It is currently argued that Tomato brown rugose fruit virus (ToBRFV), a member of the virus genus Tobamovirus, in the family Virgaviridae, is of utmost concern for tomato production globally [1]. The virus caused an outbreak on tomato plants in Israel in 2014 [2]. ToBRFV has been reported from tomato (Solanum lycopersicum L.) [1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19], pepper (Capsicum annuum L.) [20,21,22,23], and weed hosts [24] in 35 countries [25], and has been causing devastating disease outbreaks in tomato production areas [26,27,28,29]. In fact, based on the Statistica report for 2020, tomato accounts for 16% of the global vegetable production [30] and is one of the most important vegetable crops in the world [31]. It has been reported that ToBRFV cause a yield loss of 15–55% [26]. The virus excites mild to severe mosaic symptoms with dark green bulges, leaf narrowing, and deformation. The peduncles and calyces often become necrotic and unable to produce fruit, and if fruits are produced, they will be infected with the virus, developing yellow blotches, brown or black spots, and rugose wrinkling. Such fruits are not marketable [25,32]. In addition, various plants are introduced as herbaceous hosts, such as Nicotiana spp. It has been reported that ToBRFV causes local lesions on Nicotiana tabacum L. cv. Xanthi nc and N. glutionosa L., as well as systemic infection in N. benthamiana Domin and N. clevelandii A. Gray [1]. In Israel, ToBRFV was detected in Chenopodium murale L. and Solanum nigrum L. around infected tomato crops [33].

Tobamoviruses including ToBRFV could be dispersed by the transport of contaminated seeds over a long distance. Moreover, they are stable viruses [34] and remain infectious for several years outside of the host cells on different surfaces and can serve as an inoculum source for later infections whenever a suitable host is available again [25,35,36,37,38]. Once tobamoviruses are introduced or established in the greenhouse, they spread quickly in the entire greenhouse during hands-on activity or pruning, as well as different surfaces of greenhouse tables, pots, and tools [39,40]. Understanding the epidemiology of ToBRFV is essential for managing the disease properly [39]. These include proper crop management and more stringent screening procedures at international borders using quick, accurate, and affordable diagnosis [41]. ToBRFV is a quarantine virus in the U.K. and some Latin American countries (Chile and Argentina), while in the EPPO region, it is locally present and is under official control [42]. In the EU, ToBRFV is a virus subjected to emergency measures (EU 2020/1191 and further implementations). Exclusion and eradication principles of plant disease management are applied to restrict its entrance and distribution and propagation materials must be tested for ToBRFV via defined methods. For instance, detection of ToBRFV on seeds is carried out in the EU by a standardized RT-PCR or real-time RT-PCR. In the EU, tomato fruit producers dealing with ToBRFV infection in their greenhouses must remove and destroy all infected plants from the production site, at least at the end of the cropping season. Additionally, they must apply specific hygiene measures on personnel, production site structures, machinery, and pruning tools to prevent ToBRFV spread (EU 2021/1809). The efficacy of various disinfectants to inactivate tobamoviruses such as ToBRFV has been tested in vitro using bioassays [40,43,44,45,46,47,48]. These assays map infectivity of the test suspensions, but do not allow quantification of viral load.

Virus quantification involves counting virus particles or viral genome fragment(s) in a known volume to determine their concentration. Applications are in diagnostics and in research, for example, in virus–host interaction studies. Several methods have been developed to determine the viral load in a given sample, based on chemical or physical principles. These methods include electron microscopy, serological assays such as ELISA (enzyme-linked immunosorbent assay), and q(RT)-PCR (quantitative reverse-transcribed polymerase chain reaction). None of these methods can show or confirm infectivity of the virus in plant sap or virus suspensions. Plant viruses are not viable themselves and depend on a living host. Therefore, only a bioassay can show infectivity of the virus and, if necessary, quantify infectious virus particles. However, molecular methods are more sensitive than bioassay. In 1929, Holmes established a local lesion assay and showed that the number of local lesions on the inoculated host depends on the virus titer [49]. Since then, a few models and equations have been developed, aiming to accurately correlate the number of local lesions on the indicator plant with the viral inoculum titer in the inoculum. These models can be categorized according to the underlying basic statistical equations. The models and their parameters are summarized in Table 1. The model of Bald in 1937 [50] is based on a Poisson series; those of Kleczkowski [51] and Furumoto and Mickey [52,53] are based on normal distribution and a confluent hypergeometric function, respectively. Furthermore, a ‘growth curve’ model or logistic model was presented by Gokhale and Bald [54], and finally, Bald [55] introduced a modified Poisson model (Table 1).

