Introduction

Viruses cause a variety of diseases that range from mild or asymptomatic to severe illnesses that can lead to death. Viruses have a nucleic acid genome, either RNA or DNA, that is surrounded by a lipid capsid containing surface receptors that allow the virus to interact with cells. Viral inactivation occurs when the proteins on the surface of the particle change shape, and as a result, lose their ability to function properly, removing their ability to infect cells (Keller et al. 2018; Snyder et al. 2019; Whitehurst et al. 2007). Understanding viral inactivation is important for determining transmission of viruses (Yue et al. 2019; Pinon and Vialette 2018; Predmore et al. 2015), but also plays a role in vaccine development (Dumard et al. 2017; Silva et al. 2015).

One key to understanding viral inactivation is to examine the dynamics of the conformational change that occurs during inactivation. Instead of studying conformational changes during viral inactivation using the entire virus, some studies investigate conformational changes on isolated proteins (Grgacic and Schaller 2000; Silnikov and Plotnikov 2018), on empty capsids (Poryvaev 1995; Moore et al. 2016), or on virus-like particles (Ausar et al. 2006; Snyder et al. 2019). An alternative approach is to use energy considerations to infer the types of structural changes that occur during viral inactivation (Cartwright et al. 1956; Barnes et al. 1969; Burge et al. 1983). This method uses Arrhenius plots, which relate decay constants to temperature, to determine the energy required to initiate the chemical reaction that causes loss of viral infectivity (Burge et al. 1983; Madani et al. 2014; Bozkurt et al. 2015; Allison et al. 1985). The value of this activation energy can provide insight into the type of chemical bond being altered (Allison et al. 1985). While inactivation energy has been calculated for a few viruses (Allison et al. 1985; Madani et al. 2014; Bozkurt et al. 2015; de Flora 1978), there has not been a comparison of inactivation energies of different viruses. Such a comparison could help determine whether there are commonalities in the mechanisms of loss of infectivity of different viruses.

A better understanding of the energy requirements needed for viral inactivation has practical implications. Viral inactivation is crucial for keeping food and blood products safe (Li et al. 2015; Ainley and Hewitt 2018). Knowing inactivation energies of different viruses can help in optimizing thermal treatments of food or blood products to eliminate viral pathogens (Huangfu et al. 2016). Inactivated viral particles are also sometimes used as vaccines (Delrue et al. 2012), so ensuring that all virus in the sample has been inactivated is crucial for vaccine safety. Conversely, live attenuated vaccines require that the virus is thermostable and does not become inactivated during transport and storage (Hansen et al. 2016; Clenet 2018).

Understanding the processes underlying viral loss of infectivity is also important for constructing accurate mathematical models of the infection process. Most viral kinetics models assume exponential decay of virus (Baccam et al. 2006; Perelson et al. 1996; González-Parra and Dobrovolny 2015; González-Parra et al. 2018), but recent studies suggest that this might not be an accurate assumption for all viruses (Beauchemin et al. 2019; Ailavadi et al. 2019; Bozkurt et al. 2015). Incorrect modeling of the mechanism of viral decay could lead to erroneous predictions of viral time courses, particularly when using models to estimate antiviral efficacy from viral decay rates (Palmer et al. 2017; Cardozo et al. 2020, 2017). Thus a better understanding of the mechanisms underlying loss of infectivity for different viruses is important for developing accurate viral kinetics models.

In this study, we collected viral inactivation data for a variety of viruses using data drawn from the literature. We calculated viral decay rates and used the Arrhenius equation to calculate the inactivation energy for each virus. We find that there is a wide range of inactivation energies for the different viruses and that some viruses appear to have multiple inactivation pathways.

Results

Viruses with Multiple Data Sets

We found multiple data sets for several viruses including influenza, respiratory syncytial virus (RSV), coronavirus, hepatitis, and norovirus. Details of the viruses and inactivation experiments are presented in Tables 1 and 2, respectively. Graphs of the linear fits to the viral inactivation data as well as the resulting parameter estimates are contained in the supplemental material. The slopes are used to generate Arrhenius plots that are also included in the supplemental material along with linear fits and parameter estimates. The slopes of the Arrhenius plots are used to calculate inactivation energy, as described in Methods. Inactivation energies for the different viruses are shown in Fig. 1.

