Aging-induced fragility of the immune system
FFragility of an aging immune system
Eric Jones a, ∗ , Jiming Sheng b, ∗ , Jean Carlson a, ∗∗ , Shenshen Wang b, ∗∗ a Department of Physics, University of California, Santa Barbara, California 93106, USA b Department of Physics & Astronomy, University of California, Los Angeles, California 90095, USA
Abstract
The adaptive and innate branches of the vertebrate immune system work in close collaboration to protectorganisms from harmful pathogens. As an organism ages its immune system undergoes immunosenescence,characterized by declined performance or malfunction in either immune branch, which can lead to diseaseand death. In this study we develop a mathematical model of the immune system that incorporates boththe innate and adaptive immune compartments, named the integrated immune branch (IIB) model, andinvestigate how immune behavior changes in response to a sequence of pathogen encounters. We find thatrepeated pathogen exposures induce a fragility, in which exposure to novel pathogens may cause the immuneresponse to transition to a chronic inflammatory state. The chronic inflammatory state of the IIB model isqualitatively consistent with “inflammaging,” a clinically-observed condition in which aged individuals expe-rience chronic low-grade inflammation even in the absence of pathogens. Thus, the IIB model quantitativelydemonstrates how immunosenescence can manifest itself in the innate compartment as inflammaging. Inparticular, the onset of a persistent inflammatory response strongly depends on the history of encounteredpathogens; the timing of its onset differs drastically when the same set of infections occurs in a differentorder. Lastly, the coupling between the two immune branches generates a trade-off between rapid pathogenclearance and a delayed onset of immunosenescence. By considering complex feedbacks between immunecompartments, our work suggests potential mechanisms for immunosenescence and provides a theoreticalframework to account for clinical observations.
Keywords: immunosenescence, innate and adaptive immune responses, computational and systemsbiology, mathematical modeling
1. Introduction
Infectious diseases as diverse as bacterial pneumonia, influenza, tuberculosis, herpes zoster, and mostrecently COVID-19 have an increased morbidity and mortality among the elderly [1, 2, 3, 4, 5, 6]. Especiallyin conjunction with global demographics that broadly reflect increases in age across the world’s populations(both due to prolonged life expectancy and declining birth rates), the prevalence of disease among the elderlyunderscores the need for a better understanding of how physiology changes with age [7]. In particular, itis acutely important to identify the causes of immunosenescence, the readily observed yet mechanisticallyvague deterioration of immune function in aged individuals.The vertebrate immune system targets and clears pathogens through the collaborative efforts of innateand adaptive immune responses: the innate immune system reacts quickly and non-specifically to pathogenicthreats, while the adaptive immune system acts more slowly and generates a pathogen-specific responsethrough clonal expansion of cognate T and B lymphocytes. To orchestrate this division of responsibility,extensive bidirectional interactions exist between the innate and adaptive immune compartments [8, 9, 10, 11,12, 13]. For example, dendritic cells in the innate compartment mediate the presentation of antigens to theadaptive compartment [14]. Conversely, T cells in the adaptive arm reduce the production of inflammatorycytokines and thus limit tissue damage caused by the innate immune response [15, 16, 17]. For example, ∗ equal contribution ∗∗ equal contribution Preprint submitted to Journal of Theoretical Biology May 27, 2020 a r X i v : . [ q - b i o . T O ] M a y xperiments with nude mice (a mutant mouse strain with low T cell levels) showed that death can ensuewithout this adaptive suppression of inflammation [16, 17].Immunosenescence manifests itself in both the innate and the adaptive immune branches. In the adaptivebranch aging is partially driven by thymus involution, which reduces the output of new naive T cells [18, 19,20]. Furthermore, a lifetime of persistent pathogen exposures (e.g. chronic infections like cytomegalovirus)leads to oligoclonal expansion of memory T cells specific to those pathogens. These physiological mechanismslead to an “imbalanced” repertoire of immune cells that is predominately populated by memory cells specificto frequently