# Quantifying Plant Viruses: Evolution from Bioassay to Infectivity Dilution Curves along the Model of Tobamoviruses

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## Abstract

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## 1. Introduction

## 2. Models for Correlation of Local Lesion Host and Virus Concentration

#### 2.1. Poisson-Based Model and Its Variations in Tobamovirus Quantification

^{2}of leaf surface per half-leaf. Thus, there are roughly 400,000 epidermal cells on the upper surface of each half-leaf. Even with these changes, the model did not fit the data; therefore, the authors simplified the modified equation to Model II as follows:

#### 2.2. Logistic Model or Growth Curve Model in Tobamovirus Quantification

^{2}statistics. The fitting procedure provides an objective approach without relying on arbitrary parameter values. It should be mentioned that the Growth curve model resembles the Poisson model at high concentrations of virus since $\beta {\mathrm{e}}^{-\gamma t}$ is close to 0, and it represents the Poisson model. When the virus concentration is 0, t approaches $-\infty $; thus $Y=0$, meaning no lesion. At the higher concentrations toward a limit, it has an “asymptote” of N.

#### 2.3. Normal Distribution-Based Approaches in Tobamovirus Quantification

#### 2.4. Summarizing Key Factors or Assumptions Shaping Tobamovirus Quantification Models

#### 2.5. Exploring Nonparametric Approaches for Comparisons in Local Lesion Test Assays

## 3. Evaluating Goodness of Fit for Various Models Applied to Experimental Data

## 4. Machine Learning and Artificial Intelligence in Quantification of Viruses Using Local Lesions

#### 4.1. Integration of Machine Learning Techniques in Local Lesion Assay Models

#### 4.2. Application of Deep Learning for Image-Based Disease and Virus Classification and Quantification

## 5. Application of Infectivity Dilution Curve in Virucidal Efficacy of Disinfectants

#### 5.1. Preparation of the Standard Sample

#### 5.2. Designing the Inoculation Experiment and Collecting the Data

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Correction Statement

## References

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**Figure 1.**The estimated infectivity dilution curves according to the different models calculated based on the mean number of the local lesions on N. glutinosa as a local lesion host against the logarithm of virus concentrations in serially diluted virus suspensions. The raw data from Experiment No. 1 (

**A**), Experiment No. 2 (

**B**), Experiment No. 10 (

**C**), and Experiment No. 13 (

**D**) of Kleczkowski [16] were used for implementing the Kleczkowski model [16], Furumoto and Mickey Models I and II [17,18], the Growth curve model [19], and the modified Poisson model [15].

**Figure 2.**Optimizing virus concentration for accurate local lesion counting and adjusting concentration to prevent lesion aggregation. The range of virus concentration should be fine-tuned through preliminary tests to ensure that local lesions do not aggregate (top left), thereby avoiding the formation of a larger necrotic lesion. This adjustment enables easy and accurate lesion counting. LL: local lesion.

**Figure 3.**Example of randomization for six inoculum dilutions (A–F) using six half-leaf units from three well-grown leaves of a suitable local lesion host. “L.” denotes the leaf, “RH” and “LH” denote the right half-leaf unit and left half-leaf unit, respectively.

**Table 1.**The mean number of observed and predicted necrotic local lesions on N. glutinosa with serially diluted ToBSV in Kleczkowski’s Experiment No. 1 ($\mathrm{i}\mathrm{c}=1\mathrm{m}\mathrm{g}/\mathrm{m}\mathrm{L},$ $\mathrm{f}=2,\mathrm{r}=24)$ [16].

