006, A4080, A4206, C4249, T4265, C4321, T4413, G4563

1b

A10, G11 C423, A503, A588, A614, T668, A947, A1074, A1170, A1220, G1361, T1431, A1440, T1518, G1559, T1571, C1722, C1761, A1829, G2193, T2453, C2475, C2731, C2942, C2953, T2961, A3015, A3033, C3071, C3142, A3249, A3356, C3378, A3398, G3582, A(3652)G, G3697, G3789, C4076, G4415, T4427, A4461

Genotype 2

2a

A11, G28, A400, T412, A610, A640, G695, A1078, A1274, A1520, G1590, A1655, C1727, C1757, A1824, T2023, T2218, G2362, A2456, C(2495)G, T2668, G2671, T2705, A2726, T2789, T2893, C2897, C2934, G2939, G3237, T3412, A3730, C3787, A(3984)C, T4027, T4077,A1655, C1727, C1757, A1824, T2023, T2218, G2362, A2456, C(2495)G, T2668, G2671, T2705, A2726, T2789, T2893, C2897, C2934, G2939, G3237, T3412, A3730, C3787, A(3984)C, T4027, T4077

2b

A139, A144, T181, T186, G345, T463, G502, G520, T589, G610, C664, T712, G857, T899, A988, T997, G1005, C1175, A1180, G1190, C1274, C1317, T1318, C1335, C1705, A1730, A1806, T1826, A1836, A1995, G1976, A2034, T2046, A2178, T2249, C2273, A2479, T2489, T2582, C2634, T2648, G2765, A2780, T2870, C2891, T2949, G2983, C3012, A3073, C3108, C3200, G3238, C3488, T3506, A3646, A3753, T3830, T3851, G3872, A3935, G3937, C4145, A4214, G4219, T4303, A(4394)G, A4504, G4506, A4572, A4638

2c

A13, C15, A20, T27, T30, G54, T(61)TTGC, T71, G(72)GT, T81, A(83)GTG, C88, G89, C(92)AGC, T97, C(99)TGAGTGTT, A110, C111, T(116)CCA, A121, T124, A(127)TTGTGGCTCTGTCGTGCAGCCTCC, A715, A1144, A1147, A1582G1187, A1256, C1640, T1733, G1768, A2121, G2739, G2787, T2800, G2810, A2900, T2986, T3037, A3237, A3349, G3351, T3691, A3961, C4316, T4437

2k

T496, T814, A907, A941, A988, C997, A1100, C1419, T1577, G1674, C2001, G2312, A2663, T2683, T2822, G2985, G3044, C3045, T3059, C3080, C3289, A3439, A3478, A3589, T3595, A3608, C3670, G3718, A3824, T4489, A4534, G4688, G4690, T4641

2m

C313, A415, A535, A622, A808, A833, C837, G916, C1088, G1459, C1601, G1620, G1661, G2052, C2098, A2180, A2240, G2277, A2380, G2523, C2571, A2611, G2666, A2675, T2738, G2894, T2914, A3105, C3106, A3157, T3232, A3245, A3421, C3679, T3877, T4108, T4123, A4370

Genotype 3

T8, T11, A15, G28, T55, C95, T126, T245, A247, A338, A361, A400, C416, A437, T444, G445, A482, A507, G551, T631, C635, A822, C876, T898, A910, C913, A(1037)CAAC, A(1050)TC, A1102, A1129, C1147, A1175, T1184, A1249, C1250, T1282, T1360, G1556, A1590, T(1597)CA, A1834, A(1837)A, C1840, A1881, T(1907)T, T(1931)T, A(2085)AATCAAACCCA, A2132, T2236, T2238, A2270, T2284, T2334, A(2351)A, T2381, G(2411)CCG, G2494, G2556, G(2563)C, A2580, G2619, C2632, A2657, A2666, C(2675)A, T2781, C(2795)G, C2833, G2843, T2845, G2908, T(2914)G, T2922, A2977, A2991, T(3142)C, C3146, A3148, G3184, C3190, T(3196)TTAA, C3208, A3257, G3260, T(3305)T, T3312, T3451, A3529, G(3586)G, C3625, A(3640)A, C3646, C(3653)GC, T(3768)GAG, T3795, C3809, A3826, T3858, C3943, G(3972)CAGG, G3995, C4017, G4024, T(4111)C, G4203, C4208, C4234, G4299, A4426, G4437, A4465

