Downloaded by guest on September 30, 2021 mueresponse immune govern that rules deployment. simple system’s of immune existence the tra- the different suggests to qualitatively This related take jectories. consistently infections mice, are when across even response that, other, host show each the we of Finally, host. components in the the may to immunopathology beneficial reveal be as we fact disease, interpreted host often impact and phenomena fitness the that parasite quantifying both By on bay. immunity while of at from proliferation recover of parasite to turnover host holding the which allows in accelerated, strategy, Late is supply. “juvenilization” RBCs their a restricts tac- infection, and scorched-earth RBCs the destroys in and both it siege which of in host reminiscent tics, the infection, strategy the a in Early deploys cells. parasitized comple- of to killing that the fashion strategies ment coordinated defense a suggests resource-directed in distinct analysis deployed realize Our are density. components parasite these and compo- that each disease of host contribution to relative RBC nent the and quantify parasite on and effect rates, distinct vital a response with immune each the components, decompose 3 We into targets. it (RBCs) infections cells the of parasite, quantify dynamics malaria rodent the to the underlying approach of dynamics. processes modeling death population data-driven and parasite a birth on use impact quan- we a its Here, requires of evolution pathogen account an and as titative disease response mounting host immune 2019) of by 12, driver the May a review understanding pathogens for Fully (received against 2019 response. 19, immune September themselves approved and defend CT, Haven, New Hosts Medicine, of School University Yale Medzhitov, Ruslan by Edited and 48109; MI Arbor, 16802; Ann PA Michigan, Park, University University, State 16802; Pennsylvania Sciences, Life the for a etso otadprst el,wih ntr,drcl affect and directly births turn, on in response which, host cells, parasite the and of host effects of net deaths the on host focuses 4). or (1, abundance to density its difficult parasite of be on function can a impact as it type’s symptoms function, cell type’s that cell quantify a with of equipped understanding even an However, and vaccines treatments. informed had have have immunotherapeutic that for popu- activity, some and including responsible host-cell successes, distribution, mechanisms many abundance, the the their characterize in to quantify changes that and approaches involved immunity, Mechanistic lations of challenge. study a the remains host fitness the asite of dynamics and (3). nature infection as to the response we quantify known coevolution, therefore host–parasite phenomenon must and di- a pathology, infection can inter- disease, host–parasite actions, cases, understand fully host To some 2). (1, in to immunopathology and, contribute evolve which rectly in and milieu proliferate ecological within-host pathogens the shapes response This W cells blood red Wale Nina of dynamics infections and malaria disease the to parasite- immunity vs. directed cell-directed host of contribution The www.pnas.org/cgi/doi/10.1073/pnas.1908147116 eateto clg n vltoayBooy nvriyo ihgn n ro,M 48109; MI Arbor, Ann Michigan, of University Biology, Evolutionary and Ecology of Department ee etk opeetr prahta explicitly that approach complementary a take we Here, par- and host on immunity of impact the quantifying Yet, d ocnanteptoe n rtc teffo harm. from itself protect and pathogen response a the mounts host contain the host, to a infects pathogen a hen eateto noooy enyvnaSaeUiest,Uiest ak A16802; PA Park, University University, State Pennsylvania Entomology, of Department a,1 | ate .Jones J. Matthew , o-onv.bto-pcontrol bottom-up vs. top-down | lsoimchabaudi Plasmodium n h red the and chabaudi, Plasmodium f eateto ahmtc,Uiest fMcia,AnAbr I48109 MI Arbor, Ann Michigan, of University Mathematics, of Department b ee .Sim G. Derek , | immunopathology b nrwF Read F. Andrew , | c eateto ilg,Pnslai tt nvriy nvriyPr,PA Park, University University, State Pennsylvania Biology, of Department ycrnu,diylf yl:Eey2 ,teeprstsinvade, parasites these h, of 24 Every advantage of cycle: take life shape data daily We experimental synchronous, and Methods). from infections nature and malaria (Materials the to response infer host the to Response. approach Host semimechanistic the of Decomposition an them. control achieve to Results to uses employs it host weaponry a the from strategies medi- distinct the that as effectors infection elucidate the from we on distinct focusing it, as thus response ate By host deployed. the are of they effects end what to as to hypotheses and formulate and how other to each relate to components and We burden distinct parasites. parasite the on as of pressure trajectories response selective the host a how the and examine disease of of picture driver quantitative a In a both proliferation. paint parasite we and doing, anemia) so component on (i.e., each symptoms each of host impacts of the both compute course then time data- and data a the experimental use from extract We to resources. to approach variously access driven their that control parasite, components decompose or parasites malaria distinct we kill mouse qualitatively Specifically, the into to fitness. chabaudi, response parasite host and the health host aadpsto:Dt n oerltdt hspprhv endpstdi ra (DOI: Dryad in deposited been have paper this to 10.5061/dryad.nk98sf7pk related code and Data deposition: Data 1073/pnas.1908147116/-/DCSupplemental. y at online information supporting contains article This 1 BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This Submission.y Direct PNAS a is article This interest.y competing no and declare D.G.S., authors The M.J.J., and paper; manuscript. y the protocols; the on wrote and comments A.A.K. personnel, provided A.F.R. and resources, N.W. laboratory data; analyzed provided A.F.R. A.A.K. A.A.K. and and D.G.S., N.W. M.J.J., N.W., research; research; performed designed A.A.K. and N.W. contributions: Author owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To otmyi atb epu n ugsssml ue that rules simple suggests deployment. response’s and immune the helpful the to govern be harmful fact as in seen reveals host—may responses—often work This immune shortening depend. some they and which that on parasites cells by starving of and lifespans only by the disease not but on infections control pathogens, each hosts killing immune of that impact birth the find the cell We down pathogens. quantify on break and effects death, distinct We and with cells. components populations pathogen into changes response and response immune host the of much, themselves? how how, defend of and understanding pathogens an requires should questions host these the How Answering or it? pathogen to sick—the host response infected an makes What Significance b,c,d n ao .King A. Aaron and , e etrfrteSuyo ope ytm,Uiest of University Systems, Complex of Study the for Center b etrfrIfciu ies yais ukInstitutes Huck Dynamics, Disease Infectious for Center ). y a,e,f . y raieCmosAttribution-NonCommercial- Commons Creative edvlpdasimple, a developed We www.pnas.org/lookup/suppl/doi:10. NSLts Articles Latest PNAS .chabaudi’s P. Plasmodium | f7 of 1