encountered pathogens, which limit the ability of the adaptive branch to respond to novelpathogens. Indeed, the increased fraction of CD8+ T cells caused by memory inflation has been associatedwith the immune risk phenotype (IRP), which has been found to predict impaired immune function andmortality [21, 22, 23].In the innate compartment, aging is associated with the development of a chronic low-grade inflammatoryresponse even in the absence of pathogen stimulation, called “inflammaging” [24]. The elderly often experi-ence chronic inflammation and possess elevated levels of pro-inflammatory cytokines [23, 25, 26, 27], whichhave been found to be strong predictors of mortality (for example, interleukin 6 has been associated withthe IRP) [23]. Prior theories suggest that inflammaging is facilitated by long-lasting pathogen encounters,cell debris and stress, and the reduced efficiency of the adaptive immune response [24, 28, 29]. Still, themechanisms underlying the onset of inflammaging— and in particular its connection to aging in the adaptiveimmune system— require further study.In an earlier mathematical model of the adaptive immune response, Stromberg and Carlson found thatrepeated pathogen exposures could lead to an imbalanced immune repertoire that was vulnerable to rarepathogens [30]. Around the same time, Reynolds et al. developed a model of the innate immune responseimmediately following a pathogen encounter. Based on these earlier models, in this paper we construct amathematical model of the coupled innate-adaptive immune system called the integrated immune branch(IIB) model, and demonstrate how immunosenescence can develop and trigger a chronic inflammatory re-sponse. Here, as in the earlier adaptive immune model, the onset of immunosenescence arises purely froman imbalanced immune repertoire, and occurs without any further assumptions regarding the degradationof cellular function with age. The IIB model explicitly incorporates the inflammatory response of the in-nate branch, T cell dynamics of the adaptive branch, and innate-adaptive crosstalk. It recapitulates severalclinically-observed signatures of immunosenescence: the ratio of naive to memory cells decreases over time[31], repeated exposure to chronic infections (e.g. human cytomegalovirus) induces immune fragility [32],and this fragility is characterized by chronic inflammation (“inflammaging”) [31, 23].With the IIB model, we first characterize the dynamics and steady states of the immune system inresponse to a single infection event. Then, the system is exposed to a series of pathogens that form aninfection history. This sequence of infection events causes overspecialization in the adaptive compartment andtriggers chronic inflammation. In particular, the order in which infections are encountered strongly influenceshealth outcomes, and can hasten or delay the onset of chronic inflammation. Further, by tuning resourceallocation in the adaptive compartment toward pathogen clearance versus suppression of inflammation,crosstalks between immune compartments may be directly manipulated. This manipulation reveals a trade-off between a delayed onset of chronic inflammation and rapid pathogen clearance. Our model provides amechanistic explanation of how accumulated pathogen exposures can cause immune fragility that leads toinflammaging and immunosenescence, and may serve as a foundation for quantitative studies of immunecrosstalk and aging.
2. Mathematical model
Extensive mathematical and computational modeling efforts have been made to better understand boththe innate and adaptive branches of vertebrate immune system [34, 35, 36]. Additionally, a rich literatureexists regarding the inflammatory innate response [37, 38, 39, 40, 41] and the adaptive immune repertoire[42, 43, 44, 45]. In particular, Reynolds et al. studied the positive feedback between activated phagocytesand collateral tissue damage [33], and Stromberg and Carlson modeled the accumulated loss of memory celldiversity over the course of a lifetime of infections [30]. In this study, we modify and synthesize the models ofReynolds et al. and Stromberg and Carlson to develop an integrated immune branch (IIB) model, in whichthe innate and adaptive immune branches work collaboratively to clear pathogens.2 − p pathogen P i P (1) i P (2) i P (3) i antigen presentation naive cells N i memory cells M i effector cells E i adaptive response phagocytes N ∗ tissue damage D anti-inflammatorycytokines C A innate response p Figure 1:
Schematic of the integrated immune branch (IIB) model.