Table 1 Virus details for influenza, RSV, coronavirus, hepatitis, and norovirus experiments
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Table 2 Experimental details of viral inactivation experiments for influenza, RSV, coronavirus, hepatitis, and norovirus
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Fig. 1
figure 1

Energy required for the conformational change leading to viral inactivation for different viruses: (top left) influenza virus, (top right) respiratory syncytial virus, (center left) coronavirus, (center right) hepatitis, (bottom) norovirus surrogates. Strain details can be found in Table 1

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Influenza

Influenza virus causes a respiratory infection that can lead to severe illness and death (Sarda et al. 2019). Influenza’s animal reservoir is in birds (Bodewes and Kuiken 2018) and various strains have jumped from birds to humans over the years (Horman et al. 2018). One possible mode of such transmission is through the environment (Rabinowitz et al. 2010), so understanding how easily different strains of influenza decay can give insight into which strains are more likely to be transmitted through the environment. We found five papers that described influenza inactivation data for different strains of influenza. One of these papers, by Handel et al. (2013), presented viral clearance rate as a function of temperature rather than raw viral load measurements from mock infections.

Inactivation energy for different strains of influenza virus is shown in Fig. 1 (top left). The different strains of influenza have similar inactivation energies with a strain of H6N2 (Graiver) having the smallest energy of \(6.01\times 10^{-20}\pm 0.15\times 10^{-20}\hbox { J}\) and a strain of H1N1 having the largest energy of \(1.94 \times 10^{-19}\pm 0.59\times 10^{-19}\hbox { J}\). These energies are suggestive of single chemical bonds which have typical binding energies in the range of \(\sim 0.5\)–\(1.5\times 10^{-19}\hbox { J}\). It is interesting to note that a different strain of H6N2 (Lebarbenchon) had a higher energy, although since the data is from two different studies, it is unclear whether this difference is due to differences in structure between the two strains or due to differences in experimental conditions. The Arrhenius plots for influenza are generally linear (supplemental material), suggesting the Arrhenius model is a reasonable assumption for the underlying dynamics of influenza virus inactivation.

Respiratory Syncytial Virus

RSV also causes a respiratory illness that is typically mild in adults, but can be severe in infants and the elderly (Walsh et al. 2013; Stein et al. 2017). There is currently no vaccine for RSV (Vekemans et al. 2019) and one of the stumbling blocks is the stability of the virus itself (Beugeling et al. 2019), so there is interest in understanding inactivation kinetics of RSV. We found three studies with the type of data described in methods.

Inactivation energies for RSV are shown in Fig. 1 (top right). The inactivation energies for RSV are generally about an order of magnitude lower than those for influenza, ranging from \(3.8\times 10^{-21}\pm 1.5 \times 10^{-20}\hbox { J}\) to \(5.1 \times 10^{-20}\pm 2.4 \times 10^{-20}\hbox { J}\), with the exception of the data from Hambling et al. which gives an inactivation energy of \(1.58 \times 10^{-10}\pm 0.75 \times 10^{-19}\hbox { J}\). These lower energies suggest that RSV is easier to inactivate and could help explain the difficulty in developing RSV vaccines that remain active over long periods of time. It is also notable that the Hambling and Rechsteiner Arrhenius plots are not particularly linear (the DeFord data only has three data points, making it difficult to judge linearity), suggesting inactivation of RSV is not caused by a simple conformational change in a single protein. A nonlinear Arrhenius plot suggests that there are two inactivation pathways (Vyazovkin 2016).