POPULATION BIOLOGY B

A

C

D

Fig. 1. Decomposing the host immune response. (A) The daily cycle of malaria parasites in the blood stage of infection. Each day, parasite offspring (merozoites) burst from RBCs and then attempt to invade new RBCs, wherein they mature and reproduce. In our model, the host immune response mod- ulates infection by killing RBCs and adjusting their supply. Samples were taken from experimentally infected mice each morning, before parasites had reproduced, and were processed to produce time-series data on infection dynamics (see B). (B) Time series of (i.e., immature RBC), para- site, and total (mature + immature) RBC densities. (C) Eq. 1 shows how these 3 data streams can be transformed into 3 synthetic variables (components of the immune response), which describe the impacts of the immune response on parasite proliferation and host health (anemia). In particular, RBCs can be killed by a response targeted at parasitized cells or by a response that kills RBCs irrespective of their infection status. Moreover, the host can modulate the supply of . The model works by projecting the density of RBCs and parasites at the next time step (t + 1) in the absence of any killing, given the abundance of RBCs and parasites at time t and the supply of RBCs at time t + 1. The deficit between these projections and the data is then partitioned among the indiscriminate and targeted killing components. (D) This procedure yields, for each infected mouse, time series of the 3 immune-response components. By comparing these trajectories across mice, we identify robust patterns which can be interpreted in terms of host defense strategy.

reproduce, and burst out of red blood cells (RBCs), which are tion of the nutrient; the complete data and analysis of all mice destroyed in the process (Fig. 1A). With measures of the den- can be found in SI Appendix. sities of parasites and RBCs, together with the rate at which Mice exhibited markedly different infection dynamics. As immature RBCs (reticulocytes) are supplied to the bloodstream expected, the initial growth rate of infections increased with the (Fig. 1B), and supposing that parasite reproduction is limited concentration of pABA that they were administered (F3,29 = 5.4; by RBC availability alone, one can forecast how many para- P < 0.01). Furthermore, while some mice experienced severe sitized and unparasitized RBCs should be present a day later. anemia—i.e., pathologically low numbers of RBCs (e.g., Fig. 2A, Observed deviations from this forecast can thence be attributed mouse 1)—or displayed a “shoulder” in the postpeak phase of either to a host response targeted at parasitized cells (“targeted the infection (e.g., Fig. 2A, mice 1 and 2), others did not (e.g., killing”) or to one that removes RBCs irrespective of their infec- Fig. 2A, mouse 3). tion status (“indiscriminate killing”; Fig. 1C and Materials and The model was sufficiently flexible that the dynamics of infec- Methods). Repeatedly applying this process to time-series data tion of all mice were well captured (Fig. 2 A–C). Despite the collected from experimental infections, we deduced the trajecto- variation in infection dynamics, the trajectories of the 3 response ries of each of 3 functionally distinct, time-varying components components were qualitatively similar across mice (Fig. 2D). (Fig. 1D): targeted killing, indiscriminate killing, and (restriction These functions were scaled to be commensurate with RBC of) RBC supply. densities, so that their magnitudes relative to RBC density deter- We applied this approach to data (densities of reticulocytes, mined the fate of RBCs and parasites (cf. Eq. 1). In the prepeak total RBCs, and parasites) collected daily from 12 experimentally phase (∼0 to 7 d), the targeted response increased rapidly and infected and 3 uninfected mice of the same genetic background peaked in concert with parasite density, while the indiscriminate (SI Appendix, Fig. S1). To generate variability in the infection response showed no discernible trend. Meanwhile, the supply of dynamics among the mice, they were split into 4 groups, each of reticulocytes went unchanged or even, in some cases, fell. Fol- which was supplied with a different concentration of a nutrient lowing the peak in parasite density, the targeted response fell (para-aminobenzoic acid [pABA]) that alters the growth rate and as the indiscriminate response and reticulocyte supply increased. dynamics of parasite populations but is not needed by the host (5, Strikingly, the trajectories of the latter 2 components moved 6). For brevity, in the main text, we show and analyze data from in tandem during this period (Fig. 2D). Once RBC num- the same 3 mice, each of which was given a different concentra- bers recovered (approximately day 15), the indiscriminate and