An introduced pathogen prompts innateand adaptive immune responses that seek to eliminate the pathogen. The innate response (green) is adapted fromthe model of Reynolds et al . [33], in which the presence of a pathogen activates phagocytes that induce inflammationand the subsequent production of anti-inflammatory cells. The adaptive immune response (magenta) is adapted fromthe model of Stromberg and Carlson [30], in which presented pathogens (orange) activate naive and memory T cellsspecific to that pathogen, causing them to divide into effector cells that target the pathogen. In this model, thedelay in the adaptive response due to antigen presentation is hard-coded via the compartments P (1) i , P (2) i , and P (3) i using the linear chain technique. The state variables of this model are described in Table 1, the model itself is givenexplicitly in Table 2, and the parameters of this model are provided in Table 3. A schematic of the IIB model is depicted in Fig. 1, and a thorough accounting of the individual componentsof the innate (pathogen P i , phagocytes N ∗ , tissue damage D , and anti-inflammatory cytokines C A ) andadaptive (pathogen P i , naive cells N i , memory cells M i , and effector cells E i ) models is provided in Table1. The coupled model is described in full in Table 2, and parameter descriptions and values are provided inTable 3. For more complete descriptions of the separate innate and adaptive immune models, we refer thereader to the original publications [33, 30]. In the model formulated by Reynolds et al . [33] (depicted in the green box of Fig. 1), once a pathogen P i is introduced, phagocytes N ∗ (which include, e.g., neutrophils and macrophages) are recruited to thesite of the infection by activation or migration. These phagocytes kill the pathogen P i by phagocytosis,degranulation, or by creating neutrophil extracellular traps. At the same time, these phagocytes releaseinflammatory cytokines that induce inflammation and tissue damage D in the host. Damaged tissue in turnreleases additional inflammatory cytokines, further promoting phagocyte activation. Following this initialinflammatory response, a wave of anti-inflammatory cytokines C A is released to downregulate phagocyterecruitment and to reduce inflammation and tissue damage.The steady-state behavior of this model was investigated by Reynolds et al . [33], who found that thisformulation of the innate immune response led to three possible steady states: health , in which the pathogenis cleared and the phagocytes and tissue damage vanish; septic death , in which the innate response is unableto clear the pathogen; and chronic inflammation , in which the innate response clears the pathogen at theexpense of inducing a constant inflammatory response that fails to dissipate, even after pathogen clearance.In the model’s original formulation this chronic inflammation steady state was named aseptic death , butin this paper we allow for the possible interpretation of this steady state as “inflammaging,” which is notnecessarily fatal, rather than death [46, 47]. As we will show, the IIB model retains these three steady stateswhile introducing interplay between the non-specific innate response and the specific adaptive response.3otation Immune component Description P i Pathogen • Harmful exogenous stimulants (e.g., bacteria or viruses) thatactivate an immune response • Pathogen of shape i (shape space formulation) N ∗ Activatedphagocytes • Phagocytes (which include neutrophils and macrophages) that areactivated by any pathogen P i or by pro-inflammatory cytokines • Responsible for removing pathogens P i , but cause collateral tissuedamage DD Tissue damage • Caused by activated phagocytes N ∗ • Causes release of pro-inflammatory cytokines that recruit additionalphagocytes N ∗ C A Anti-inflammatorycytokines • Small protein molecules that reduce the efficiency and recruitmentof activated phagocytes N ∗ • Production encouraged by activated phagocytes N ∗ and tissue dam-age D , and also by effector cells E (innate-adaptive crosstalk) N i Naive cells • Mature T cells with receptor specificity represented by shape i thatare agnostic to previous pathogen encounters • Divide and differentiate into memory M i and effector E i cells whenactivated by pathogens P i • Subject to homeostasis control mechanisms M i Memory cells • Long-lived cells differentiated from naive cells N i with the samepathogen specificity • Divide and differentiate into memory M i and effector E i cells whenactivated by pathogens P i • Subject to homeostasis control mechanisms E i Effector cells • Short-lived cells differentiated from naive N i and memory M i cells • Remove pathogen P i and produces anti-inflammatory cytokines C A Table 1:
Major biological components in the integrated immune branch (IIB) model.
Model equationsare provided in full in Table 2.