Genotype 4

A15, A17, A20, C36, C374, C376, G586, T644, G667, T673, A745, A996, A1088, A1102, G1212, G1273, A1319, G1320, A1338, C1365, G1372, T1378, A1403, T1523, C1664, T1681, A1733, G1735, T1752, G1757, A1763, C1772, C1780, A1825, T1901, A1910, A1949, T2041, G2051, A2071, G2073, A2281, C2303, G2377, C2428, C(2583)T, A2595, C2598, T2616, A2627, T2661, C2684, G2687, G(2709)T, G2750, T2785, C2803, T2810, T2852, T2864, A(2916)T, T2938, C(2942)C, T2951, G2971, A3009, T3020, G3052, T3056, G3105, T(3137)G, A3169, C3248, T(3305)T, T3312, C3387, A3458, A3469, C(3492)C, G3504, T3565, A3630, T(3687)A, T3725, A3727, T3729, T3772, T(3793)T, T3855, C4012, A4171, A4194, T4297, T4415, A4456, T4492

Genotype 5

A44, A434, T474, A547, T568, G570, C573, A583, C629, C649, C670, C673, A757, T721, C796, C857, T864, T910, C911, G1039, T1049, G(1060)C, A1070, T1076, G1101, A1131, A1157, A1254, C1348, C1355, G1366, G(1368)TCAA, C1396, C1465, T1471, A1490, G1505, A1603, G1605, A1638, T1711, T(1852)G, C1872, A1949, T2041, G2051, T2163, T2224, C2327, A(2338)G, A2377, A2440, T2472, A2479, G2525, G2533, A2562, C2647, G2651, G2677, G2681, G2690, C2704, G2706, T2716, G2720, T2724, G2726, T2781, G2797, A2799, G2871, A2882, G2963, T2977, C2992, C3019, G3029, A3120, A3184, G3214, T3273, T3278, A3288, T3343, T3463, G3486, A3510, C3523, A(3573)G, A3598, T3619, A3632, G3634, G3647, T3711, T3733, T(3816)G, G3840, G3873, A(3947)G, G4091, T4331

Genotype 6

6с

G525, G562, G570, T762, T765, T894, T1019, A1513, A1566, A1676, T1682, C1826, G1853, C1872, A1888, T1920, A1970, T(2229)G, C2232, T2241, T2316, T2436, C2645, A3213, G3424, G3594, A3754, G3764, A3819, G3855, A3906, T3916, G4032, T4152, G4311, T4441, T4458, T4496

6f

A752, C1013, T1100, G1260, G1262, A1352, G1564, A(1653)A, G1680, C1697, T(1779)C, A1828, T1874, G1902, G2216, C2348, T2354, T2475, C2493, A2685, A(2825)T, C2856, A2928, G3112, G(3136)G, A3200, G3269, A3363, G3372, A3436, G3553, A3758, C3899, T3974, C(4134)A, C4192, T4229

6i

T866, C919, T1059, G1312, A1412, C1678, T1696, T1939, T2351, A2537, T2681, C2687, G2897, T2900, C2921, A3338, T3378, A3462, G3992, T4283, G4424

6j

G431, T689, C726, G764, A870, A905, T1061, A1178, G1227, G1451, G1491, C1699, T1700, T2582, T2928, A3443, T3650, A3715, T3863, A4139

6k

A308, G564,C670, A763, A766, C838, A841, A962, G1008, A1039, T1100, A1273, C1341, C1347, T1435, G1466, G1517, C1518, G1601, G1620, A1633, G1725, T1763, C1958, G1961, T2090, A2119, G2429, T2605, T2677, C2702, G2819, T3010, A3017, T3025, T3171, A3685, T4355

6p

T162, T393, G511, C1173, C1189, T1727, T1735, A2107, A2235, C2263, T2274, A2293, T2415, T2436, A2569, C2600, G2639, A2733, G2783, T2895, A2944, G3046, C3171, C3562, G3817, T3882, A(4003)GC, A4096, T4138, A4203, T4278, T4429,

6v

T348, C349, C353, A422, G468, G647, A779, C822, T990, T995, C1189, T1239, A1240, A1365, T1404, C1453, C1497, C1512, G1560,T1712, G1828, C1830, A1966, A2018, C(2058)CCGG, T2075, A2221, A2285, G2377, C2446, A2467, T2477, A2508, A(2544)TA, A2568, T2622, A2660, A2802, A2829, T2845, T2917, T3062, G3157, G(3177)G, G3587, A3599, T3615, A3668, G3686, T3761, A3820, T3851, T4071, C4149, G4215, T4220

Kinetic Modeling

1. Introduction

A mathematical model of the system is an important step in our project. This model improves our understanding of the molecular processes’ mechanisms and helps in design optimization.

The goals of the model are the following:

  1. To confirm our expectations of system functioning, such as the potential to detect nucleic acids in a reasonable time
  2. To determine optimal conditions (sgRNA initial concentration, CasX initial concentration, etc.),
  3. To determine detector sensitivity - the minimum concentration of nucleic acid in a sample that can be detected using our test system,
  4. To determine the time required to carry out one test.