A biological assay is based on the viability or infectivity of a pathogen. In the case of plant viruses, a bioassay using a susceptible host plant is the only available method to verify pathogenicity. So far, the evaluation is mostly qualitative, i.e., the pathogen is infectious or non-infectious. A quantitative evaluation requires a reproducible relationship/regression to be established between the number of local lesions induced by the virus after artificial inoculation and the virus concentration in the inoculum.

In this study, we report (i) the accuracy of the different models for quantifying ToBRFV in virus suspensions and plant homogenates with a known virus concentration, and (ii) the suitability of the models for the prediction of virus concentrations in a plant homogenate with an unknown virus concentration.

Although bioassays play a key role in several fields of plant virology, such as host range determination [57,58,59], symptomatology [60,61], virus replication, plant–pathogen interactions [62,63], and determination of function(s) of viral proteins or genes and host genes (gene knockdown via virus induced gene silencing) [64,65], the biological assay has always been paled into insignificance in virus quantification, because the sensitivity and reproducibility of this method might be misevaluated. Undoubtedly, molecular methods such as q(RT)-PCR or digital (RT)-PCR could detect very low concentrations or copy numbers of virus genomes [66,67], which is beyond the ability of a bioassay. The establishment of a successful bioassay or infectiosity test requires a minimum number of virus particles which is equal to the infective dose or the lowest values of boundary or the lowest concentration of virus particles that could be detected by this method. A similar phenomenon is known for plant pathogenic bacteria which is needed for attachment and expression of the pathogenic genes for the establishment of an infection [68] or the establishment of infection caused by fungi [69]. However, bioassays are the only methods to confirm infectiosity of plant pathogenic viruses, and neither qRT-PCR nor any other sensitive molecular method is able to detect the infectiosity of a virus suspension.

Local lesion assays must be carefully planned and conducted to minimize the variations and errors due to environmental conditions such as light cycle, temperature, species and age of local lesion host, and the position of leaves on the plant, as well as nutritional condition and methodology of inoculation. Keeping plants in darkness or low light intensity for 24 h prior to inoculation tends to increase the number of local lesions and will affect local lesion development. Any substances added during inoculation, such as phosphate-based inoculation buffers and particles of carborundum or diatomaceous earth, could positively influence local lesion formation [70]. Phosphate and abrasives will increase the number of local lesions [71], while any ribonuclease present will inhibit local lesion formation. Bentonite, which interferes with ribonuclease, will increase the number of local lesions produced as shown by naked TMV RNA, but not by intact virions [70]. It is suggested that if the source of inoculum is changed, for example, different processes of purification, the data obtained from randomized block designs may be subjected to analysis of variance (ANOVA) to determine the significance of differences between the number of lesions produced by different inocula, to make sure the inocula do not differ greatly from one another. Randomization is important, not just between leaves, but between plants in a treatment group. The results of this study showed that the position of the leaf or half-leaves was not statistically significant and did not affect the number of local lesions induced by ToBRFV in N. tabacum cv. Xanthi nc and N. glutinosa) (Table 5). However, the host plant played an important role in the quantification of ToBRFV. Therefore, N. glutinosa is deemed a better host than N. tabacum cv. Xanthi nc for the quantification of ToBRFV in bioassay. It has been shown that there were no significant differences in susceptibility between leaves in different positions when plants were grown under reduced light intensity [72,73]. The influence of the various factors mentioned above could be kept at bay by applying appropriate experimental designs and using statistical analysis in the evaluation of the data obtained [73]. When the number of inoculated half-leaf units from N. glutinosa plants exceeds 16, the accuracy of local lesion methods increases [73,74]. Therefore, using at least 24 half-leaf units for each dilution makes the accuracy of the method adequate in a way that statistically, there was no significant difference between the leaf positions.

The numbers of local lesions produced by different leaves when inoculated with the same virus preparation deviate significantly from a normal distribution, and the standard errors of x values depend on their magnitude. Therefore, before fitting the models, data should be appropriately transformed [56]. The author suggested the equation z=log 12 [x+c+√(x2+2cx)], where c is an arbitrary parameter. The parameter c could be optimized for each experiment. However, in this study, c = 20 offered the best transformation. Using this transformation is equivalent to using Y^, the z-equivalent of half-leaf count. To calculate Y^, first, the local lesion counts for a fixed concentration were transformed to normal distribution based on the above equation for z. Y^ is the inverse transformation of the mean of z-values. For more details, the readers are referred to [56].