The IIB model also incorporates the adaptive immune response (shown in the magenta box of Fig. 1),which is based on the shape-space adaptive immune model of Stromberg and Carlson [30]. By assigningdiscrete “shapes” to pathogen epitopes and adaptive immune cells, this formulation allows pathogen-specificimmune memory and immune responses to be developed [48]. Thus, an introduced pathogen P i of shape i induces an adaptive response consisting of naive cells N i , memory cells M i , and effector cells E i thatall specifically target the introduced pathogen. There are S max available shapes. In the original model ofStromberg and Carlson, pathogens P i of shape i could interact with adaptive cells of some different shape j with a lowered binding affinity, but in this paper for computational efficiency we require that adaptiveresponses be activated by a pathogen of identical shape.The process of antigen presentation delays the activation of the adaptive immune response. This phe-nomenon is encoded in the IIB model with the linear chain technique (shown in the orange box of Fig. 1), inwhich the populations P (1) i , P (2) i , and P (3) i are intermediate states during antigen presentation [49]. Even-tually, the presented antigen P (3) i induces naive cells N i to divide into memory cells M i and effector cells E i ;and memory cells M i to divide into additional memory cells M i and effector cells E i . Once created, thesepathogen-specific effector cells E i work to clear the pathogen P i . The IIB model is described in full in Table 2, with descriptions and values of the parameters givenin Table 3. Next, we emphasize the modifications that synthesized the two separate innate and adaptive4 quation Interpretationd P i d t = k pg P i (cid:32) − | P | P ∞ (cid:33) − k pm s m µ m + k mp | P | P i − k pn f ( N ∗ ) P i − pγP i E i − ∆ ∗ P i Pathogen P i of shape i changes according to: • logistic growth, carrying capacity P ∞ ( |·| denotes the 1-norm) • inhibition by a non-local immune response • clearance by innate phagocytes N ∗ , effect is mediated by anti-inflammatory cytokines C A via f ( · ) • clearance by adaptive effector cells E i • sequestration by dendritic cells for antigen presentationd P (1) i d t = ∆ (cid:104) P i − P (1) i (cid:105) d P (2) i d t = ∆ (cid:104) P (1) i − P (2) i (cid:105) d P (3) i d t = ∆ (cid:104) P (2) i − P (3) i (cid:105) − βγP (3) i ( N i + M i ) • antigen presentation occurs with hard-coded delay (linearchain technique) of 3 / ∆ units of time on average requiredfor a pathogen P i to transition to compartment P (3) i • compartments P (1, 2, 3) i correspond to intermediate statesduring antigen presentation • once antigen arrives in compartment P (3) i it activates naivecells N i and memory cells M i d N i d t = − αγN i P (3) i + θ N − δ N N i | M | + | N | R Naive cells N i of shape i change according to: • division into effector cells E i (with rate f ) and memory cells M i (with rate 1 − f ) • constant production at rate θ N • return to homeostatic equilibrium (timescale 1 /δ N )d M i d t = (2 − f ) αγN i P (3) i + (1 − f ) αγM i P (3) i − δ M M i | M | + | N | R Memory cells M i of shape i change according to: • division into effector cells E i (with rate f ) and memory cells M i (with rate 1 − f ) • growth from naive and memory cell division • decay at rate δ M d E i d t = 2 fα ( M i + N i ) γP (3) i − δ E E i Effector cells E i of shape i change according to: • production by naive and memory cells proportional to antigenpresentation rate α • decay at rate δ E d N ∗ d t = s nr Rµ nr + R − µ n N ∗ Innate phagocytes N ∗ change according to: • activation by the presence of other phagocytes, pathogen, ortissue damage (encapsulated by R ) • decay at rate µ n d D d t = k dn f s ( f ( N ∗ , C A )) − µ d D Tissue damage D changes according to: • induced by activated phagocytes N ∗ , but ameliorated by thepresence of anti-inflammatory cytokines C A via f ( · ) • decay at rate µ d d C A d t = s c + k cn f ( N ∗ + k cnd D, C A )1 + f ( N ∗ + k cnd D, C A ) − µ c C A + (1 − p ) k ce | E || E | + E / Anti-inflammatory cytokines C A change according to: • production at constant rate s c • production related to phagocyte and tissue damage levels • decay at rate µ c • stimulation by effector cells | (cid:126)E | R = f ( k nn N ∗ + k np P + k nd D ) f ( x, C A ) = x (cid:16) C A C ∞ (cid:17) f s ( y ) = y x dn + y • R is an aggregation of signals that trigger the innate immuneresponse • f ( x, C A ) mediates the value of x according to the level ofanti-inflammation cytokines C A • f s ( y ) was phenomenologically fit by Reynolds et al . in theiroriginal formulation [33]Table 2: Full equations of the integrated immune branch (IIB) model that govern the dynamics of theimmunological state variables described in Table 1 . A full list of parameter values and descriptions is givenin Table 3. arameter Value Description Source Parameter Value Description Source k pg pathogen logistic growth rate [33] P ∞ pathogen logistic carryingcapacity [33] k pm pathogen clearance rate bynonspecific response [33] s m source rate of nonspecificresponse [33] µ m decay rate of nonspecificresponse [33] k mp rate of nonspecific exhaustiondue to pathogen [33] k pn rate of pathogen clearance byinnate response [33] γ p β P (3) j depletion byantigen presentation α θ N R δ N δ M f δ E s nr maximum phagocyterecruitment rate [33] µ nr phagocyte recruitmenthalf-saturation constant [33] µ n phagocyte decay rate [33] k dn rate of tissue damage dueto phagocytes [33] µ d tissue damage decay rate [33] s c source rate ofanti-inflammatory cytokines [33] k cn maximum activation ofanti-inflammatory cytokinesby phagocytes and tissuedamage [33] k cnd conversion rate betweentissue damage and phagocyteabundance [33] µ c anti-inflammatory cytokinedecay rate [33] k nn conversion rate betweenphagocyte abundance andaggregate innate response R [33] k np conversion rate betweenpathogen abundance andaggregate innate response R [33] k nd conversion rate betweentissue damage and aggregateinnate response R [33] k ce E /
10 half-saturation constant forcytokine production byeffector cells C ∞ scaling factor foranti-inflammatory cytokineabundance [33] x dn phenomenologically-inferredhalf-saturation constant [33] S max number of pathogen shapes inshape space [30] Table 3:
Typical parameters of the immune model in Table 2.
