Life cycle synchronization is a viral drug resistance mechanism
[['Viral infections are a major cause of human morbidity and mortality [1] .', 'While vaccines to prevent viral illnesses have existed for over a century , it is only in the past several decades that drugs directly targeting viral replication have been developed .', 'Antiviral drugs now exist for pathogens including the human immunodeficiency virus ( HIV ) [2] , hepatitis B [3] and C [4] viruses , influenza A and B viruses [5] , herpes simplex viruses [6] , cytomegalovirus [7] , Epstein Barr virus [8] , and varicella zoster virus ( chickenpox virus ) [9] .', 'These drugs each target a specific phase of the virus’s life cycle , and by binding to a viral protein or otherwise interfering with a critical step in viral replication are able to reduce the virus’s growth rate .', 'Examples of viral functions targeted by antiviral drugs include binding of the viral particle to the target cell membrane , transcription of the viral genome , integration of the virus in the host cell genome , or post-translational cleavage of viral proteins .', 'Antiviral treatments that are initially successful at reducing viral loads may eventually be rendered ineffective , in individual patients or in entire populations , by the emergence of drug-resistant strains [7 , 10–15] .', 'Drug resistance occurs when a viral strain gains a mutation that allows it to replicate efficiently despite the presence of the drug , and this strain subsequently outcompetes the wild-type strain to reach high levels in the viral population .', 'Resistance can be conferred by mutations that interfere with the ability of the drug molecule to inhibit the intended viral target .', 'For example , for antivirals that block the fusion of viral particles with the target cell membrane , the mutations which confer resistance can alter the shapes and chemical properties of viral proteins to either prevent drug binding or allow the virus to enter the cell despite the presence of the drug .', 'There may , however , be another mechanism by which resistance can develop in viral populations .', 'In a 2000 paper [16] , Wahl and Nowak hypothesized that a heretofore unobserved effect , which they termed cryptic resistance , may prevent a viral population from being suppressed by an antiviral drug , without it needing to evolve the ability to alter drug binding or even complete its life cycle in the presence of the drug .', 'This insight was motivated by the realization that drug levels are not constant during the course of viral treatment , and hence the viral fitness in the presence of the drug is also time-varying .', 'Like most medications , antiviral drugs are administered in discrete doses of constant size separated by approximately equal time intervals .', 'Shortly after a dose , the drug is absorbed and drug levels are high , and the relevant stage of the viral life cycle is maximally inhibited .', 'However , between doses , drug levels decay , and may eventually reach low levels where they are no longer suppressive .', 'This pattern repeats periodically over the course of treatment .', 'These authors suggested that the virus could avoid the effects of the drug by always completing the targeted phase of its life cycle when drug concentrations are at a minimum .', 'If the length of the viral life cycle is a mutable trait , then in the presence of drug treatment it may evolve to become approximately equal to the duration of time between successive doses .', 'The virus population would then become synchronized with the pattern of drug levels .', 'In this manner , the virus could sustain itself indefinitely by “hiding” from the highest concentrations of the drug , even though it has no means of counteracting the effects of drug molecules when they are present .', 'Lifecycle timing , at least in some bacteriophages , is known to be a mutable trait subject to life history trade-offs [17–24] .', 'Separately , antibiotic “tolerance” in bacteria is contrasted with traditional “resistance” in that it only implies the ability to temporarily survive high drug levels [25] .', 'Tolerance can be heritable and traced back to particular mutations , and in certain in vitro settings , can even involve changes to the timing of particular growth cycle-dependent life cycle stages [26 , 27] .', 'However , since Wahl and Nowak’s original paper , no in vivo , in vitro , or in silico studies have examined whether cryptic resistance , perhaps more aptly called “tolerance by synchronization” , could actually evolve during antiviral treatment .', 'Here , we use mathematical models to show that tolerance by synchronization can plausibly arise in a viral population subjected to antiviral treatment .', 'We start by augmenting well-established models for viral infection dynamics to account for distinct phases of the viral life cycle .', 'This model includes a maturation rate , which can take on different values that result in different viral life cycle lengths .', 