Models for the correlation of the local lesion number to the virus concentration were developed as our understanding of virus–plant interactions increased. The Bald 1937 model is based on the Poisson distribution and it is assumed that a single virus particle can cause infection. Moreover, it is assumed that the leaf surface of the local lesion host can be infected with the same probability. Therefore, all the susceptible regions or entry points of a leaf have the same probability of infection with regard to the distribution of particles inside the regions, which follows the Poisson distribution. This model has two parameters, including the maximum number of local lesions observed in the assay and an unknown parameter which may account for the relative infectivity of any virus sample [50]. This model is also called the ‘one-particle-one-region’ model. The probability of causing all infections depends on the average number of virus particles inside the susceptible region. It is further assumed that this number is directly proportional to the plant virus concentration. This theory does not allow for any variation in the susceptibility between different susceptible regions of the host since it assigns the same probability for the entry points [51]. This model was not used in this study since it is a special case of the Furumoto and Mickey model.

Furumoto and Mickey [52,53] also followed the Bald 1937 model [50], the one-particle-one-region assumption. The main difference between these two models is that Furumoto and Mickey assumed that epidermal cells vary in their susceptibility to infection. There are a number of assumptions in the Furumoto and Mickey model: (i) virus particles, k in number, available outside a cell have a Poisson distribution with mean, α, proportional to concentration; (ii) the number of virus particles entering the cell with a fixed probability x of penetration has a binomial distribution with parameters k and x; and (iii) x has α, β distribution with parameters α and β and they arrive at the following model: Y = Nα(1+ cV/β). At that time, this hypermetric function was too complicated to use for fitting the data. Therefore, the authors simplified the modified equation to the formulae ‘model II’ as follows: Y/N=1− e−cV, which is the same model as described by Bald [50] with a different definition of N. Here, N is a hypothesized (not observed) number, which is usually estimated by inspection and extrapolation as the limit of lesions that appear at high concentrations of inoculum. Y/N is the expected proportion of infected regions in a total N of susceptible regions against the logarithm of virus concentration. Hence, Bald [50] can be assumed as a special case and was not investigated separately.

The Kleczkowski model [51] is based on the assumption that regional susceptibility (e.g., leaf surface) varies in such a way that the logarithm of minimal effective concentrations, necessary to cause the formation of the lesion, is normally distributed. In this model:(1)Y=Nλ2π  ∫−∞texp {−12 (t−ξλ)2} dt where Y is the expected number of lesions per half-leaf, N is the mean number of ‘susceptible regions’ per half-leaf (which is a hypothesized number), t is the virus concentration in the inoculum or dilution of infective sap, ξ=log x0, x0 = virus concentration or dilution of infective sap when 50% of the susceptible regions develop lesions, and λ is the standard deviation. This equation has three parameters, N, ξ, and λ, all of which are unknown and must be fitted to the experimental data.

Gokhale and Bald [54] derived the relationship between the expected proportion of infected regions measured by p = Y/N and the logarithm of concentration of virus (t = log x) as a growth curve model. In this model, they assumed that the rate of increase in p as a function of t is proportional to p and its deficiency (1-p). The resulting equation becomes:(2)YN=11+β e−γt where β and γ are positive constants of the model.

Bald et al. 1990 considered along the growth curve model a modified Poisson model resembling the Furumoto and Mickey model II. This modified Poisson model uses the Furumoto and Mickey model II to estimate C values for each observation, which in turn are used to estimate V and N. This model needs to be optimized. To this end, for each i, C˜iVi is calculated from Yι=N (1− e−C˜iVi) {−C˜iVi= ln(1−YiN) }. In the next step, the log (C˜iVi) is regressed against the log (CVι)=log mi, logs of the observed concentrations, to obtain log(C˜iVi)=a+b log (mi). These estimated parameters are used in the main equation (3)Y^ı= N (1−e−Amib) where A =10a.

