entropy Article Survival of Virus Particles in Water Droplets: Hydrophobic Forces and Landauer’s Principle Edward Bormashenko 1 , Alexander A. Fedorets 2 , Leonid A. Dombrovsky 2,3 and Michael Nosonovsky 2,4,* 1 Department of Chemical Engineering, Biotechnology and Materials, Engineering Science Faculty, Ariel University, Ariel 40700, Israel; [email protected] 2 X-BIO Institute, University of Tyumen, 6 Volodarskogo St, 625003 Tyumen, Russia; [email protected] (A.A.F.); [email protected] (L.A.D.) 3 Joint Institute for High Temperatures, 17A Krasnokazarmennaya St, 111116 Moscow, Russia 4 Department of Mechanical Engineering, University of Wisconsin–Milwaukee, 3200 North Cramer St, Milwaukee, WI 53211, USA * Correspondence: [email protected]; Tel.: +1-414-229-2816 Abstract: Many small biological objects, such as viruses, survive in a water environment and cannot remain active in dry air without condensation of water vapor. From a physical point of view, these objects belong to the mesoscale, where small thermal fluctuations with the characteristic kinetic energy of kBT (where kB is the Boltzmann’s constant and T is the absolute temperature) play a significant role. The self-assembly of viruses, including protein folding and the formation of a protein capsid and lipid bilayer membrane, is controlled by hydrophobic forces (i.e., the repulsing forces between hydrophobic particles and regions of molecules) in a water environment. Hydrophobic forces are entropic, and they are driven by a system’s tendency to attain the maximum disordered state. On the other hand, in information systems, entropic forces are responsible for erasing information, if the energy barrier between two states of a switch is on the order of k T, which is referred to as Landauer’s principle. B We treated hydrophobic interactions responsible for the self-assembly of viruses as an information- processing mechanism. We further showed a similarity of these submicron-scale processes with the Citation: Bormashenko, E.; Fedorets, A.A.; Dombrovsky, L.A.; Nosonovsky, self-assembly in colloidal crystals, droplet clusters, and liquid marbles. M. Survival of Virus Particles in Water Droplets: Hydrophobic Forces and Keywords: viruses; bioinformatics; information; droplet cluster; Landauer’s principle Landauer’s Principle. Entropy 2021, 23, 181. https://doi.org/10.3390/ e23020181 1. Introduction Received: 1 January 2021 The recent COVID-19 pandemic has focused the attention of biophysicists and of Accepted: 28 January 2021 the broad research community on viruses. Indeed, viruses constitute an amazing class of Published: 30 January 2021 biological objects due to their intermediate position between living and non-living objects. Viruses have a genome encoded in a nucleic acid (either RNA or DNA) and replicate Publisher’s Note: MDPI stays neutral themselves; however, they do not possess the complex biochemical molecular apparatus with regard to jurisdictional claims in needed for the translation and transcription of the genetic information. Instead, they use published maps and institutional affil- the apparatus of an invaded living cell. In addition, viruses do not have a metabolism or iations. maintain homeostasis, which disqualifies them from being considered true living objects. On the other hand, parts of viruses have common features with physico-chemical self- assembling supramolecular structures, such as micelles, liposomes, and vesicles. This makes a thermodynamic analysis of the virus life cycle a significant objective for gaining general Copyright: © 2021 by the authors. insights on self-assembly processes in physical chemistry. Licensee MDPI, Basel, Switzerland. While the length of time that virus particles can survive in dry conditions remains debated, This article is an open access article they clearly prefer a water environment [1,2]. The recent study by van Doremalen et al. [3] distributed under the terms and showed that the SARS-CoV-2 virus remained stable in water droplets suspended in air for conditions of the Creative Commons an extended time. Earlier studies have suggested that viruses containing lipids are more Attribution (CC BY) license (https:// viable in moist air than in dry air [4]. The latter seems clear because the viruses can serve creativecommons.org/licenses/by/ as nuclei of condensation of water vapor. 4.0/). Entropy 2021, 23, 181. https://doi.org/10.3390/e23020181 https://www.mdpi.com/journal/entropy Entropy 2021, 23, 181 2 of 12 containing lipids are more viable in moist air than in dry air [4]. The latter seems clear Entropy 2021, 23, 181 because the viruses can serve as nuclei of condensation of water vapor. 