2 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1908147116 Wale et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 igo h neto,ams l ftelse fRC ol be could al. RBCs et of Wale losses the of all begin- almost the infection, At the cells. of unparasitized ning which and response, parasitized indiscriminate Rather, the both 43%). to removed to due 18 were emergence, losses range parasite RBC interdecile [across most to 33% (maximum mice] attributable destruction responsible [among losses RBC never mean of the was of proportion it emergence half height, time] its than parasite at more of was for contribution destruction RBCs the RBC from when to bursting Even parasites of 3C ). to fraction small (Fig. attributable a were Together, only supply. losses Notably, RBC anemia. RBC of induced restriction forces the 3 as in these well as reduction host, the 33%) and to 12 3A). range, on (Fig. potential for, (interdecile reproductive accounted parasite 22% limitation a RBC RBC and maximum, average, response its targeted the At of limitation. offspring impacts combined parasite the potential to reproductive their how- due of realize rapidly, to unable majority Very were parasites (erythrocytes). ever, the RBCs mature and from emerged rate, maximum their destruction parasite 3). on (Fig. component anemia response on quantified and each we of strategies, and effect defense disease, host the host putative and identify Par- fitness to hence and parasite Pathology on components on response Response Host targeted Fitness. the the of asite Effect and the magnitude, Parsing again. in once increased the decreased response as magnitude trajectories. responses of model order the same supply of their the estimate of smoothed of irrespective the are RBCs on responses and (ribbon) in these purple) interval shown killing”; confidence that are 90% (“targeted Note mice and only (pink). all line) cells for reticulocytes (solid parasitized trajectories mean resupply target model the that that fitted are and responses and Plotted host blue) RBCs. Data distinct killing; rate. 3 growth (indiscriminate of parasite status trajectories stimulates infection Estimated that (D) nutrient S2. a and pABA, S1 of C ( solution RBCs total 0% and a (B), and reticulocytes (A), RBCs parasitized of densities i.2. Fig. B iiainrsle rmRCdsrcinb h parasite the by destruction RBC from resulted limitation RBC near at grew populations parasite outset, infection’s the At h oe cuaeycpue h aaadyed h yaiso ulttvl itnths epne.(A–C responses. host distinct qualitatively 3 of dynamics the yields and data the captures accurately model The obte nesadteipc fec fthe of each of impact the understand better To

density/ µl blood D C B A 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 6 6 6 6 5 6 ...... 5 6 7 8 4 6 2 4 6 8 7 5 5 6 5 7 0 2 4 6 05 os os mouse mouse 2 mouse 1 01 20 15 10 0 n3mc hc ee(ett ih)fda005 ocnrto,000%concentration, 0.0005% concentration, 0.005% a fed right) to (left were which mice 3 in ) 5 day 01 20 15 10 os eoee rmaei.Ti a u oteconcomitant the to due was many This of anemia. from destruc- destruction recovered the mouse parasite as of well 70%) as 3A), to RBCs. (Fig. unparasitized 38 average range on indiscriminate responsible tion the (interdecile was of component 53% charac- response magnitude this was for the peak, anemia, its in At from increase response. an recovered by mice terized and declined bers the bring control. para- the to under response supplemented the population targeted parasite strategies the to by These cells available sick. infected of host resources “slaughter” the the make and limit RBCs site respectively, uninfected to strategies, of combined earth” killing which “scorched the and and “siege” supply represent count, reticulocyte RBC total of 2; restriction (Fig. 8, infection to not of 0 d did days 8 first mice uninfected did the infected than in more mice RBCs, any reticulocytes of in supply the losses Strikingly, increase 3B). huge (Fig. losses incurring day’s sup- failed despite previous RBCs reticulocyte the new of for of compensate supply restriction day’s to the each (interdecile as addition, anemia, cell In exacerbated ply unparasitized 9). 1 to were parasitized every of 1.3 cells more range for time parasitized average 4 killed the days, on host around these removed On days, the cells. few when unparasitized than a 100%), density, only to parasite 99 were peak range, there interdecile indeed, 99.5%; indiscrim- and, the (mean, by response cells unparasitized inate of removal the to attributed ept hspspa nraei niciiaeklig the killing, indiscriminate in increase postpeak this Despite num- parasite which in infection, of phase postpeak The 05 01 20 15 10 F model data 1,13 3 3 = Parasitized RBCs T Reticulocytes . otal RBCs 2, P Targeted killing Indiscriminate killing Reticulocytes Total RBCs Parasitized RBCs .) eahrclysekn,the speaking, Metaphorically 0.1). = esrd(lc)adfitd(orange) fitted and (black) Measured ) NSLts Articles Latest PNAS Figs. Appendix, SI | f7 of 3