The parameters listed in this table are used togenerate Fig. 5, while the other figures are created with slightly modified parameters as detailed in the SupplementaryInformation. Most innate parameters were originally described in the Reynolds et al. model [33], while most adaptiveparameters were originally described in the Stromberg and Carlson model [30]. Parameter values that are the sameas those used in the original models are bold-faced. immune models.In the IIB model, the innate and adaptive components are linked in two ways. First, the two compart-ments are implicitly linked through the pathogen population: a higher pathogen load P i not only activatesmore phagocytes N ∗ in the innate compartment, but also leads to a higher rate of antigen presentation andsubsequent activation of naive N i , memory M i , and effector E i cells. Thus, depletion of pathogen by eitherresponse (by phagocytes N ∗ or by effector cells E i ) affects both compartments.Second, the two compartments are explicitly linked since effector cells E i can create anti-inflammatorycytokines C A that weaken the innate response. The suppression of inflammatory responses by effectorcells has been observed experimentally [15, 16, 17]. In the IIB model, effector cells are allocated eitherto clear pathogens or to promote the production of anti-inflammatory cytokines, in proportion to p and1 − p , respectively (dashed line in Fig. 1). The pathogen removal efficiency p may be varied from 0 to 1,so that in the limit that effector cells are solely responsible for pathogen clearance ( p = 1) no additionalanti-inflammatory cytokines are produced. Therefore, the synthesized model is capable of quantitativelycomparing the two adaptive immune functions of pathogen clearance and inflammation attenuation.The IIB model introduces homeostatic constraints that regulate the capacity of naive and memory cells.The rates of both homeostatic responses are dependent on the sum of the bulk naive cell population | (cid:126)N | ≡ time p a t h og e n a bund a n ce . . . . . . . p a t h og e n c l e a r a n ce r a t e P i (pathogen)pathogen clearance (adaptive)pathogen clearance (innate) Figure 2:
Pathogen abundance (orange, solid) is regulated by the innate and adaptive immune responsesin the IIB model.
The clearance rates of the innate response (green dash-dotted, rate given by k pn f ( N ∗ ) P i ) andthe adaptive response (purple dashed, rate given by pγP i E i ), as described in the d P i d t equation of Table 2, are plotted.The innate response is activated immediately, while the adaptive response is delayed due to the antigen presentationprocess (encoded with the linear chain technique P i → P (1) i → P (2) i → P (3) i ). Ultimately the combined immuneresponses manage to clear the pathogen. The parameters used to generate this figure are given in Table 3 and inTable S1 of the Supplementary Information. (cid:80) i N i and the bulk memory cell population | (cid:126)M | ≡ (cid:80) i M i . In the process of clearing a pathogen, memorycells accumulate. Afterwards, to satisfy the homeostatic constraints, naive cells must become less abundantthan they were before the infection. In the Supplementary Information, we derive analytic approximations tothe immune dynamics that are generated by these homeostatic relaxations; when the timescale of pathogenclearance is much shorter than the timescale of homeostatic relaxation, these expressions can be used as partof a dynamic programming approach to significantly speed up numerical simulations.