2. Model development

In order to create a mathematical model, we paid attention to individual stages of the detection process:

  • LAMP amplification
  • CasX/gRNA complex formation
  • DNA binding
  • CasX collateral activity
  • Signal development

Detection process
Figure 1. Main events of the detection process.

In the present model, we focused on the amplification stage, СasX/gRNA complex formation, and DNA binding. Due to the lack of experimental data for CasX protein in literature, we decided to use the data obtained for other Сas proteins, in particular Сas12a, to make an approximate extrapolation of the results to our test system.

The work was done with help of the MATLAB SimBiology app and SimBiology Model Analyzer.

You can download our model from GitHub here.

Detection process
Figure 2. Graphical Representation of the SimBiology Model.

2.2 Important Variables and Chemical Species

In this part, the set of variables representing the concentrations of various chemical species in the system are described (notations in Table 1). All these variables are functions of time.

Table 3. Variables used in the model
Variable Meaning
cas12a Concentration of unbound Cas12a in the reaction system
gRNA Concentration of unbound sgRNA
cas12a_gRNA Concentration of the complex of Cas12a with sgRNA
tardet_DNA Concentration of the unbound target DNA in the probe
cas12a_gRNA_DNA Concentration of the complex of Cas12a, sgRNA, and target DNA

2.3 Mathematical description of the system

2.3.1 LAMP amplification

We used the empiric kinetic model of LAMP proposed by Subramanian et al. [26]

  • k is the concentration of amplicon at infinite time
  • a is the lower bound
  • b is the maximum slope of the amplification curve
  • m is the time at which the growth rate during LAMP is maximum
Table 4. Lamp model parameters at different initial DNA concentration
Initial concentration of DNA (femtomole/ml) a (nanomole/ml) b (1/min) c (nanomole/ml) m (min)
3.89 6.71 0.73 45.90 11.1
41.1 6.20 0.52 46.46 10.48
411 3.49 0.34 49.00 9.05

The parameters used here were determined empirically for a specific case, highlighted in the original source[26].

We understand that for our situation they may be slightly different. Creating a model, we assume that the differences will not be significant.

2.3.2 Completion of amplification

An event was added to the model that sets the transition from amplification to detection. At a certain point, we change the reaction conditions. We carry out the LAMP reaction at 62 °C and detection using the CasX/gRNA complex at 37 °C.
At the same time, we add RNA and CasX to the reaction mixture.
The certain time of the event was determined by us (see results and discussion).

2.3.3 Degradation of sgRNA

Reaction: gRNA -> null
Reaction rate: v = kdeg*gRNA

2.3.4 Cas12a/sgRNA complex formation and dissociation

Reaction: Cass12a + gRNA <-> Cas12a/gRNA
Reaction rate: v = k1*gRNA*Cas12a -k-1*Cas12a/gRNA

The constants were obtained in the study of the formation of the complex Cas9/gRNA[27]. We assume that for Cas12a these quantities have at least a close order of magnitude.

2.3.5 Binding and unbinding of target DNA

Reaction: Cas12a/gRNA + targetDNA <-> Cas12a/gRNA/DNA
Reaction rate: v = k2*Cas12a/gRNA*targetDNA -k-2*Cas12a/gRNA/DNA

2.3.6 The Parameters Used in the Model
Table 5. Biological Parameters Used in the Model
Name Description ValueUnits Source
kdeg Rate constant of degradation of gRNA 0.0069 1/sec [27]
k1 Rate constant of Cas12a/gRNA complex formation0.108 1/(nM*sec) [27]
k-1 Rate constant of Cas12a/gRNA complex dissociation 1.0E-5 1/sec[27]
k2 Rate constant of Cas12a/gRNA/DNA complex formation 6.6 1/(nM*min) [28]
k-2 Rate constant of Cas12a/gRNA/DNA complex dissociation3.6E-4 1/min [28]

3. Results and discussion

3.1 LAMP reaction time

Our first task was to determine the minimum time needed for the amplification stage. To determine it, a simulation was carried out without adding Cas12a and gRNA to the reaction mixture. We were interested in three cases with different DNA content in the sample: 3.89 femtomole/ml, 41.1 femtomole/ml, 411 femtomole/ml, as these three concentrations differ in order of magnitude. Also, experimental data only for these concentrations but not lesser is available from the literature.

Detection process
Figure 3. Time dependence of the target DNA concentration during LAMP

It can be seen that by 20 minutes in all cases the curves reach a plateau around 40-45 nanomole/ml.

According to our results, 20 minutes will be enough for LAMP, therefore, the time before transfer to the next stage was chosen 20 minutes, it was used later in the simulation.
Moreover, this stage is given 20-30 minutes in most CRISPR–Cas12-based tests. In particular, this value can be seen in the detection protocol for CRISPR–Cas12-based detection of SARS-CoV-2 [29]. We can assume that the obtained results can be used for further modeling and test system development.