Coronavirus

Coronaviruses cause respiratory infections that range from the common cold to more serious illnesses such as severe acute respiratory syndrome (SARS), Middle East respiratory syndrome (MERS), and the recent COVID-19 pandemic (Paules et al. 2020; Corman et al. 2019). While primarily transmitted through respiratory droplets (Kutter et al. 2018), some coronavirus, like the one responsible for COVID-19, have been shown to remain active on surfaces for a long period of time (Kampf et al. 2020), allowing for transmission through contact with the surface. We found four papers describing the thermal inactivation of various coronaviruses: transmissible gastroenteritis virus (TGEV), mouse hepatitis virus (MHV), and the coronavirus responsible for SARS (SARS-CoV). TGEV and MHV, both viruses that infect animals, are considered experimental surrogates for SARS-CoV (Casanova et al. 2010; Farnsworth et al. 2006; Dellanno et al. 2009).

Inactivation energies of coronaviruses are shown in Fig. 1 (center left). Coronavirus inactivation energies are slightly higher than those of influenza, ranging from \(1.187 \times 10^{-19}\pm 0.016 \times 10^{-19}\hbox { J}\) to \(3.29 \times 10^{-19}\pm 0.24 \times 10^{-19}\hbox { J}\). It is not entirely clear if these are single bonds or double bonds—single bonds range from \(\sim 0.5\)–\(1.5 \times 10^{-19} \hbox { J}\) while double bonds are in the range of \(\sim 2.0\)–\(5.0 \times 10^{-19}\hbox { J}\). Coronavirus energies fall in both ranges. Coronavirus Arrhenius plots appear to be linear (supplemental material), suggesting a simple viral inactivation mechanism for this virus family.

Hepatitis

There are five viruses that can cause different forms of hepatitis (A, B, C, D, & E). These are not different strains of a single virus, but rather viruses originating from different virus families (Rasche et al. 2019) that all cause inflammation of the liver and can exhibit different clinical manifestations (Su et al. 2002; Chu et al. 2001). Hepatitis A is caused by hepatovirus A (HAV), a single-stranded RNA virus from the picornavirus family (Cristina and Costa-Mattioli 2007). HAV does not have a traditional viral envelope, but the viral capsid is released in a quasi-envelope made of membranous vesicles (McKnight et al. 2017). Hepatitis B is an unusual reverse-transcription, partially double stranded DNA virus—one DNA strand contains the full genome, while a second shorter strand contains only half to one third of the nucleotides (McNaughton et al. 2019). HBV is an enveloped virus from the hepadnavirus family (Howard 1995). Hepatitis C is caused by an enveloped, single-stranded, positive sense, RNA virus of the Flavivirus family (Echeverria et al. 2015). Hepatitis D is caused by the hepatitis delta virus (HDV) that cannot cause infection on its own, but requires the presence of HBV (Abou-Jaoude and Sureau 2007). HDV is an enveloped, negative sense, single-stranded RNA virus (Elena et al. 1991). Hepatitis E is caused by the hepatitis E virus (HEV), a nonenveloped, positive sense, single-stranded RNA virus of the hepevirus family (Ahmad et al. 2010). Hepatitis A and E are primarily transmitted through food and water contamination (Miranda and Schaffner 2019), so there is interest in understanding how long they remain in the environment. We found six papers with sufficient data to assess the thermal stability of various hepatitis viruses, one of which (de Flora) only included decay rates as a function of temperature rather than viral load measurements of mock infections.

Inactivation energies for hepatitis viruses are presented in Fig. 1 (center right). Hepatitis viruses show a large range of inactivation energies from \(2.79 \times 10^{-20}\pm 0.29 \times 10^{-20}\hbox { J}\) for HEV to \(3.28 \times 10^{-19}\pm 0.32 \times 10^{-19}\hbox { J}\) for HAV. The HAV inactivation energy is suggestive of a double bond, while the remaining hepatitis viruses are more in line with single bond energies. Studies have shown that HAV can persist for several days on food and surfaces (Leblanc et al. 2019; Cook et al. 2018), which is in line with the higher energy required for inactivation of this virus. The Arrhenius plots for all hepatitis viruses are linear indicating a single chemical reaction pathway causes inactivation of the virus.