3. Results
In the IIB model, once a pathogen is introduced it initiates a cascade of immune responses in the innateand adaptive compartments, and these responses combat the logistic growth of the pathogen and attemptto drive it to extinction. Fig. 2 depicts a representative pathogen encounter and clearance, and plots thepathogen abundance (orange) as well as the pathogen clearance rates due to the adaptive effector cell (purple)and innate phagocyte (green) responses given by the quantities pγP i E i and k pn f ( N ∗ ) P i , respectively, as givenin Table 2. Note that the adaptive response is specific to the pathogen shape, while the innate response isnonspecific. For clarity only the lumped contributions of the innate and adaptive compartments to pathogenclearance are plotted in Fig. 2. The populations of every immunological variable are plotted for severalscenarios in Fig. 3.In Fig. 2 the logistic growth of the pathogen drives the initial pathogen spike, which is mildly temperedby a non-local immune response as described by Reynolds et al. [33]. Phagocytes are immediately recruitedand attack the pathogen, leading to the increase in innate pathogen clearance (green). Simultaneously, thecollateral tissue damage inflicted by phagocytes causes the production of anti-inflammatory cytokines, whichsuppress further phagocyte recruitment and tissue damage. Anti-inflammatory cytokines in conjunction with7 decreasing pathogen population cause the decrease in innate pathogen clearance. Once the pathogen ispresented to the adaptive immune branch— a delay that is hard-coded in the IIB model with the auxiliaryimmunological variables P (1) i , P (2) i , and P (3) i — the naive and memory cells specific to the presented antigendivide into effector cells. These effector cells subsequently contribute to the increase in adaptive pathogenclearance (purple). Ultimately, with the given parameter values (provided in the Supplementary Information)the innate and adaptive responses overpower the pathogen and drive it to extinction. In the process, memorycells specific to this pathogen shape proliferate and provide future protection in case the same pathogen isfaced again in the future, since the higher initial abundance of pathogen-specific memory cells will result ina more immediate adaptive response. The IIB model described in Table 2 exhibits steady states when the time derivatives of all the populationsvanish. This coupled model inherits many of the steady state characteristics of the constituent innate andadaptive immune models. In particular, this model exhibits steady states of (a) health , characterized byvanishing pathogen and immune response; (b) chronic inflammation , in which the pathogen clears but theinnate immune response is sustained in a positive feedback loop; and (c) septic death , characterized by thechronic presence of pathogen and activated immune responses. Realizations of these three steady states aredisplayed in Fig. 3, and the parameter sets used to generate each outcome are provided in Table 3 and inTable S1 of the Supplementary Information. In Fig. 4, phase diagrams demonstrate how different parameterregimes and initial conditions lead to different steady states. To observe the presence of these steady statesmathematically, note that a quantity P i may be factored out of the pathogen dynamics d P i d t , from which itis clear that at steady state the pathogen population ¯ P i must either be 0 or some nonzero quantity thatsatisfies P i d P i d t = 0. The three steady states immediately follow from the implications of choosing ¯ P i to bezero or non-zero. (a) Health steady state— If ¯ P i = 0 at equilibrium, then the intermediate pathogen states must vanish aswell ( ¯ P (1) i = ¯ P (2) i = ¯ P (3) i = 0). In the absence of presented antigen, the memory cells M i decay with timescale1 /δ M . When this timescale is slow relative to the homeostatic dynamics of the naive cells (whose dynamicsare of timescale 1 /δ N ), the naive cells N i tend towards their homeostatic equilibrium ¯ N i as described inEq. (S11) in the Supplementary Information. Lastly, all effector cells E i decay with timescale 1 /δ E , whichis assumed to be fast compared to the naive and memory cell dynamics. Thus, in the absence of pathogen,the adaptive immune response turns off and becomes dormant. In a steady state with ¯ P i = 0 the innateimmune response can either be “inactive” or it can be “active,” which lead to the steady states of health or chronic inflammation , respectively. When the innate immune response is inactive, the activated phagocytes N ∗ and tissue damage D are both zero. This implies that the aggregate innate response R is zero as well.Lastly, in the absence of the innate response and effector cells, anti-inflammatory cytokines equilibrate toa constant level. It is straightforward to check that setting ¯ P i = ¯ N ∗ = ¯ D = 0 and ¯ C A = s c /µ c leads to asteady state in this model.This health steady state is demonstrated numerically in Fig. 3a. In this figure, an initial pathogenresponse activates innate (green) and adaptive (purple) responses that eventually vanish. The naive andmemory cells change over the course of the adaptive immune response, and then remain at constant steadystate values. (b) Chronic inflammation steady state— When ¯ P i = 0 but the innate immune response is active, themodel reaches the chronic inflammation steady state. This steady state is inherited from the Reynolds etal . innate immune model [33], and occurs due to a positive feedback loop between tissue damage D andphagocytes N ∗ (as can be schematically understood based on Fig. 1). In particular, there exist equilibriumquantities ¯ N ∗ and ¯ D that precisely balance the activation of phagocytes and accumulation of tissue damagewith their respective decays µ n ¯ N ∗ and µ d ¯ D . This chronic inflammation steady state is shown in Fig. 3b:the pathogen is cleared and effector cells dissipate, but the innate response is perpetually sustained. (c) Septic death steady state— Lastly, the steady state in which the pathogen population is sustained iscalled septic death. For a steady state with nonzero pathogen ¯ P i , the values of the intermediate pathogenstates ¯ P (1) i , ¯ P (2) i , and ¯ P (3) i will be nonzero as well. Subsequently, the presented pathogen ¯ P (3) i sustains theactivation of naive, memory, and effector cells. In the innate compartment, the nonzero pathogen presenceimplies a nonzero aggregate innate response ¯ R , which implies a nonzero equilibrium population of phagocytes8
50 100 150 200 time . . . . . a bund a n ce health SS: pathogen P i = D = time a bund a n ce inflammation SS:chronic pathogen P i = D > time a bund a n ce septic death SS: pathogen P i > D > P i (pathogen) E i (effector cells) N i (naive cells) M i (memory cells) N ∗ (phagocytes) D (tissue damage) C A (anti-inflammatory cytokines) a) b)c) Figure 3:
The IIB immune model exhibits (a) health, (b) chronic inflammation, and (c) septic deathsteady states.