'Fluctuating drug concentrations are incorporated as a periodic time-dependent infectivity of the virus .', 'We evaluate the success of this tolerance strategy via two different methods .', 'First , we examine viral fitness in a single-strain infection by determining the growth rate and long-term infection size , and we compute the life cycle durations that optimize each of these values .', 'Next , to predict how an infection evolves , we study competition between multiple strains .', 'Specifically , we search for strains that can outcompete others and can persist despite drug treatment .', 'We discover that strains that are synchronized to the drug dose schedule—that is , have life cycle durations that are a near-integer multiple of the time between drug doses—can dominate the infection and cause sustained treatment failure , therefore conferring tolerance .', 'These strains would avoid detection by most genotypic drug resistance assays , which look for mutations only in the viral protein targeted by the drug therapy , and by in vitro phenotypic susceptibility assays , which apply constant , not periodic , drug levels .', 'Our results suggest that new experimental methods are needed to identify this potentially important new mechanism of antiviral resistance .'], ['The standard viral dynamics model makes the simplifying assumption that infected cells produce new virus particles as soon as they are infected [28] .', 'In reality , a virus must complete many stages of its life cycle before new virions are created .', 'These stages may include uncoating of the viral particle , transcription and translation of the viral genome , copying of the viral genome , assembly of viral proteins , or even cell cycle-dependent events .', 'While the exact steps involved in production vary among different viruses , all have in common a delay between infection of a cell and viral production [29] .', 'This intracellular delay is a prerequisite for drug tolerance via synchronization .', 'There are two common methods for incorporating delays into a dynamic model: first , by introducing a series of maturation phases , each represented by a state variable , and second , by using delay differential equations .', 'We explore both methods in this paper .', 'For the first method ( Fig 1A ) , we posit a series of n immature phases wi , ( similar to [30] ) :', 'x ˙ ( t ) = λ - β ( t ) x ( t ) y ( t ) - d x x ( t ) w ˙ 1 ( t ) = β ( t ) x ( t ) y ( t ) - ( m 1 + d w ) w 1 ( t ) w ˙ i ( t ) = m i - 1 w i - 1 ( t ) - ( m i + d w ) w i ( t ) ∀ 2 ≤ i ≤ n y ˙ ( t ) = m n w n ( t ) - d y y ( t ) ( 1 )', 'The size of the population of healthy target cells is described by the state variable x; these cells are produced at rate λ and die at per capita rate dx .', 'We consider the infected cell population as being subdivided into two subpopulations: “immature” ( wi , where the subscript i indicates the particular immature phase if there are more than one ) and “mature” ( y ) infected cells .', 'Immature cells in phase i progress to become immature cells in phase i + 1 ( or fully mature cells if i = n ) at per capita rate mi , and immature cells in phase i die at per capita rate dw .', 'Mature infected cells produce virus and lead to infection of healthy cells at rate proportional to the product of both their levels and the infectivity rate β ( t ) , and die at per capita rate dy .', 'We allow for the infectivity β to be time-dependent , since we assume that drug treatment acts on this parameter and that drug levels may vary over time ( detailed in next section ) .', 'The maturation time τ is the time required for a newly infected cell in the first immature infected state w1 to progress and become fully mature in state y .', 'We assume , for simplicity , that each maturation step occurs at the same rate , so mi = mn for all i .', 'The probability distribution of maturation times is therefore a Gamma ( Erlang ) distribution [31] that depends on the number of maturation steps , n , and the rate constant , mn:', 'p ( τ ) = m n n τ n - 1 e - m n τ ( n - 1 ) !', '( 2 ) We set the maturation rate , mn , to be a linear function of the number of maturation steps , n , such that mn = nm .', 'With this choice of mn , the average maturation time is independent of the number of maturation steps ( i . e . , 〈τ〉 = n/mn = 1/m ) .', 'The standard deviation in maturation times , however , is inversely proportional to both the maturation rate , m , and the square root of the number of maturation steps ( i . e . , σ τ = 1 / ( m n ) ) ( Fig 1B ) .', 'Therefore , for a given number of intermediate phases , n , strains with lower expected maturation times ( higher maturation rates ) have less deviation in their time to maturation than strains with longer expected maturation times .', 'Moreover , for a given maturation rate , m , more maturation steps would allow for the virus to better control its maturation time; in the limit of large n , the maturation time is fixed and equal to 1/m .', 'The second method