**2. Abiotic stresses and relationship to virus outbreaks**

Earlier we introduced the definition of general stress response (GSR) which is an advanced subject describing multiple gene expression, mutation, protein transcription, mRNA translation, intracellular endoplasmic reticulum repair, DNA recombination and repair, epigenetic imprinting and motility [23]. It also includes specific RNA polymerases, such as in alphaproteobacteria, where the GSR is under the transcriptional control of the alternative sigma factor EcfG. EcfG regulates genes for proteins that are associated with the regulation of motility (escape) and biofilm formation (adhesion), by binding to the RNA polymerase to redirect general protein transcription towards stress response genes [12]. The stress response can include conversion from non pathogenic to pathogenic mechanisms to acquire

*Trajectories of RNA Virus Mutation Hidden by Evolutionary Alternate Reality Thermodynamic… DOI: http://dx.doi.org/10.5772/intechopen.100481*

nutrients under harsher, more competitive conditions. Infections prepare the nowpathogenic bacteria to withstand diverse host environments [24] defined by any range of abiotic stresses, whether in acidity, alkalinity, radioactivity, temperature extremes, nutrient and resource scarcity, drought or any mixed combinations of stresses and durations. Viruses may exploit the presence of these stress responses, including the RNA-dependent RNA polymerases for replication of their genomes or, in retroviruses, the reverse transcriptase to produce new viral DNA which can be integrated into the host DNA under its integrase function [25]. Interestingly, the arrival of virulence and infection of genes at specific, appropriate times, frequencies and sites also stimulates patterns that resemble wide-sweeping oscillations of outbreaks (**Figure 2**) [24, 26].

Formalisms in statistical mechanics and thermodynamics have been used previously in order to describe the lifecycle of pathogenic viruses, from mutation to evolution and infection [5].

Viral mutation rates are caused by a number of processes including:


Retroviruses are viruses with RNA-containing virions and a cellular DNA stage [27]. Para-retroviruses are viruses with DNA-containing virions and a cellular RNA stage [20]. Both mutate and evolve at rates similar to riboviruses. Riboviruses are non-reverse transcribing RNA viruses [28].

#### **Figure 2.**

*Comparison of drought and non-drought virus infection patterns, where drought represents an example of abiotic stress impact on infectiousness-patterns: Circles represent cycles of growth, and cycles of nutrient (gas) exchange between symbiont species in a given habitat; Drought triggers vertical (chronic re-infection of a host), likely due to the limited host-population growth in times of drought-related resource limitations. Horizontal infection results in chronic virus re-infection, and can include host DNA to virus transfer. Source: the author, F.H. Campbell.*

In general, the list of habitat stresses on bacterial mutation rates can result in:


In Drake et al., mutation-rate calculations for DNA-type viruses are based on the effective genome size *Ge* for transforming a mutant frequency *f* into a mutation rate, where *f* is measured for large populations that had accumulated mutants in the putative absence of selection. In Zhao et al., the mutation rate in the SARS-CoV genome was estimated to be 0.80–2.38 � 10–3 nucleotide substitution per site per year, well within the magnitude of RNA viruses. The most recent common ancestor of the 16 sequences was inferred to be present as early as the spring of 2002, the outbreak of SARS [37]. Khailany et al. describe the current SARS-CoV-2 with genome size between 29.8 kb to 29.9 kb and 116 mutations implicated in the severity of infection and spread - including the three most common mutations: 8782C > T in ORF1ab gene, 28144 T > C in ORF8 gene and 29095C > T in the N gene [38]. For comparison, examples of mutation rates for non-SARS viruses in general are shown in the table below (**Table 1**).

Pathogenic RNA viruses that encode complex RNA-dependent RNA polymerase bearing a 3<sup>0</sup> exonuclease domain will mutate slowly [40, 41] and indeed, the SARS-CoV-2 viruses mutate in four months in order to accumulate knowledge about the infective host [19] and successfully bypass the host immunity, including those who were early-vaccinated such as with mRNA, mod-mRNA vaccines and possibly


*Trajectories of RNA Virus Mutation Hidden by Evolutionary Alternate Reality Thermodynamic… DOI: http://dx.doi.org/10.5772/intechopen.100481*

#### **Table 1.**

*Mutation rates of non-SARS pathogenic viruses and genome size. Adapted from Sanjuán et al. [39].*

others will inevitably show success by activation of cellular anti-viral proteins known as zinc antiviral proteins (ZAP) and APOBEC-3. ZAP and APOBEC-3 diminish a virus by detecting its foreign CG-dinucleotide before it infects, simply by comparing it to its own native RNA as part of natural innate immunity response. However, the slow-rate (four months) SARS mutations allow the virus to successfully bypass this antiviral protein in mass-vaccinated humans.

Thermodynamic models in the research all consistently recognize that a cell is infected with one or more virus particles, and that each infecting genome is copied iteratively such that complementary strands accumulate in the host, eventually producing final strands of the same polarity as the infecting strand, so that these final strands are then packaged and released throughout the host [30]. It is assumed that "final" strands rarely (or never) re-enter the beginning of the cycle within a single infection. In this way, the mutation frequency *f* is the same as the mutation

rate *μ* per replication. And so, if *n* number of complementary strands are copied from a template and if *μ* is the mutation rate per copying event, then the number of mutations will be *nμ*, and *f* ¼ *nμ=n* ¼ *μ*.