Components of the adaptive response are plotted in purple, while components of the innate responseare plotted in green. (a) An inoculated pathogen activates phagocytes, which in turn induce tissue damage. Followingantigen presentation, naive cells divide into memory cells and effector cells. The phagocytes and effector cells jointlysuppress the pathogen, which goes extinct, and the tissue damage gradually decays resulting in the health steadystate. (b) The innate and adaptive immune responses clear the pathogen, but in the process the innate response entersa positive feedback loop between phagocyte recruitment and tissue damage leading to persistent tissue damage andphagocyte activation, called the chronic inflammation steady state. (c) The innate and adaptive immune responsesdo not clear the pathogen, leading to the septic death steady state characterized by the presence of pathogen andtissue damage. The chronic inflammation steady state was obtained with smaller innate clearance rate k pm andsmaller tissue damage decay rate µ d than were used to obtain the health steady state. The septic death steady statewas obtained with a larger proportion of cognate cells that divide into effector cells f and a larger pathogen growthrate k pg than were used to obtain the health steady state. Explicit values of the parameters used for each panel aregiven in Table 3 and in Table S1 of the Supplementary Information. ¯ N ∗ , which in turn implies a nonzero equilibrium population of tissue damage ¯ D . Therefore, the septic deathsteady state is characterized by activity in both the innate and the adaptive immune compartments. Naiveand memory cells of the adaptive compartment continue to predominantly divide into effector cells; eventuallyall adaptive cells are exhausted and vanish while failing to clear the pathogen. This steady state is depictedin Fig. 3c.The rest of this paper uses a parameter regime that does not exhibit the septic death steady state: inparticular, simulations of this paper set f (the proportion of cognate cells that divide into effector cells)equal to 0 .
4, which causes memory cells to accumulate until they are able to produce enough effector cells9 aive cell IC M e m o r y c e ll I C Naive cell IC
Naive cell IC
Naive cell IC M e m o r y c e l Naive cell IC M e m o r y c
50 100 150 200
Health Chronic inflammation Septic death
Figure 4:
Phase diagram of immunological steady states as a function of naive cell and memory cellinitial conditions (ICs).