for modeling intracellular delay uses delay differential equations with a fixed delay , τ = 1/m , between infection and start of virion production ( similar to [32–34] ) :', 'x ˙ ( t ) = λ - β ( t ) x ( t ) y ( t ) - d x x ( t ) y ˙ ( t ) = β ( t - τ ) x ( t - τ ) y ( t - τ ) e - d w τ - d y y ( t ) ( 3 ) As for the basic viral dynamics model , we can define the basic reproductive ratio , R0 , as the average number of new infections generated by a single infected cell over the course of its lifetime .', 'If β ( t ) = β is constant , then , in the multi-stage model , R0 is given by', 'R 0 = λ β d x d y ( n m n m + d w ) n ( 4 )', 'Similarly , in the fixed-delay model , R0 is given by', 'R 0 = λ β d x d y e - d w / m ( 5 ) In the limit of large n , the systems described by Eqs ( 1 ) and ( 3 ) are equivalent , and thus so are the expressions for R0 given by Eqs ( 4 ) and ( 5 ) .', 'If there is the possibility for an immature cell to die before producing virus ( i . e . , if dw > 0 ) , then R0 is maximized when the maturation rate , m , is maximized ( so that infected cells mature as quickly as possible ) .', 'If immature cells do not die ( i . e . , if dw = 0 ) , then R0 is independent of the maturation rate , m .', 'As in the basic model , R0 is sufficient to qualitatively determine the outcome of the system of equations .', 'If R0 > 1 , then the infection will persist and reach an equilibrium , and if R0 < 1 , then the infection will decline and eventually go extinct [30 , 35] For both models of viral dynamics , we also implemented a multi-strain competition between strains with different average maturation times ( see S1 Text for equations ) .', 'When β ( t ) = β is constant , an R0 value can be derived for each strain .', 'When dw = 0 , all strains have the same R0 value and can co-exist at values that can be calculated analytically .', 'When dw > 0 , the strain with the shortest maturation time has the highest R0 value and eventually outcompetes all other strains .', 'In addition , we also created stochastic versions of each of the single- and multi-strain models , where the rate of each reaction is equal to that in the differential equation formulation , and each reaction increases or decreases a state variable by 1 .', 'The stochastic process was simulated with the Gillespie next reaction method [36] .', 'In stochastic versions of the model , extinction can happen even when R0 > 1 .', 'Note that throughout this paper , we use a common assumption to simplify the viral dynamics model and reduce the computational burden of simulations .', 'For the vast majority of infections , the dynamics of free virions tend to be much faster than the dynamics of cells .', 'Virus is produced in large quantities and is rapidly cleared in vivo .', 'This implies that the free virus population tends to reach a “quasi-steady state” level with respect to the level of infected cells , implying that a separation of timescales can be applied to the system .', 'Consequently , we do not explicitly track free virus but instead assume that its level is proportional to the abundance of infected cells .', 'With this assumption , our infectivity parameter β ( t ) is actually a composite parameter given by β ( t ) = b ( t ) k/c , where b ( t ) is the infectivity of a free virion , k is the rate constant for production of free virus by mature infected cells , and c is the rate constant for clearance of free virus .', 'Ordinary differential equations were numerically integrated with the Scipy odeint algorithm in Python 2 . 7 [37] , and delay differential equations were numerically integrated with the Scipy-based DDE solver ddeint [38] .', 'For results presented in the main text , we choose parameter values that roughly correspond to HIV infection ( Table 1 ) .', 'Throughout the paper , we often present results for the case of no death of immature infected cells ( i . e . , dw = 0 ) , since in this case , the value of R0 in the presence of constant drug levels is independent of the maturation rate , m , and the number of maturation stages , n , which makes it easiest to see how R0 changes under periodic drug levels .', 'However , we also present results for cases with other values of dw , including the most natural assumption: that immature infected cells die at the same rate as uninfected cells ( i . e . , dw = dx ) .', 'Since immature infected cells are not yet producing new virions , they are less likely to', 'a ) experience direct cytotoxic effects of virus production and release , and', 'b ) be presenting viral epitopes and triggering cytolytic immune responses , so their death rate may resemble that of healthy uninfected cells .', 'We model the effect of an antiviral drug on the infection by assuming that it reduces the infectivity in a manner that depends on the drug concentration , D ( t ) , which varies over time .', 'We first model the periodic time-dependence of drug levels as an on-off switch .', 'The drug is taken every T days and completely inhibits new