2 of 12 Understanding the effect of temperature and air humidity on the survival of airborne viruses is very important for preventing the spread of infectious diseases. Harper [5] found that influenza and several other viruses survived better at low temperatures and Understanding the effect of temperature and air humidity on the survival of airborne viruseshigh relative is very humidity important (RH). for preventing Similar laboratory the spread ofobservations infectious diseases. were made Harper by [other5] found re- thatsearchers influenza [6–10]. and Viruses several can other survive viruses on survivedhuman skin better and at on low household temperatures and contaminated and high rela- tivesurfaces humidity [10–12]; (RH). however, Similar they laboratory do not observationssurvive on the were surface made of by ordinary other researchers materials woven[6–10]. Virusesfrom cotton can survivefibers. All on these human observations skin and on sugge householdst that and viruses contaminated need water surfaces or moisture [10–12 to]; however,survive [13]. they do not survive on the surface of ordinary materials woven from cotton fibers. All theseMany observations viruses use suggestatmospheric that virusesmicrodroplets need water to migrate or moisture for significant to survive distances. [13]. Re- che etMany al. [11] viruses estimated use atmosphericthe downward microdroplets flux of viruses to in migrate aerosols for created significant by sea distances. spray on Rechethe order et al. of [ 1110]9 estimatedper m2 per the day. downward These viruses flux of from viruses marine in aerosols sources created were by transported sea spray onin the orderatmosphere of 109 per for msignificant2 per day. distances. These viruses Note from that marine the number sources of were viruses transported in seawater in the is atmospheregigantic. According for significant to some distances. estimates, Note ever thaty liter the numberof seawater of viruses on Earth in seawater contains is 10 gigantic.11 virus Accordingparticles. to some estimates, every liter of seawater on Earth contains 1011 virus particles. Most livingliving organisms organisms maintain maintain the the stable stable conditions conditions needed needed for their for survival their survival through athrough complicated a complicated process referred process to referred as homeostasis. to as homeostasis. Viruses do Viruses not maintain do not their maintain own home- their ostasis.own homeostasis. Our hypothesis Our hypothesis is that viruses’ is that preference viruses’ forpreference an aquatic for environment an aquatic environment is related to theiris related need to to their maintain need thermal to maintain stability, thermal in particular, stability, one in required particular, for one information required processing for infor- duringmation theirprocessing “life cycle.” during their “life cycle.” Virus particles (virions) can be viewed as nanoparticles (Figure1 1);); however,however, viruses viruses are built of biopolymers (nucleic(nucleic acids and proteins) andand otherother organicorganic componentscomponents suchsuch as lipids. TheseThese organic organic compounds compounds are are sensitive sensitive to environmentalto environmental conditions. conditions. Many Many viruses, vi- suchruses, as such coronaviruses, as coronaviruses, are inactivated are inactivated at temperatures at temperatures of 55–60 of◦C[ 55–6010,12 °C]. From[10,12]. a thermo-From a dynamicthermodynamic point of point view, of virions view, arevirions mesoscale are mesosc structures.ale structures. With a typical With a linear typical size linear between size 20between nm and 20 300nm and nm, 300 they nm, are they much are largermuch thanlarger a than typical a typical atomic atomic scale, scale, but they but they are still are muchstill much smaller smaller than macroscalethan macroscale structures structures because because their molecular their molecular masses (usuallymasses (usually ranging 6 9 22 betweenranging between 10 Da to 10 106 DaDa) to are 10 much9 Da) smallerare much than smaller the Avogadro than the number Avogadro (NA =number 6.08 × 10(NA ).= As6.08·× far 10 as22 their). As geneticfar as their information, genetic information, the genome the of onegenome of the of smallestone of the porcine smallest circovirus porcine (circovirus17 nm) is built(17 nm) of 1760 is built base of pairs, 1760 whereas base pair thats, whereas of the largest that Pandoraof the largest virus Pandora (micron-sized) virus 6 is(micron-sized) built of 2.8 × is10 builtbase of pairs.2.8 × 106 base pairs. Figure 1. Schematic of an enveloped coronavirus (redrawn(redrawn fromfrom https://www.scientificanimations.https://www.scientificanima- com/wiki-imagestions.com/wiki-images).). The lengthlength scalescale betweenbetween 1 1 nm nm and and 0.1 0.1 mm, mm, which which is largeris larger than than an atomican atomic scale