POPULATION BIOLOGY A mouse 1 mouse 2 mouse 3 6 unrealized reproduction destroyed by targeted killing destroyed by indiscriminate killing 4 emerged from reticulocytes emerged from erythrocytes

2 offspring/ parasite offspring/ B 0 4 106 surplus 6 3 10 deficit

l blood turnover 2 106

1 106 RBC/ μ

1.00 C unparasitized & destroyed by indiscriminate killing parasitized & destroyed by emerging parasites 0.75 parasitized & destroyed by indiscriminate killing

0.50 parasitized & destroyed by targeted killing survived

0.25 fraction of RBCs 0.00 0 5 10 15 20 0 5 10 15 20 0 5 10 15 20 day

Fig. 3. Contribution of the different components of the host response to parasite fitness and host disease. (A) Contribution of the host to the (suppression of) parasite reproduction in 3 different mice (left to right), each of which was fed a different concentration of a nutrient that stimulates parasite growth. The dashed line indicates the maximum number of offspring that could be produced per parasitized cell in conditions of unlimited RBC availability; the fill area indicates the estimated number of offspring that successfully emerged (pinks), were destroyed by each of the killing responses (blues), or were not produced due to the limited availability of RBCs (brown). The black horizontal line indicates 1 offspring/parasite: When the blue area descends below this line, the parasite population is decreasing in size. (B) The uncolored part of the bar indicates the number of the previous day’s losses that were compensated for by the present day’s supply of reticulocytes (turnover); the colored section indicates the extent to which the present day’s supply of reticulocytes exceeded yesterday’s losses (“surplus”; black) or failed to compensate for them (“deficit”; red). (C) The relative contribution of parasites and each of the host responses to the fate of RBCs through time. Note that parasites can contribute to RBC destruction directly, by emergence, or indirectly via the targeted killing response. The white vertical line in A and C indicates the time of peak parasite density. Shown are the decompositions for the same 3 mice used in all other figures. Equivalent plots for the 9 other mice analyzed can be found in SI Appendix, Fig. S3.

increase in the supply of reticulocytes, which more than com- and the fall in the targeted killing response (Fig. 4A). Landmark pensated for the destruction of RBCs (Fig. 3B). In contrast a also marks the point where the magnitude of the reticulocyte to the prepeak phase, here, the host controlled parasite pop- supply and indiscriminate killing responses became tightly corre- ulation growth not by making RBCs scarce, but by altering lated, growing and waning with each other for the duration of the their demographic profile. Specifically, because the indiscrimi- infection (Fig. 4C). Landmark b marks the beginning of a third nate response increased in tandem with reticulocyte supply, the phase, where the indiscriminate response reached its peak and combined effect was to increase the turnover rate of RBCs, began to fall, along with the supply of reticulocytes. The growth markedly reducing their average age. Thus, although RBCs rate of the parasite population and targeted killing response became more abundant, parasites that successfully invaded an became decoupled and their trajectories more idiosyncratic in RBC still had a low probability of reproducing, since the RBC this phase. While the targeted response tended to grow during that they had invaded was likely to be cleared before they did this latter phase, only in some mice did parasite density stop so. Strategically speaking, this “juvenilization” strategy allows the falling or grow again, so as to form a “shoulder” in the parasite host to recover from anemia while restraining parasite growth. density curve, before finally falling to undetectable levels. In the final phase (days 15 to 21), both the indiscriminate killing and supply responses returned to roughly their initial Discussion levels. The targeted response, by contrast, remained at height- Understanding the character and dynamics of the host response ened levels and, in some cases, increased. to infection is essential if we are to apportion responsibility for Coordination of the Host Response. Though infection dynamics pathology between parasite and host, elucidate the role of the vary among mice, the components of the host response fol- immune response in shaping parasite traits, and, ultimately, pre- lowed stereotypical trajectories (Fig. 2D). This suggests that the dict the dynamics of infections. Here, we used a simple account- components may be deployed in a coordinated manner. To inves- ing scheme to decompose the host response into 3 functionally tigate this possibility, we plotted the trajectories of each response distinct components and to infer their respective dynamics. This against one another and against parasite density. This analysis decomposition allows us to formulate hypotheses regarding the revealed that the infection rolled out in 3 phases, separated by 2 strategic significance of aspects of the immune response. landmarks (denoted a and b in Fig. 4). Our analysis suggests that host responses to infection that In the first phase, the targeted response grew with the parasite have been interpreted as immunopathology may in fact serve population, as the reticulocyte supply fell and the indiscriminate as effective defense strategies. The restriction of the supply of response slowly grew. At landmark a, the parasite population and reticulocytes to the bloodstream at the outset of malaria infec- targeted killing response stopped growing and began to decrease. tions, the accelerated clearance of erythrocytes toward the end Notably, there was no time lag between the fall in parasite density of infections, and the destruction of uninfected erythrocytes