Virus Concentration (mg/mL) | Mean No. of Observed LL * | Computed Y Based on | ||||
---|---|---|---|---|---|---|

Kleczkowski Model | Furumoto and Mickey Model I | Furumoto and Mickey Model II | Growth Curve Model | Modified Poisson Model | ||

1 | 145.5 | 153.9 | 150.7 | 145.5 | 151.5 | 147.9 |

0.5 | 139.3 | 132.8 | 130.0 | 144.8 | 134.5 | 137.1 |

0.25 | 117.9 | 110.5 | 109.5 | 135.7 | 113.6 | 117.1 |

0.125 | 105.8 | 88.4 | 89.4 | 107.9 | 90.5 | 91.8 |

0.0625 | 52.3 | 67.7 | 70.1 | 71.5 | 67.8 | 67.2 |

0.03125 | 44.0 | 49.5 | 52.0 | 41.7 | 48.0 | 46.7 |

0.015625 | 37.4 | 34.5 | 36.1 | 22.6 | 32.5 | 31.4 |

0.0078125 | 25.8 | 22.9 | 23.1 | 11.8 | 21.2 | 20.6 |

0.00390625 | 17.3 | 14.4 | 13.7 | 6.0 | 13.5 | 13.3 |

0.001953125 | 9.6 | 8.6 | 7.6 | 3.0 | 8.4 | 8.5 |

0.000976563 | 5.0 | 4.9 | 4.1 | 1.5 | 5.2 | 5.4 |

Model parameters ** | ${\mathrm{N}}_{\mathrm{K}}$: 225.48 | ${\mathrm{N}}_{\mathrm{F}\mathrm{M}}$: 30.11 | ${\mathrm{N}}_{\mathrm{F}\mathrm{M}}$: 145.46 | ${\mathrm{N}}_{\mathrm{L}}$: 188.46 | ${\mathrm{N}}_{\mathrm{M}\mathrm{P}}$: 151.50 | |

λ: 1.21 | C: 147.91 | c/β: 10.82 | β: 0.244 | A: 2.23 | ||

ξ: −0.57 | γ: 1.65 | b: 0.67 | ||||

c: 2.16 | ||||||

Error X^{2} | 10.4 | 12.3 | 78.4 | 10.7 | 10.3 |

**Table 2.**The mean number of observed and predicted necrotic local lesions on N. glutinosa with serially diluted TMV in Kleczkowski’s Experiment No. 2 ($\mathrm{i}\mathrm{c}=0.2\mathrm{m}\mathrm{g}/\mathrm{m}\mathrm{L},$ $\mathrm{f}=2,\mathrm{r}=24)$ [16].

Virus Concentration (mg/mL) | Mean No. of Observed LL * | Computed Y Based on | ||||
---|---|---|---|---|---|---|

Kleczkowski Model | Furumoto and Mickey Model I | Furumoto and Mickey Model II | Growth Curve Model | Modified Poisson Model | ||

0.2 | 145.1 | 147.9 | 144.2 | 145.0 | 145.0 | 142.7 |

0.1 | 123.8 | 123.5 | 121.6 | 141.6 | 125.2 | 127.7 |

0.05 | 110.0 | 99.0 | 99.5 | 122.5 | 101.8 | 103.8 |

0.025 | 69.8 | 75.9 | 78.1 | 87.8 | 77.4 | 77.4 |

0.0125 | 57.4 | 55.6 | 58.1 | 53.9 | 55.2 | 54.1 |

0.00625 | 33.0 | 38.7 | 40.5 | 30.1 | 37.2 | 36.1 |

0.003125 | 25.0 | 25.6 | 26.1 | 15.9 | 24.0 | 23.3 |

0.0015625 | 36.6 | 16.1 | 15.5 | 8.2 | 15.0 | 14.8 |

0.00078125 | 8.0 | 9.6 | 8.7 | 4.2 | 9.2 | 9.3 |

0.000390625 | 3.4 | 5.4 | 4.6 | 2.1 | 5.6 | 5.8 |

0.000195313 | 4.0 | 2.9 | 2.4 | 1.0 | 3.4 | 3.6 |

0.0000977 | 1.8 | 1.4 | 1.2 | 0.5 | 2.0 | 2.2 |

Model parameters ** | ${\mathrm{N}}_{\mathrm{K}}$: 224.71 | ${\mathrm{N}}_{\mathrm{F}\mathrm{M}}$: 33.14 | ${\mathrm{N}}_{\mathrm{F}\mathrm{M}}$: 145.08 | ${\mathrm{N}}_{\mathrm{L}}$: 188.55 | ${\mathrm{N}}_{\mathrm{M}\mathrm{P}}$: 149.09 | |