Norovirus Surrogates

Noroviruses cause serious gastrointestinal illnesses (Sell and Dolan 2018) and are commonly found in the environment (Goh et al. 2019). Due to the high infectivity of human norovirus (Manuel et al. 2018), Tulane virus and mouse norovirus are often used as surrogates for experimental investigations (Farkas 2015; Hirneisen and Kniel 2013; Belardo et al. 2008). We found four papers using norovirus surrogates with sufficient data for our analysis.

Inactivation energies for norovirus surrogates are shown in Fig. 1 (bottom). The inactivation energies for these viruses are generally a little higher than the inactivation energies for most of the other viruses we examined, ranging from \(1.42 \times 10^{-19}\pm 0.14 \times 10^{-19}\hbox { J}\) to \(2.95 \times 10^{-19}\pm 0.76 \times 10^{-19} \hbox { J}\), suggestive of a double bond being altered. While the data is limited, there is some evidence that the Arrhenius plots are not linear for these viruses, suggesting more complex mechanisms for inactivation of noroviruses.

Other Viruses

We found experimental data for a variety of other viruses, listed in Table 3. Details of the inactivation experiments are given in Table 4. The fits to this data, along with the Arrhenius plots and their fits are included in the supplemental material. The inactivation energies are shown in Fig. 2. Four of the viruses have notably high inactivation energies; rhinovirus, poliovirus (Dimmock data), HIV, and Alkhumra hemorrhagic fever virus all have energies of \(3 \times 10^{-19}\hbox { J}\) or higher, indicating a change in a double bond. The remaining viruses have inactivation energies near \(2 \times 10^{-19}\hbox { J}\) or below, suggesting changes in single bonds lead to inactivation of these viruses. Interestingly, there are two data sets for poliovirus that give very different estimates of inactivation energy. The Dimmock data gives a high inactivation energy while the Snowden data gives a low inactivation energy. The Arrhenius plot for the Dimmock poliovirus is not linear, but has a larger slope at higher temperatures. The Snowden data uses low temperature data (\({25}\,^{\circ }\hbox {C}\) and below), so is on the more shallow part (lower slope) of this curve, so this is a possible reason for the discrepancy.

Table 3 Virus details for other viruses
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Table 4 Experimental details for other virus
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Fig. 2
figure 2

Energy required for the conformational change leading to viral inactivation for different viruses

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Discussion

While there are other environmental conditions that will cause loss of viral infectivity, such as changes in pH (Nims and Zhou 2016), salinity (Carratala et al. 2013), and UV light (Totaro Garcia and Monte Barardi 2019), in this manuscript, we considered only temperature because it allows us to find the inactivation energy through use of the Arrhenius equation. We found the inactivation energies for a variety of viruses. The value of the inactivation energy tells us something about the type of chemical bond broken during the inactivation process. The majority of the viruses had energies below \(1.5 \times 10^{-19}\hbox { J}\) which is suggestive of a single bond being changed during the inactivation process. Rhinovirus, poliovirus, HIV, AHFV, and HAV all had high inactivation energies, indicating a double bond was likely being altered. Coronavirus inactivation energies were not clear-cut, and could be either single or double bonds.

The Arrhenius equation can be used to describe viral inactivation only if there is a single protein undergoing a conformational change during the process. We found that most of the viruses had data that was linear in the range of temperatures used in the experiments (indicated by R values close to 1). However, most viruses are likely to show multiple pathways for viral inactivation. For example, feline calicivirus was found to have at least two inactivation mechanisms; one involving a reaction with singlet oxygen, and one conformational change induced by other reactive oxygen and nitrogen species (Aboubakr et al. 2016). The MS2 bacteriophage was also found to have two different chemical reactions that led to inactivation of the virus (Wigginton et al. 2010). It is surprising then that we find so many linear Arrhenius plots. One reason for this is that many experiments used only three temperatures, making it difficult to detect nonlinearities in the Arrhenius plot. Another possibility is that there is a dominant reaction in the temperature ranges considered in these experiments, making the Arrhenius plot in that range linear. In order to detect nonlinearities and multiple inactivation pathways, more temperatures over a wider range will need to be used in inactivation experiments.