4 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1908147116 Wale et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 uhr ugsigta B iiainaoei ufiin to al. sufficient et Wale is alone several limitation with RBC debated, hotly that been suggesting have dynam- authors infections the to malaria control”) of (“top-down ics killing direct and control”) be to prove way, some this Indeed, in the disease. considered its (13). when host in adaptive may, and as it illness well responses of as consider aspects fitness mounted, must parasite host simultaneously on one the effects other, not, of of component or given context pathological a princi- is whether general the evaluating response illustrates in thus the that, analysis allowing ple Our while recover. survival to parasite host reducing compartment thereby blood turnover, accelerates conjunction , in clearance, augmented RBC with increased phase, para- an later of the potential destruc- in in reproductive the sites; the early shrink and cells particular, supply uninfected of reticulocyte In tion of populations. restriction the parasite infection, of that, malaria control of evidence the anemia provides the 3 analysis to (Fig. contribute Our infections do inter- 12). phenomena these been (7, while literature times, erythropoiesis the erythropoiesis at “ineffective” restricted in or “inappropriate” have, example, dubbed For been Each has and pathological. 7–11). primates as in refs. preted infections (e.g., malaria are of infections rodents rate. whose features growth mice parasite 3 well-known alters same that are the nutrient from a are pABA, of trajectories concentration These different blood. a of received microliter which per of units each in 3, are and RBCs 2 Figs. and in parasites displayed marked of is Densities day indicated. subsequent period Landmarks Each the 20. infection. the and intended; of 15, than point 10, parasites starting fewer 5, in the days summarized indicates indicating as dot occur, dots black-outlined that large large, The with response. dot, host a the with of components 3 the between 4. Fig. h eaiecnrbtoso eorelmtto (“bottom-up limitation resource of contributions relative The h opnnso h muersos r iial elyd vnaogmc ipaigdfeetifcindnmc.(A–C dynamics. infection different displaying mice among even deployed, similarly are response immune the of components The B and D C B A supply (R) Reticulocyte killing (N) Indiscriminate killing (W) Targeted density (K) Parasite ,te locnrbt motnl to importantly contribute also they C), N:Tetmn fteelnmrsi ossetars l iei h nlss ihteecpino ieta received that mice 2 of exception the with analysis, the in mice all across consistent is landmarks these of timing The (NB: D. h ahdrdln niae htprst est nrae nsm,btntal ieduring mice all, not but some, in increases density parasite that indicates line red dashed The ( D) S4.) and S1 Figs. Appendix, SI Indiscriminate killing (N) Targeted killing (W) Targeted killing (W) 10 10 10 10 10 10 10 10 10 10 10 10 10 10 5 6 5 6 7 5 6 7 ...... 5 6 5 7 5 5 6 5 7 5 5 5 6 5 10 10 10 5 5 2 0 10 10 10 3 b b 5 5 mouse . . 10 5 5 a a a a 4 10 10 10 6 6 5 1 10 10 10 6 6 6 b b . . a a b b 5 5 10 6 -7 a a a a 7 10 10 10 Reticulocyte supply(R) Reticulocyte supply(R) 5 2 5 Parasite density(K) a 10 a a a Time 10 10 3 5 5 os mouse3 mouse 2 b . . b 10 5 5 a 10 -12 4 and ( 10 10 da 10 b b b b 6 6 5 y b indnmc ih ebitbsdo hswr.Interestingly, work. this on based infec- built of be models might predictive dynamics simple, tion that consistent suggesting dynam- were mice, components infection across these to between response relationships host the ics, the of components different parasite in peak the 3A). surrounding fitness Fig. window density; period 5-d parasite to short 4- impacts the signifi- the within significantly (i.e., not during limitation would except resource RBCs densities, where of parasite transfusion boost the our cantly example, that For predicts performed. experimental be work that densities suggest RBC lim- we of resource growth, manipulation of parasite role limiting the in examine itation regulating further of To mechanism been infections. important not malaria an has as turnover pre- resource highlighted in why previously abundance explains reticulocyte likely on studies data vious of assumptions. absence model on the relied Similarly, efforts reticulo- previous of where measurements supply, explicit of previous cyte of with use removal our discrepancy phase direct from this arises acute and that findings suspect the limitation We resource in cells. of parasitized growth which combination population in a one parasite is by data slows we the host with explanation, consistent an the most such model the encompass that to find enough our While flexible (14–16). is phase acute model the in dynamics infection explain s 10 ) 10 10 dniytastosbtenrgmn fdpomn ftecomponents the of deployment of regimens between transitions identify b b 6 huhteewsvraini h eaiecnrbto fthe of contribution relative the in variation was there Though b 6 6 b a a . . 5 5 10 7 10 10 10 5 5 2 10 10 10 3 a a 5 5 a a . . 10 5 5 b b 4 10 10 10 6 6 5 10 10 10 b b a b a b 6 21 6 6 . . 5 5 10 7 decreasing increasing NSLts Articles Latest PNAS h relationships The ) | f7 of 5