When the developments of the models are compared, they share or differ in a few key basic assumptions which could be summarized as follows: (a) infection can start from a single virus particle that was introduced into a susceptible region of the host tissue; (b) each epidermal cell is a susceptible region; (c) cells differ in the probability of penetration by a virus particle; (d) all susceptible regions are identical; (e) a minimum dose of virus particles is needed to start an infection in a susceptible region; (f) the susceptibility of the regions varies in such a way that the logarithms of minimal infective doses are normally distributed. The Bald 1936 model follows assumptions a, b, and d; the Furumoto and Mickey models are based on assumptions a, b, and c; and the Kleczkowski model is based on assumptions e and f. In contrast, in the growth curve model, there were no clear explicit physical assumptions (e and f). It is a mainly data-based model and has been used accordingly for modeling disease development or for describing bacterial growth curves. The modified Poisson model is a modified version of the Poisson model to which, depending on the slope of the infection–dilution curve, it could be adopted. It is worth mentioning that the general performance of the presented models for ToBRFV is in accordance with the previously published data for TMV to which the models have been originally established [57]. This indicates that the underlying assumptions for these models could also be suitable for ToBRFV. Our results could not reject any of the models and their assumptions.

The application of a spike sample with a defined virus concentration enables the validation of the models in the prediction of the correct virus concentration in an unknown sample. Our results show that the host plant used in local lesion assays also has a significant effect on the accuracy of the models to determine correct virus concentrations in virus inocula. Since the underlying assumptions of these models about the susceptible regions are different, it is hard to infer which physical interpretation, such as susceptibility/tolerance of host or physical characteristics of the leaf surface, is the main reason for the higher accuracy of the model in N. glutinosa in comparison to N. tabacum cv. Xanthi nc. Based on the data presented in Table 4, it might be assumed that the production of more local lesions, especially in lower concentrations, might increase the accuracy of the prediction of virus concentration. In low concentrations, the growth curve, Kleczkowski, and modified Poisson models showed the best fit for high concentrations, and the modified Poisson model and Furumoto and Mickey model II converge to a maximum local lesion closer to the observed values. Therefore, we suggest using the modified Poisson model for predicting the concentrations of the ToBRFV in unknown samples.

Like other quantification methods such as qRT-PCR, for each new bioassay trial, a new dilution curve needs to be derived, because the slope of the dilution curve might not be constant among all individual experiments. As the average number of local lesions of each virus concentration in different trials might vary, this can affect the slope of the applied model. This observation was already made when the original models for TMV were developed [51].

It should be mentioned that the minimum number of virus particles that could cause a local lesion is still unknown. However, all the models can predict the minimum load of the virus needed for the production of a lesion. However, the interpretation of the minimum load depends on the assumption of the models. In the modified Poisson model and Furumoto and Mickey models I and II, it corresponds to the concentration of a virus suspension in which one particle can infect one cell (one-particle-one-region assumption). In the case of the Kleczkowski model, it corresponds to the distribution of a minimal dose of virus for the production of a lesion, and the growth curve model has no physical interpretation.

The inherent limitation of bioassay-based models is the need to observe at least one local lesion in any half-leaf unit to estimate the virus concentration. This means for any concentration that does not cause local lesions, models might underestimate the concentration as a negative control. This could be remedied by increasing the number of repetitions and decreasing the dilution factor from 10 or 5 to 2.

Therefore, in our experiment, we calculated two different virus concentrations: (a) the average of one lesion on all inoculated half-leaf units and (b) the observation of only one lesion in a total of 24 half-leaf units. In the case of ToBRFV on N. glutinosa in this study, based on the Kleczkowski model, they were calculated as 0.00321 mg/mL and 8.37 × 10⁻⁶ mg/mL for items a and b, respectively. It should be mentioned that real-time RT-PCR could detect a lower concentration of the virus, and it is more sensitive than a bioassay; therefore, based on plant health regulations, RT-PCR and real-time RT-PCR are recommended for the detection of the virus.

We showed the capability of the presented models based on bioassays in the estimation of the virus concentration in an unknown sample after fitting the models on serially diluted virus particles with a defined concentration (standard curve based on local lesion numbers). Thus, there is opportunity to quantify the virus concentration. In the case of disinfection treatments or any physical treatment (such as thermotherapy), the reduction in the virus titer can be measured, and subsequently, the efficacy of the treatment can be calculated. Based on our knowledge, it is the first report of the quantification of ToBRFV based on bioassay and it offers new insights through the assessment of viral load. In addition, the presented analysis and assessment of bioassay data could also be used in other fields of application where quantitative evaluation is required but chemicals/ingredients hamper RT-PCR, such as screening for antiviral agents, polymers, and virucides. For example, quantitative changes in virus titers during disinfection treatments on seeds and even on different surfaces in greenhouses can be determined. Thus, the efficiency of those treatments can be ascertained in detail, and weak points caused by the process or the user can be identified and used to develop new control strategies.