λ: 1.19 | C: 382.55 | c/β: 37.18 | β: 0.09 | A: 3.83 | ||

ξ: −1.01 | γ: 1.73 | b: 0.7 | ||||

c: 3.8 | ||||||

Error X^{2} | 33.8 | 127.2 | 30.4 | 34.1 | 35.2 |

**Table 3.**The mean number of observed and predicted necrotic local lesions on N. glutinosa with serially diluted TMV in Experiment No. 10 with $\mathrm{i}\mathrm{c}=1\mathrm{m}\mathrm{g}/\mathrm{m}\mathrm{L},$ $\mathrm{f}=3.16,\mathrm{r}=12$ by Kleczkowski [16].

Virus Concentration (mg/mL) | Mean No. of Observed LL * | Computed Y Based on | ||||
---|---|---|---|---|---|---|

Kleczkowski Model | Furumoto and Mickey Model I | Furumoto and Mickey Model II | Growth Curve Model | Modified Poisson Model | ||

1 | 320.7 | 296.9 | 320.7 | 320.7 | 298.7 | 317.8 |

0.316 | 228.9 | 263.8 | 258.1 | 320.4 | 270.3 | 287.3 |

0.1001 | 216.9 | 210.8 | 196.2 | 288.0 | 217.8 | 212.7 |

0.0316 | 171.9 | 145.6 | 136.5 | 165.0 | 146.1 | 130.7 |

0.01002 | 72.3 | 84.1 | 82.5 | 65.5 | 79.6 | 71.4 |

0.00317 | 44.1 | 39.6 | 41.0 | 22.4 | 37.0 | 36.6 |

0.001004 | 13.3 | 15.0 | 16.5 | 7.3 | 15.7 | 18.2 |

0.000317 | 4.8 | 4.5 | 5.8 | 2.3 | 6.4 | 8.9 |

Model parameters ** | ${\mathrm{N}}_{\mathrm{K}}$: 320.67 | ${\mathrm{N}}_{\mathrm{F}\mathrm{M}}$: 54.68 | ${\mathrm{N}}_{\mathrm{F}\mathrm{M}}$: 320.67 | ${\mathrm{N}}_{\mathrm{L}}$: 320.67 | ${\mathrm{N}}_{\mathrm{M}\mathrm{P}}$: 320.67 | |

λ: 0.96 | C: 351.47 | c/β: 22.79 | β: 0.074 | A: 2.60 | ||

ξ: −1.39 | γ: 1.86 | b: 0.64 | ||||

c: 2.53 | ||||||

Error X^{2} | 13.8 | 16.9 | 73.5 | 15.3 | 29.6 |

**Table 4.**The mean number of observed and predicted necrotic local lesions on N. glutinosa with serially diluted TMV in Experiment No. 13 with $\mathrm{c}=20\mathrm{m}\mathrm{g}/\mathrm{m}\mathrm{L},$ $\mathrm{f}=5,\mathrm{n}=12$ by Kleczkowski [16].

Virus Concentration (mg/mL) | Mean No. of Observed LL * | Computed Y Based on | ||||
---|---|---|---|---|---|---|

Kleczkowski Model | Furumoto and Mickey Model I | Furumoto and Mickey Model II | Growth Curve Model | Modified Poisson Model | ||

20 | 242.2 | 238.9 | 228.6 | 242.2 | 235.9 | 236.8 |

4 | 209.2 | 200.3 | 192.9 | 242.2 | 202.0 | 205.7 |

0.8 | 135.5 | 157.2 | 157.3 | 240.6 | 159.2 | 158.5 |

0.16 | 123.7 | 114.4 | 121.8 | 154.0 | 114.0 | 110.3 |

0.032 | 81.0 | 76.5 | 86.5 | 44.3 | 74.5 | 71.5 |

0.0064 | 52.3 | 46.8 | 52.6 | 9.6 | 45.2 | 44.3 |

0.00128 | 23.0 | 26.0 | 24.0 | 2.0 | 26.0 | 26.6 |

0.000256 | 12.2 | 13.1 | 7.3 | 0.4 | 14.5 | 15.8 |

Model parameters ** | ${\mathrm{N}}_{\mathrm{K}}$: 319.03 | ${\mathrm{N}}_{\mathrm{M}\mathrm{P}}$: 22.13 | ${\mathrm{N}}_{\mathrm{M}\mathrm{P}}$: 242.17 | ${\mathrm{N}}_{\mathrm{L}}$: 292.20 | ${\mathrm{N}}_{\mathrm{M}\mathrm{P}}$: 248.74 | |