POPULATION BIOLOGY we uncovered patterns of coregulation that contravened the reticulocytes and erythrocytes was calculated by multiplying their respective standard assumptions of many models of within-host infection proportions in the blood by the total RBC density. dynamics. Specifically, mechanistic models of immunity have commonly described the immune response as a predator–prey Model Structure. To decompose the host response to infection, we formu- interaction, whereby the immune response (the “predator”) lated a model of the interaction among RBCs, parasites, and 3 host-response grows as a function of the density of the infected cells (the components. The model tracked the concentrations of erythrocytes, Et ; retic- ulocytes, Rt ; and merozoites (parasite offspring), Mt , as functions of time t. “prey”) (17–19). Our analysis (Fig. 4) shows that the waxing Given these quantities, together with the values on day t of the targeted and waning of the targeted killing response is not a function of and indiscriminate killing responses (Wt and Nt , respectively), the model parasite abundance alone. A broader class of models may thus postulates that be required to accurately capture the within-host dynamics of    infections. Mt Kt = (Rt + Et ) 1 − exp − A complete understanding of the immune response requires Rt + Et   that we not only map its effects on parasite and host cells, as we Wt + Nt Mt+1 = β Kt exp − [1] do here, but also understand the mechanisms that mediate those Rt + Et   effects. Intriguingly, not only does our model describe phenom- Mt + Nt Et+1 = (Rt + Et ) exp − , ena common in the malaria literature (see above), but the patterns Rt + Et of coregulation echo findings in the wider immunological litera- ture. For example, the antagonism between the parasite-killing where Kt is the concentration of parasitized RBCs. Following empirical work response/parasite density and the supply response (Fig. 4D) is (25, 26), we assumed that all RBCs were equally susceptible to the parasite. α reminiscent of the antagonism of erythropoiesis by TNF and According to Eq. 1, each of the Kt parasitized cells contributes β merozoites hemozoin, which halt the production of reticulocytes (20, 21). to the population of day t + 1, if it is not first removed by 1 of the 2 killing The identification of the mechanisms underlying observed responses (Nt and Wt ). Note that the magnitudes of the killing responses patterns is unlikely to be routinely straightforward, however. are expressed in units of RBC density. The third host-response component We expect that, in general, multiple cell types and signaling is the supply of new reticulocytes into the bloodstream, R. We assume that molecules will mediate the responses we describe. For example, reticulocytes mature into erythrocytes in precisely 1 d (27). The form of Eq. there are several mechanisms that might be responsible for the 1 arises as the expectation of a stochastic urn process whereby each RBC increased removal of uninfected cells during malaria infections faces a chance of becoming parasitized or destroyed by the host response in proportion to the relative abundances of W , N , and M . As such, Eq. 1 is (8, 22, 23). Experimental manipulation of infection dynamics, in t t t deterministic, conditional on Nt , Wt , and Rt . Stochasticity enters the model combination with measurements of a panel of putative media- via the assumption that these variables are Gaussian Markov random fields tors [as per the procedures used in systems (24)], (GMRFs), with respective standard deviations σN, σW , and σR. Finally, the has the potential to tease apart which of the array of cell types variables R, E, and K are related to the data via an explicit model of measure- are the most sensitive predictors of each of the different com- ment errors. Specifically, measurements of parasite, reticulocyte, and total ponents of the host response that we describe. Population-level RBC densities on day t are assumed to be log-normally distributed around approaches, such as ours, that focus on the quantitative effects of their true values (Kt , Rt , and Et + Rt , respectively). the immune response are an invaluable complement to cellular- level approaches focused on immune mechanisms. By combining Model Fitting and Smoothing. The model has the form of a partially observed Markov process (28), for which efficient inference algorithms have been these approaches, we stand to gain a holistic understanding of implemented. Since our mice were inbred and of the same age, we assumed infection and immunity. that they shared values of the GMRF parameters σN, σW , and σR as well as the initial conditions E0, R0, W0, and N0 and measurement errors σPd, σRetic, Materials and Methods and σRBC. Since pABA concentration affects parasite reproduction rate, we Hosts and Parasites. Hosts were 15 6- to 8-wk-old C57BL/6J female mice. estimated a common value of β for each pABA treatment, but allowed each Twelve mice were infected intraperitoneally with 106 P. chabaudi para- mouse its own inoculum size, to account for experimental variation in par- sites of the pyrimethamine-resistant AS124 strain; 3 were left uninfected asite injection volume and to allow the inclusion of data from 2 mice that but received a sham injection of dimethyl sulfoxide to control for effects of received fewer parasites than was intended. We estimated inoculum size receiving an injection. To create variation in infection dynamics, 3 mice were and β via multiple linear regression applied to the first 4 d of data. We assigned to each of 4 treatments that received a 0.05%, 0.005%, 0.0005%, or estimated the remaining 10 parameters (σN, σW , σR, σPd, σRetic, and σRBC, 0% solution of pABA as drinking water, from a week before parasites were plus the initial conditions E0, R0, W0, and N0) using the IF2 algorithm (29) as inoculated. Uninfected mice received a 0% pABA solution as drinking water. implemented in the R packages pomp (28, 30) and panelPomp (31). Further details about model fitting can be found in SI Appendix. Infection Monitoring. Infections were monitored daily from the day of inoc- ulation (day 0) to day 21 postinoculation. A total of 14 µL of blood was ACKNOWLEDGMENTS. We thank James Fraser, the Huck Institutes Flow taken from the tail: 5 µL for the assessment of parasite density via qPCR Cytometry Facility (both at Pennsylvania State University), and David Adams (University of Michigan) for assistance with the design and implementation and 2 µL for the quantitation of total RBC density via a Coulter Counter of the flow cytometry protocol; and the members of the A.A.K., Woods, and (Beckman Coulter), as described (5). A further 2 µL was used for the Zaman groups (University of Michigan) for comments on the manuscript. quantitation of the relative abundance of reticulocytes (young RBCs) and This work was supported by NIH Grants R01AI101155 and U54GM111274 (to erythrocytes (mature RBCs) via flow cytometry (SI Appendix), and the A.A.K.) and by an NSF-supported Infectious Disease Evolution Across Scales remainder of blood for other assays not described herein. The density of Research Coordination Network research exchange grant (to N.W.).