3.3.2 Behavior of system components simulation

After determining the transition time to the second step, we simulated the whole detection process.
In this case, an initial concentration of DNA 3.89 femtomole/ml was used, and after 20 minutes Cas12a and gRNA were added to the system with concentrations of 50 nanomole/ml and 62.5 nanomole/ml, respectively. These concentrations are used in the DETECTR protocol [30].

Detection process
Figure 4. Obtained the concentration of the components dependence on time

So, the system behavior corresponds to literature data and our expectations to make a quick detection system. The final concentration of the Cas12a/gRNA/DNA complex exceeds 20 nanomole/ml. It reaches a plateau 300 minutes after the start of the experiment, but it should be noted that a major part of the complex is formed in the first 150-200 minutes (taking into account the amplification stage). We can assume that the development of the signal can be seen even earlier, however, in order to determine this time accurately, it is necessary to consider the CasX collateral activity. At the moment, we do not have enough experimental data from the literature.

3.3 The effect of DNA concentration in a sample

We ran a simulation for three different initial concentrations of target DNA in the sample.

Detection process
Figure 5. Comparison of the dependence of the Сas12a/gRNA/DNA complex concentration on time at different initial DNA concentrations (3.89 femtomole/ml, 41.1 femtomole/ml, 411 femtomole/ml).

As a result, we obtained curves that almost completely overlap with each other. It means that in the studied concentration range during 20 minutes of amplification equivalent amounts of DNA for detection are produced. In this case, we can use our detection system only for qualitative, but not quantitative estimations of the target present in the sample. However, DNA can be determined in femtomolar concentrations.

3.4 Protection against RNA degradation

We thought about ways to increase the speed and yield of the reaction. One of the possible strategies is to protect RNA from degradation. We ran a simulation that neglected RNA degradation.
In this simulation, the initial concentration of DNA was 3.89 femtomole/ml.

Detection process
Figure 6. Changes in the concentration of the Cas12a/gRNA/DNA complex and gRNA in with and without gRNA degradation.

As expected, protection of gRNA from degradation increased the final concentration of the Cas12a/gRNA/DNA complex, at the same time the signal will develop earlier than in the presence of gRNA degradation.
We can manage it using the HUDSON method (Heating Unextracted Diagnostic Samples to Obliterate Nuclease) [31]. HUDSON is the incubation of a sample in a special reaction mixture at a high temperature that leads to the inactivation of both the virus and RNases, preventing the destruction of viral RNA by enzymes. The duration of this step is approximately 10 minutes. It can protect not only the viral RNA but also the gRNA.

4. Conclusions

  • The modeling has shown that the method is suitable for the detection of viral nucleic acid.
  • It has been estimated that it is possible to detect femtomolar concentrations of the target nucleic acid.
  • The LAMP should take about 20 minutes, the detection stage takes about 3 hours, but most of the complex is already formed in 2 hours, and the signal may appear even earlier and can be determined during lab experiments.
  • Within the range of the studied values, the initial DNA concentration does not affect the concentration of the Сas/gRNA/DNA complex, and hence the development of the signal. The method can be used for qualitative but not quantitative assessment.
  • Modeling showed that in any case, we can detect about 6.02*108 copies/ml. The serum contains up to 108 copies of HCV RNA per ml[32]. Our test can potentially be more sensitive, we need more experimental data for lower concentrations.
  • We can reduce the time required for detection and increase the signal intensity by protecting the RNA in the system from degradation. Thus, we will use the HUDSON method.

5. Challenges for the future

We still have several tasks to improve our kinetic model. First, in the future, we plan to consider the stage of reverse transcription, since the project is aimed at detecting haplotypes of RNA-containing viruses.
Also, it would be useful to focus on CasX collateral activity and simulate signal development in silico. This will allow us to determine more accurately the development time sufficient for signal detection. This time is expected to be less than the time required for the reaction to complete.
Due to the lack of literature data, we used the reaction constants for other Cas proteins. We are going to obtain the values for CasX. In addition, we are going to define the parameters of the LAMP model for our fragments.

References

  1. «WHO | Variant analysis of SARS-CoV-2 genomes».
  2. Forster and others., «Phylogenetic network analysis of SARS-CoV-2 genomes».
  3. Tang and others., «On the Origin and Continuing Evolution of SARS-CoV-2».
  4. «https://nextstrain.org/blog/2020-06-02-SARSCoV2-clade-naming».
  5. Mercatelli and Giorgi, «Geographic and Genomic Distribution of SARS-CoV-2 Mutations».
  6. «https://www.gisaid.org/epiflu-applications/phylodynamics/».
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