infections for a time fT thereafter , such that β ( t ) = 0 for that time; we refer to this time as the on window .', 'For the remaining time between doses , we assume the drug to be completely inactive , such that β ( t ) = β0 for that time; we refer to this time as the off window .', 'We also refer to f as the efficacy of the drug; a perfect drug therapy would have efficacy equal to 1 ( see Fig 1C ) :', 'D ( t ) = { 1 , if t mod T < f T 0 , if t mod T > f T β ( t ) = β 0 ( 1 - D ( t ) ) ( 6 ) We also considered drug dynamics that follow a simple pharmacological model .', 'When the drug is taken consistently , drug levels D ( t ) peak immediately at Cmax following each dose and then decay exponentially with half-life th , reaching a minimum value C min = C max 2 - T / t h , before the next dose .', 'Infectivity is reduced in a concentration-dependent manner that is described by a Hill dose-response curve , where β0 is the infectivity in the absence of treatment , IC50 is the concentration at which 50% inhibition occurs , and M quantifies the steepness of the decay curve:', 'D ( t ) =Cmax2−t/thβ ( t ) =β01+ ( D ( t ) IC50 ) M ( 7 ) Drug efficacy can be varied in this model by changing Cmax , th , IC50 , or M . However , wherever Eq ( 7 ) are used , we choose to vary th only .', 'For any parameter combinations used in this model , we can always find a corresponding f value for the on-off model in Eq ( 6 ) such that the time-average rate of infection is equal between the two models .', 'Indeed , throughout the paper , we express overall drug efficacy values using the single quantity f for both models .', 'In addition to modeling perfect adherence to periodic drug treatment , we consider imperfect adherence .', 'We assume there is a fixed probability of taking each dose at the scheduled time or missing it completely , and that each dose is taken independently .', 'In the on-off model , a missed dose results in a full drug period with D ( t ) = 0 .', 'In the pharmacological model , drug continues to decay after a missed dose , and a subsequent dose increases the concentration by Δ = Cmax − Cmin .', 'Example values of R0 ( t ) under this model are shown in S1 Fig . When viral fitness is time-varying , as is the case under fluctuating drug concentrations , the above calculations for R0 no longer hold .', 'A time-averaged R0 value ( R ¯ 0 ) could be calculated that takes into account the time-dependence of the infectivity , R ¯ 0 = R 0 ( 〈 β ( t ) 〉 ) .', 'However , as we will show below , this average R0 is no longer sufficient to describe the outcome of the model .'], ['In this paper , we showed that it is possible for a virus population to synchronize its life cycle with the pattern of drug therapy .', 'This process allows for strains to persist and cause treatment failure during anti-viral treatments where success would be expected .', 'Although originally called “cryptic resistance” when it was first proposed by Wahl and Nowak [16] in 2000 , we have opted for the updated term “tolerance by synchronization” , which reflects the current terminology in microbiology for differentiating between the ability to grow despite sustained ( “drug resistant” ) versus transiently ( “drug tolerant” ) high drug levels .', 'Here , tolerant strains survive repeated , transiently high drug levels via heritable life cycle timing .', 'The main condition needed for emergence of tolerance by synchronization is tight control of viral life cycle timing .', 'This tight control ( i . e . low variance ) may be achieved even if each life cycle stage has random duration , as long as there are sufficiently many stages .', 'In order for viral synchronization to be a feasible mechanism for drug tolerance , the life cycle length of wild-type virus must be at least close in magnitude to the dose interval ( or an integer multiple thereof ) since it may be unrealistic to assume that a virus could dramatically change its life cycle length .', 'To this end , we examined the viral generation time—defined as the average time from the moment one cell is newly infected until one of its offspring infects a new cell—and the recommended dosing schedules for viral infections for which targeted therapy is available ( Table S1 Table ) .', 'This includes HIV , hepatitis B virus , hepatitis C virus , herpes simplex virus 1 and 2 , cytomegalovirus , and influenzavirus A and B . We found that in all cases , the conditions for possible synchronization were met .', 'Although current experimental methods of characterizing resistance generally preclude identification of synchronization-based mechanisms ( detailed below ) , there are some hints of effects in which synchronization may play a role .', 'For example , for HIV it is known that resistance mutations to protease inhibitors can occur outside the protease gene ( e . g . [44] ) , and for hepatitis C virus , there are many examples of clinical failure without a known resistance mutation , or multi-drug resistant strains with no known mechanism ( e . g . [45] and references therein . ) The “resistance” mechanism described here is aptly “cryptic” in the sense that it would evade detection by all existing in vitro tests for drug susceptibility .', 'Genotypic resistance tests typically look for amino acid changes in the viral sequence which codes for the protein targeted by the drug , and particularly regions important for drug binding .', 'Since a gene influencing viral life cycle length could appear anywhere in the genome , such tests would likely miss these mutations .', 'In order to adapt these tests , experiments would need to be done to identify genetic loci associated with life cycle length and then adapt resistance screens to look for changes at these sites .', 'Phenotypic resistance tests suffer a similar problem: they measure in vitro viral replication against a series of drug levels , but since these levels will be constant within the culture media , synchronization cannot occur and strains conferring tolerance will appear fully susceptible .', 'These tests would need to be conducted in a device , such as a bioreactor or microfluidic chip , that could recreate drug profiles experienced in vivo to be able to detect tolerance via synchronization .', 'While we have shown that tolerance via life cycle synchronization is a possible means of evading therapy in silico , to our knowledge this effect has never been evaluated experimentally .', 'A first step would be to create an in vitro viral culture system that could deliver periodic drug concentrations , and to find a model viral infection system in which genetic determinants of life cycle control are already established .', 'Additionally , we would like to look for evidence of this strategy emerging in patients on antiviral therapy .', 'A first step could be to identify patients who have only partially suppressed viremia despite high adherence and who have virus that appears drug-sensitive by the genotypic and/or phenotypic resistance tests described above .', 'Although this work is the first we are aware of to explore the evolution of viral life cycles in response to drug treatment , previous work has explored other determinants of life cycle length evolution , in particular for bacteriophages [17–24] .', 'A classic question has been how long a phage should wait before lysing a host cell , when there is naturally a trade-off between benefit of delaying lysis to accumulate viral progeny within the cell , and the need to rapidly spread to other potential target cells .', 'Models of this process have characterized the determinants of lysis time in terms of , for example , host cell density and intracellular host resources [18 , 19] , but have not , to our knowledge , considered periodic effects .', 'We have incorporated ideas from this work into our model , showing that drug dosing period acts in combination with trade-offs between slowing maturation ( to produce more progeny ) and increasing maturation ( to either spread faster or avoid death ) to determine the optimal life cycle length .', 'The emergence of tolerance by viral life cycle synchronization can only lead to therapy failure , on its own , if trough drug levels are not fully suppressive .', 'Trough levels depend on drug dose and the kinetics of absorption and clearance ( e . g . Cmax and th ) , and suppression at trough levels depends on the viral fitness ( R0 ) in the absence of drug , and the parameters of the dose-response curve ( Eq ( 7 ) ) .', 'For drugs with a short half-life , a steep dose-response curve , and a narrow therapeutic window , it is more likely that worries about toxicity prevent reaching Cmax levels high enough to ensure that even trough concentrations prevent viral replication .', 'Cryptic resistance is most likely to occur in this regime .', 'Even if viral replication is suppressed for the wild-type strain throughout the dose interval , synchronization could augment partially-resistant mutations that act by standard mechanisms ( e . g . altering drug binding ) .', 'Here , we have assumed that the viral infectivity is instantaneously affected by the current drug level .', 'In reality , some drugs may need to undergo further steps , such as breakdown into active forms , active transport into cells , etc . , which could delay their effect .', 'These processes may alter the form of the periodic drug levels , but the periodic nature—and hence the potential for viral synchronization—will be preserved .', 'However , if the drug binds irreversibly to a cellular target that does not turnover or intracellularly to a viral target that is not continually produced , or does so reversibly but with a very slow dissociation rate , then there may be no periodicity in drug effect despite a periodicity in concentrations .', 'We assumed that the drug acts on the infection of new target cells by free virus .', 'However , the drug could also act on another phase of the life cycle , which could be represented as blocking the transition from one stage of immature infected