1. M. E. Hochberg, An ecosystem framework for understanding and treating disease. 7. K. H. Chang, M. M. Stevenson, Malarial anaemia: Mechanisms and implications of Evol. Med. Public Health 2018, 270–286 (2018). insufficient erythropoiesis during blood-stage malaria. Int. J. Parasitol. 34, 1501–1516 2. A. L. Graham, J. E. Allen, A. F. Read, Evolutionary causes and consequences of (2004). immunopathology. Annu. Rev. Ecol. Evol. Syst. 36, 373–397 (2005). 8. M. G. Salmon, J. B. De Souza, G. A. Butcher, J. H. L. Playfair, Premature removal of 3. S. M. Hedrick, Understanding immunity through the lens of disease ecology. Trends uninfected erythrocytes during malarial infection of normal and immunodeficient Immunol. 38, 888–903 (2017). mice. Clin. Exp. Immunol. 108, 471–476 (1997). 4. R. Zinkernagel, On observing and analyzing disease versus signals. Nat. Immunol. 8, 9. G. N. Jakeman, A. Saul, W. L. Hogarth, W. E. Collins, Anaemia of acute malaria 8–10 (2007). infections in non-immune patients primarily results from destruction of uninfected 5. N. Wale, D. G. Sim, A. F. Read, A nutrient mediates intraspecific competition between erythrocytes. Parasitology 119, 127–133 (1999). rodent malaria parasites in vivo. Proc. R. Soc. Biol. Sci. 284, 20171067 (2017). 10. S. Looareesuwan et al., Reduced erythrocyte survival following clearance of malarial 6. P. F. Fenton, G. R. Cowgill, M. A. Stone, D. H. Justice, The nutrition of the mouse. 8. parasitaemia in Thai patients. Br. J. Haematol. 67, 473–478 (1987). Studies on pantothenic acid, biotin, inositol and p-aminobenzoic acid. J. Nutr. 42, 11. S. Looareesuwan et al., Erythrocyte survival in severe falciparum malaria. Acta Trop. 257–269 (1950). 48, 263–270 (1991).