The majority of viruses investigated here had linear Arrhenius plots, the exceptions being RSV, norovirus, and poliovirus. There is already some evidence that viral decay for these viruses differs from that of other viruses (Beauchemin et al. 2019; Ailavadi et al. 2019; Tamrakar et al. 2017; Incardona 1974). These studies suggest that decay for these viruses is not a simple exponential, with norovirus being modeled by a Weibull function (Ailavadi et al. 2019), RSV decay being modeled best by a two-population model (Beauchemin et al. 2019), and poliovirus being modeled by either a damped exponential (Tamrakar et al. 2017) or biphasic decay (Incardona 1974). Some of these models suggest multiple pathways for viral inactivation. In particular, the two-population model (Beauchemin et al. 2019) could describe a virus population consisting of a wild-type virus and one whose surface proteins are more or less resistant to thermal inactivation (Keller et al. 2018). There are a number of different models that can be used to describe viral decay (Dean et al. 2020; Fischer et al. 2004) and there does not seem to be an obvious best mathematical description of viral inactivation for all viruses.

One limitation of this study is the limited data. The majority of data we found in the literature consisted of measurements of viral inactivation at only three or four temperatures. This limits our ability to judge whether the Arrhenius assumption is reasonable, since it is difficult to judge whether the Arrhenius plots are linear with so few temperature points. Another limitation is using a small range of temperatures, thereby getting an incomplete picture of the Arrhenius plots. Some of the data we collected clearly have nonlinear Arrhenius plots, and biphasic Arrhenius plots have also been observed for some viruses (Burge et al. 1983). This could potentially lead to an incorrect value for the inactivation energy as might have been the case for the low poliovirus inactivation energy found for the Snowden data which used temperatures below \({25}\,^{\circ }\hbox {C}\). Viral titer measurements might also be a source of error in these experiments (LaBarre and Lowy 2001), particularly at later time points when virions might have settled into aggregates that form single plaques in the titration assay. Finally, our ability to effectively compare the inactivation energies for different viruses is limited by the inconsistency in experimental conditions. Viral decay is known to be affected by not only temperature, but other environmental factors such as pH (DeFord et al. 2019; Randazzo et al. 2017), relative humidity (Yeargin et al. 2016), and pressure (Daher et al. 2017).

Materials and Methods

Mock Infection Experiments

Mock infection experiments start with some amount of initial viral inoculum placed in a container where there are no cells for the virus to infect. Infectious viral titer measurements are then taken over several hours or days to determine the loss of viral infectivity over time. We searched the literature for studies of viral inactivation using mock infection experiments at different temperatures. We required a minimum of 3 time points at each temperature to allow for measurement of the viral decay rate, as well as an estimate of the error in the measurement; and a minimum of 3 different temperatures. We found 30 papers with such experiments using a variety of different viruses (Table 5). Data was extracted from figures using WebPlotDigitizer. Details of the medium used in each experiment, temperatures at which measurements were made, and the cell culture used to measure infectivity are included in tables in the results section.

Table 5 Sources of data used in this study
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Data Analysis

Viral clearance rate was determined by linear regression of \(\log _{10}\) of virus as a function of time. Linear regression was performed using the polyfit function in the numpy package of python. The slope estimated from this fit is the viral clearance rate.

Our assumption is that a single conformational change in a viral protein leads to inactivation of the virus (Vyazovkin 2016). Under this assumption, the temperature dependence of the viral clearance rate should be given by the Arrhenius equation,

$$\begin{aligned} c = c_{\mathrm{max}} e^{-\frac{E_{\rm a}}{k_{\rm B} T}}, \end{aligned}$$
(1)

where c is the viral clearance rate, \(E_{\rm a}\) is the energy required to inactivate a single virion, \(k_{\rm B}\) is the Boltzmann constant, \(c_{\mathrm{max}}\) is the maximum clearance rate, and T is temperature in Kelvin. This function was also fit using linear regression of \(\ln (c)\) and 1/T. The slope of the fitted line is \(E_{\rm a}/k_{\rm B}\), so we can find the inactivation energy by multiplying slope by the Boltzmann constant.