cell to another .', 'Tolerance could potentially occur in these scenarios as well , since the main requirement for its existence is for synchronized strains to possess an evolutionary advantage over the others .', 'We saw that , in general , this is achieved through a tight control over the viral life cycle length .', 'For some viral infections , treatment is administered as combinations of different drugs , often with the same dosing schedules , that act on different stages of the virus life cycle .', 'In this case it is much harder for synchronization to confer a benefit , as it may be impossible for the virus to complete the multiple targeted stages of its life cycle at the time when both drug levels are low .', 'However , therapy failure could occur by a combination of resistance mechanisms—altered drug binding for one drug , and synchronization for the remaining drug .', 'In some viral infections , multiple infections of the same target cell may be common .', 'When infection contains multiple viral strains , complex dynamics within multiply-infected cells can alter evolutionary dynamics .', 'For example , recombination , by a variety of mechanisms , can occur and can have complex effects on selection [46] .', 'Phenotypic mixing or multiplicity reactivation can lead to production of virions with mismatches between genotype ( nucleic acid carried ) and phenotype ( structural and functional proteins carried ) , which also greatly complicates evolutionary predictions [47 , 48] .', 'Finally , within-cell competition can select for different traits than between-cell competition , for example leading to competitor colonizer trade-offs [49] .', 'Future models , designed to more precisely capture the details of particular viral infections , could include multiply-infected cells .', 'Our results show that common methods for calculating R0 have limited use when considering periodically administered therapies .', 'Even though a version of R0 can easily be constructed which takes into account the time-averaged viral fitness in the presence of fluctuating drug levels , this quantity does not discriminate between strains that can persist versus go extinct in the presence of the drug .', 'This is because the process of synchronization does not just apply to strains that have life cycle lengths very close to integer multiples of the drug period , and hence benefit most from the effect .', 'It also alters the long-term fitness of all strains .', 'Strains that are most asynchronous do worse than predicted by the time-averaged R0 .', 'This failure of existing methods for R0 is due to the combined presence of both time-dependent effects and a stage-structured model ( e . g . immature versus mature cells ) .', 'We have derived a method for calculating a version of R0 that does account for synchronization , and although there appears to be no simple expression for this quantity , it can be calculated numerically and can predict which strains will persist under periodic drug levels .', 'The system we analyze in this paper has parallels to population-level epidemic models in which there may be periodic fluctuations in disease parameters .', 'While the most common source of periodicity is seasonality [50] , which likely occurs on a timescale much longer than the generation time of infection , other periods , such as weekly changes in contact rates due to work/school days versus weekends , may occur on timescales for which interactions with the generation time are more relevant .', 'In fact , mathematicians studying such models have independently suggested constructs for the basic reproductive ratio under periodic model coefficients [51] , proved that their definitions represent persistence thresholds [52] , suggested algorithms to actually compute these quantities [53] , and determined the scenarios under which the simpler time-averaged approach is correct [53] .', 'They have even observed a phenomenon they call “resonance” [54] , in which the early growth rate of such models is enhanced if the period of environmental change is close to some natural timescale of the infection , which is analogous to the effect we observe and call synchronization .', 'While we have discussed tolerance via synchronization in the context of viral infections , this is by no means the only possible case .', 'Other microbial causes of infection , such as bacteria and protozoans , could also use this mechanism to avoid life-cycle-stage-specific drug targeting , assuming their life cycle length is greater than or equal to the drug period .', 'Similarly , cancer chemotherapy may be administered with dose intervals in the right range for cell cycle synchronization to occur .', 'These cellular organisms , as opposed to viruses , may not actually have to evolve synchrony via genetic changes , but may have the cellular machinery to make them capable of regulating cell-cycle length phenotypically .', 'In fact , in particular laboratory protocols used to grow and evolve bacterial cultures in