6 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1908147116 Wale et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 0 .A lr,G huhi uorncoi atrmycnrbt oteaamaof anaemia the Casals-Pascual C. to contribute 21. may factor necrosis immune- Tumour Chaudhri, modelling G. to Clark, A. theory I. predator-prey 20. Applying Perkins, E. S. Fenton, A. 19. 8 .Wdr,Eooia n vltoaypicpe nimmunology. in principles evolutionary and Ecological Wodarz, D. 18. Metcalf E. J. C. 16. balance immunological The Steen, den Van E. P. Opdenakker, G. T.-T. Pham, Deroost, K. 12. 7 .I el rdtrpe qain iuaiga mueresponse. immune an simulating equations Predator-prey Bell, I. G. 17. Effect I. Mideo infections. N. malaria 15. acute of dynamics The Roode, de C. J. Yates, A. Antia, R. 14. Ewald, W. P. 13. aee al. et Wale ihhemozoin with erythrophagocytosis. (1988). and 99–103 dyserythropoiesis causing by malaria (2010). interactions. parasite interspecific within-host mediated, (2006). 705 9–1 (1973). 291–314 number. propagation effective the using dynamics malaria rodent the in malaria. in parasite and host between fteprst’ e lo elpreference. cell (2008). blood 1449–1458 red parasite’s the of 1994). nesadn n rdcigsri-pcfi atrso pathogenesis of patterns strain-specific predicting and Understanding al., et vlto fIfciu Disease Infectious of Evolution nvitro in attoigrgltr ehnsso ihnhs malaria within-host of mechanisms regulatory Partitioning al., et upeso feyhooei nmlra nmai associated is anemia malarial in erythropoiesis of Suppression al., et lsoimchabaudi Plasmodium and nvivo. in Blood ESMcoil Rev. Microbiol. FEMS 5927 (2006). 2569–2577 108, . rc .Sc od e.BBo.Sci. Biol. B Ser. Lond. Soc. R. Proc. m Nat. Am. Ofr nvriyPes xod U.K., Oxford, Press, University (Oxford Science 1–3 (2008). 214–238 172, Parasitology 8–8 (2011). 984–988 333, 0–5 (2016). 208–257 40, r .Haematol. J. Br. cl Lett. Ecol. ah Biosci. Math. 1027–1038 137, 694– 9, 275, 70, 16, 1 .Bret C. 31. King A. A. 30. Atchad Y. Nguyen, D. Ionides, Markov L. observed E. partially for inference 29. Statistical Ionides, L. E. Nguyen, of D. King, outcome A. A. and maturation. 28. reticulocyte course disordered the and alters Normal Ney, transfusion A. P. Blood 27. Stevenson, CBA/Ca M. M. of Yap, erythrocytes S. immature G. and 26. mature of Invasion Brown, started. N. getting K. Just Jarra, immunology: W. Systems Furman, 25. D. Tato, M. C. Davis, M. M. 24. Fernandez-Arias C. 23. Safeukui I. 22. 018/124921.646 (2019). 10.1080/01621459.2019.1604367 Assoc., Stat. 2019. August 19 Accessed https://kingaa.github.io/pomp/. 2.0.13.1. Version package, R (2015). maps. 719–724 Bayes 112, perturbed iterated, via models variable latent pomp. package R the via processes (2011). 152–157 chabaudi Plasmodium of line (1989). cloned a by mice Immunol. anemia. malarial (2016). promoting erythrocytes fected . the in removal erythrocyte and clearance ,E .Inds .A ig ae aaaayi i ehnsi models. mechanistic via analysis data Panel King, A. A. Ionides, L. E. o, ´ 2–3 (2017). 725–732 18, op ttsia neec o atal bevdMro processes, Markov observed partially for inference Statistical pomp: al., et aai nue nmatruhC8 eldpnetparasite cell-dependent T CD8+ through anemia induces Malaria al., et tal. et Sifcini mice. in infection AS lsoimcaad chabaudi chabaudi Plasmodium nisl hshtdleieatbde eonz unin- recognize antibodies phosphatidylserine Anti-self , ,S te,A .Kn,Ifrnefrdnmcand dynamic for Inference King, A. A. Stoev, S. e, ´ .Sa.Softw. Stat. J. net Immun. Infect. mBio –3(2016). 1–43 69, elHs Microbe Host Cell NSLts Articles Latest PNAS 0431 (2015). e02493-14 6, . rc al cd c.U.S.A. Sci. Acad. Natl. Proc. 7136 (1994). 3761–3765 62, Parasitology ur pn Hematol. Opin. Curr. 194–203 19, 157–163 99, | f7 of 7 .Am. J. Nat. 18,

POPULATION BIOLOGY