But, thermodynamic research of habitats does not establish relationships between mutations and spreadrate /infectiousness locations in a habitat and what drives the location: Is it just the population dysbiosis? Is it just the habitat stress?

For example, *J* might represent a infectious spread rate and *N <sup>j</sup>* the infected population, the number of mutations occurring in a pathogenic outbreak could be described an effective infection rate *μij* per habitat.

*Ji* <sup>¼</sup> <sup>P</sup>*<sup>n</sup> <sup>j</sup>*¼1*μijN <sup>j</sup>* for pathogenic virus infection spread rate requiredwhere, *<sup>μ</sup>ij* is the

infection matrix which in the limit as *lim N <sup>j</sup>*!0 *∂Ji ∂Ni* � � and is symmetric when *<sup>μ</sup>ij* <sup>¼</sup> *<sup>μ</sup>ji* and

which could be crudely integrated over an entire habitat per host-species nonhomogeneously over time. However, this sort of model evaluation is largely unable to describe the wavelike nature of outbreaks in the infections caused by virus mutation following an ecological threat. In addition, no part of it satisfactorily allows sensitivity to the interaction between the host and virus, as a thermodynamic instability which would result in the oscillatory periodic moment of spread. We need a method to include entropy production *<sup>∂</sup><sup>s</sup> <sup>∂</sup><sup>t</sup>* þ ∇*Js* ¼ *σ*; *σ* ≥0 and the flux of pathogenic virus throughout a habitat in response to a habitat stress, resulting in a non-uniform infectiousness.

But how can we forecast thermodynamic stability of a habitat in this equation? What are the specific thermodynamic limits and how is this represented or accommodated in mutation responsive virus nature?

We might try to show that, when an ecosystem's resources are severely constrained, a higher re-infection rate occurs. This requires investigation of models from the research to do with the replication conditions in RNA viruses that predominate poststress outbreaks. If so, we find from Drake et al. and Pathak and Temin [32, 42]:

	- a. Transcription by the host RNA polymerase produces one RNA genome.
	- b. Reverse transcriptase then catalyzes two replications in order to generate a DNA-based chromosome that integrates into the host chromosome,

including of a different cell for packaged retroviruses, or of the same cell in the case of a retrotransposon.

c. Thereafter it assumes a far lower mutation rate so that the resulting mutant frequency is the sum of the mutation rates of all three steps. Drake [43] notes that retro-element rates are roughly an order of magnitude lower than the RNA-virus rates and that retroviral mutation rates do not appreciably reduce specific infectivity and render more resistance to increased mutation rates (e.g., Spleen necrosis virus, which is obliterated only after a roughly 13-fold increase.)

After obtaining the entropy production and mutation rates for given species of infectious viruses, we need an understanding of the host immunity resistance proteins and their interactivity with virus mutability [41, 44]. Mutability of the viruses is correlated inversely with genome size [30, 41]. Unfortunately the solution for modeling becomes much more complex because each host immunity resistance proteins are transient in very short intervals of expression and mutating virus variants are population-wide processes rather than merely intracellular-driven [41].

It is worthwhile to insert a comment here: For example, SARS-CoV-2 viruses colonize specifically anaerobic proteobacteria commonly found in the gut of livestock. These bacteria likewise have a range of mutations according to abiotic environmental stress related gene-signaling. They include *Prevotella* (found in the gut of bovine, ovine, swine, avian livestock); Streptococcus (bovine, ovine and camel), *Bacterioides* (gut of swine, and hind-gut of avians) and *Mycoplasma pneumoniae*, *Haemophilus influenzae and Pseudomonas aeruginos,* which can be hosted by all the previously listed livestock. It is interesting to observe that livestock experience the most significant of stresses in rapid successive seasonal intervals (every six and nine months) when livestock are brought in large herds to be slaughtered. The slaughter process supports full resistance mutation processes resulting in the pathogenic conversion of these bacteria: animal confinement stress, heat-stress, food-stress (particularly before slaughter), dehydration stress, anxiety-panic stress, and trauma to the tissue from slaughter (and related death practices, such as live-animal steaming) and, of course, maternal stress towards offspring also butchered en measles. Vascular swelling from butchering [45–47] is part of the explosive discharge of gut-related bacterial organisms from slaughterhouse events into the ambient environment: This explains the relatively constant high pergenome mutation rate observed (0.003 per round of copy) [41] and at levels of 1,000,000 animals per week per slaughterhouse neighborhoods and livestock postbutchering products are all visibly the same location where COVID19, dementia, gastrointestinal diseases outbreaks are their absolutely highest [45, 48, 49]. In the period of 2019 through the year of this chapter's writing, COVID19 disease outbreaks were consistently describable as oscillatory or wavelike with dense centers and radiating lines of trajectory between the centers [50–52]. The locations did not repeat but also showed a pattern of shifting so that new outbreak locations or "hotspots" were observed. In mapping these outbreaks, the author noticed a clever relationship to mathematical lissajous-like oscillations. Would it be possible to describe the relationship between infectious spread so-called waves of outbreaks as a lissajous parametric trajectory?