the presence of antibiotics , an effect called “tolerance by lag” has been observed which bears some similarities to the viral life cycle synchronization that we describe here .', 'In the context of antibiotic resistance , “tolerance” is defined as the ability to temporarily survive high levels of bacteriocidal antibiotic , and can occur by either genetic or non-genetic mechanisms .', 'When bacteria are moved from a stressful environment where growth has been suppressed ( for example , crowded culture media ) , to a resource-rich environment ( e . g . , diluted into new media ) , there is a well-documented “lag” phase before cell growth and division resumes .', 'If cultured bacteria are repeatedly allowed to grow until stasis-via-overcrowding before being diluted and transferred , and if the transfer always involves a transient period of ( bacteriocidal ) antibiotic-treated media , then the population will evolve an altered lag time which matches with the length of antibiotic exposure [25–27] .', 'While this work suggests bacteria too could use synchrony as a resistance mechanism , it remains unclear whether the in vitro growth protocol designed to force a lag phase at the time of treatment is relevant to any process that naturally occurs during infection .']]
['Introduction', 'Model', 'Discussion']
['Viral infections are one of the major causes of death worldwide , with HIV infection alone resulting in over 1 . 2 million casualties per year .', 'Antiviral drugs are now being administered for a variety of viral infections , including HIV , hepatitis B and C , and influenza .', 'These therapies target a specific phase of the virus’s life cycle , yet their ultimate success depends on a variety of factors , such as adherence to a prescribed regimen and the emergence of viral drug resistance .', 'The epidemiology and evolution of drug resistance have been extensively characterized , and it is generally assumed that drug resistance arises from mutations that alter the virus’s susceptibility to the direct action of the drug .', 'In this paper , we consider the possibility that a virus population can evolve towards synchronizing its life cycle with the pattern of drug therapy .', 'The periodicity of the drug treatment could then allow for a virus strain whose life cycle length is a multiple of the dosing interval to replicate only when the concentration of the drug is lowest .', 'This process , referred to as “drug tolerance by synchronization” , could allow the virus population to maximize its overall fitness without having to alter drug binding or complete its life cycle in the drug’s presence .', 'We use mathematical models and stochastic simulations to show that life cycle synchronization can indeed be a mechanism of viral drug tolerance .', 'We show that this effect is more likely to occur when the variability in both viral life cycle and drug dose timing are low .', 'More generally , we find that in the presence of periodic drug levels , time-averaged calculations of viral fitness do not accurately predict drug levels needed to eradicate infection , even if there is no synchronization .', 'We derive an analytical expression for viral fitness that is sufficient to explain the drug-pattern-dependent survival of strains with any life cycle length .', 'We discuss the implications of these findings for clinically relevant antiviral strategies .']
['Viral infections such as HIV , hepatitis B , hepatitis C , and influenza may be treated with antiviral drug therapy .', 'These drugs generally block a specific phase of the virus’s life cycle , preventing it from replicating in the body .', 'Often , a virus population can evolve drug resistance by acquiring mutations that prevent the drug from binding and inhibiting it .', 'Here , we propose a new mechanism of drug resistance .', 'We use mathematical models and stochastic simulations to show that virus populations can build resistance to antiviral therapies by synchronizing their life cycle with the dosing pattern of the drug .', 'This process , which we refer to as “drug tolerance by synchronization” , can allow the virus to increase its overall fitness in the presence of the drug without altering drug binding .', 'We show that viral strains whose life cycle lengths are approximately integer multiples of the time between drug doses possess an advantage during drug therapy .', 'They can outcompete unsynchronized strains and lead to therapy failure with drugs that would otherwise have been successful .']
['antimicrobials', 'cell death', 'medicine and health sciences', 'viral transmission and infection', 'antiviral therapy', 'drugs', 'cell processes', 'immunology', 'microbiology', 'viral structure', 'preventive medicine', 'developmental biology', 'pharmaceutics', 'pharmacology', 'vaccination and immunization', 'public and occupational health', 'antimicrobial resistance', 'life cycles', 'virions', 'antivirals', 'cell biology', 'virology', 'microbial control', 'biology and life sciences', 'drug therapy']