λ: 2.03 | C: 1527.89 | c/β: 6.32 | β: 0.766 | A: 1.08 | ||

ξ: −0.06 | γ: 0.9 | b: 0.34 | ||||

c: 1.04 | ||||||

Error X^{2} | 5.52 | 8.86 | 858.51 | 7.20 | 9.19 |

**Table 5.**Overview of bioassays used to determine the efficacy of disinfectants to inactivate tobamoviruses sorted by the object to be disinfected. In each case, the available information on the virus species, the inoculum, and the virus load, as well as the assessment method used, is provided.

Object | Virus | Type of Inoculum | Inoculum Load | Type of Bioassay | Assessment Type | Reference |
---|---|---|---|---|---|---|

clothing | ToBRFV | Infected N. clevelandii leaves | (1:5, w/v) | Local lesion | Semi-quantitative | [56] |

Greenhouse surfaces | ToBRFV | Infected tomato leaves | (1:5, w/v) | Local lesion | Qualitative | [54] |

CGMMV | Contaminated surface | unknown | Systemic | Qualitative | [57] | |

ToBRFV | Virus particles in non-infected Plant sap | 1 mg/mL | Local lesion | Quantitative | [25] | |

Plant sap | TMV, ToMV | Infected tomato leaves | (1:5, w/v) | Systemic | Qualitative | [58] |

ToBRFV, CGMMV | (1:5, w/v) | [59] | ||||

ToBRFV | (1:10, w/v) | [60] | ||||

Plant sap, knives, trays | CGMMV | Infected cucumber leaves | (1:5, w/v) | Systemic | Qualitative | [61] |

Seeds | ToBRFV | Seeds from infected plant | Unknown | Systemic | Qualitative | [62] |

ToBRFV | Local lesion | Qualitative | [63] | |||

CGMMV | Systemic | Qualitative | [64] | |||

Shoes | ToBRFV | infected N. clevelandii leaves | (1:5, w/v), (1:10, w/v) | Local lesion | Semi-quantitative | [65] |

Soil | ToBRFV, CGMMV | Infected tomato/cucumber leaves | (1:5, w/v) | Systemic | Qualitative | [66] |

CGMMV | Infected dry N. benthamiana leaves | (1:20, w/v) | Systemic | Qualitative | [67] |

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## Share and Cite

**MDPI and ACS Style**

Nourinejhad Zarghani, S.; Monavari, M.; Nourinejhad Zarghani, A.; Nouri, S.; Ehlers, J.; Hamacher, J.; Bandte, M.; Büttner, C.
Quantifying Plant Viruses: Evolution from Bioassay to Infectivity Dilution Curves along the Model of Tobamoviruses. *Viruses* **2024**, *16*, 440.
https://doi.org/10.3390/v16030440

**AMA Style**

Nourinejhad Zarghani S, Monavari M, Nourinejhad Zarghani A, Nouri S, Ehlers J, Hamacher J, Bandte M, Büttner C.
Quantifying Plant Viruses: Evolution from Bioassay to Infectivity Dilution Curves along the Model of Tobamoviruses. *Viruses*. 2024; 16(3):440.
https://doi.org/10.3390/v16030440

**Chicago/Turabian Style**

Nourinejhad Zarghani, Shaheen, Mehran Monavari, Amin Nourinejhad Zarghani, Sahar Nouri, Jens Ehlers, Joachim Hamacher, Martina Bandte, and Carmen Büttner.
2024. "Quantifying Plant Viruses: Evolution from Bioassay to Infectivity Dilution Curves along the Model of Tobamoviruses" *Viruses* 16, no. 3: 440.
https://doi.org/10.3390/v16030440