In IIB model, the immune system can reach health, chronic inflammation, or septic deathsteady state following a pathogen encounter, depending on the level of cognate naive and memory cells when thepathogen is introduced. The proportion f of cognate cells that divide into effector cells significantly influences thesteady state phase diagram and septic death can only occur when f ≥ . θ N = δ N = δ M = 0 in Table 2) during single infection events and initialpathogen level is P i = 1. Other parameters for generating the phase diagrams are as stated in Table 3. Except incurrent figure, f = 0 . to suppress the pathogen. When f is larger than 0 . f for different naive and memory cell initial conditions is plotted in Fig. 4. In the following text, wefocus on the transition from health to chronic inflammation, a process that is phenomenologically similar toinflammaging. Next we consider the immunological consequences that result from encountering a sequence of infectionevents. Infection sequences are composed of discrete infection events, and each infection event consists ofthe time course following the encounter with a particular pathogen shape until a steady state of the system(i.e. health, chronic inflammation, or septic death) is reached. For each infection event an immune responseis generated by simulating the IIB model, given in Table 2. When pathogen encounters are evenly spacedin time, the number of infection events acts as a measure of age. This infection sequence encodes a lifetimeof infection events, is different for different individuals, and serves as a vehicle with which to explore thevariable immunological outcomes experienced by different individuals over their lifetimes.More concretely, the IIB model is simulated for n tot infections that are ∆ T = 1000 time units apart. Thetime ∆ T is chosen to be sufficiently large so that the system reaches a steady state between infection events(i.e., infection events are well separated in time). The shape space in the IIB model is discrete, consisting of S max = 36 available pathogen shapes. For each infection event, the probability p i that a pathogen of shape i is encountered is given by p i = ζe − i/ξ , i = 1 , , . . . , S max , (1)where ξ = 20 / ζ satisfies (cid:80) S max i =1 p i = 1. This distribution allows for some pathogen shapes to bemore common than others, and is similar to the one originally used by Stromberg and Carlson [30]. Alifetime of infections is explicitly encoded in the infection sequence { S (cid:96) } , where each S (cid:96) is the pathogenshape encountered for the (cid:96) th infection event. Then, for each infection event (cid:96) = 1 , , . . . , n tot , a single unitof pathogen P S (cid:96) is added to the system at time t (cid:96) = 1000( (cid:96) − d) Infection events A v e r age e ff e c t o r c e ll E A v e r age a c t i v a t ed neu t r oph il N * Infection events A v e r age e ff e c t o r c e ll E A v e r age a c t i v a t ed neu t r oph il N * A v e r age a c t i v a t ed phago cy t e s N * f r e q u e n c y d e n s i t y f r e q u e n c y d e n s i t y infection events
40 60 80 100
Infection events F r a c t i on o f hea l t h y i nd i v i dua l s HealthASD
40 60 80 10000.20.40.60.81 infection events f r a c t i o n o f i n d i v i d u a l s i n d i ff e r e n t s t e a d y s t a t e s healthCI a) b) c) e) infection events t o t a l n a i v e c e ll s t o t a l m e m o r y c e ll s a v e r a g e e ff e c t o r c e ll s p e r i n f e c t i o n a v e r a g e a c t i v a t e d p h a g o c y t e s p e r i n f e c t i o n t r i a l - a v e r a g e d e ff e c t o r c e ll s t r i a l - a v e r a g e d a c t i v a t e d p h a g o c y t e s a v e r a g e e ff e c t o r c e ll s p e r i n f e c t i o n a v e r a g e a c t i v a t e d p h a g o c y t e s p e r i n f e c t i o n Figure 5:
Timing of the transition to chronic inflammation (CI) is highly variable and depends onprevious pathogen encounters. (a, b) Activity of the innate (green) and adaptive (purple) immune responsesover the course of 100 infection events for two different infection sequences drawn from the same statistical distribution.As a proxy for these responses, the average number of effector cells (cid:104) E (cid:105) ≡ T (cid:82) t (cid:96) +1 t (cid:96) | (cid:126)E ( t ) | d t and phagocytes (cid:104) N ∗ (cid:105) ≡ T (cid:82) t (cid:96) +1 t (cid:96) N ∗ ( t ) d t for each infection event (cid:96) are plotted. The sharp transitions indicate the onset of the chronicinflammation state, and occur at the 57th and 82nd infection events, respectively. (c) An ensemble average ofthe innate and adaptive immune responses over 1000 infection sequences (each drawn from the same pathogendistribution) smooths the variability in transition timing, though the distribution of immune responses is bimodal(c, inset). CI: chronic inflammation (d) The distribution of transition times to chronic inflammation is concentratedat earlier times (on average after 76 infections). (e) The accumulation of memory cells (blue) and depletion of naivecells (black) drives immune fragility and vulnerability to new pathogen shapes (50 infection sequences shown). Thesefigures are generated with the parameters given in Table 3, and with randomly generated pathogen sequences asdescribed in Eq. 1. and 7, the system is initialized with zero memory cells M i (0) = 0 and a uniform distribution of naive cells N i (0) = 200 across all possible pathogen shapes i = 1 , , . . . , S max .There are four important timescales in the IIB model: the time τ infec required for pathogen clearance,the interval ∆ T between infection events, and the timescales of naive and memory cell homeostasis control.Pathogen clearance is the fastest process, during which the homeostasis control still has little effect. Thetimescales of naive and memory cell homeostasis are characterized by the reciprocal of their decay rates, givenby 1 /δ N and 1 /δ M , respectively. Due to the longevity of immune memory, the interval between infections∆ T was chosen to be much shorter than the timescale of memory decay. Additionally, as in Strombergand Carlson naive cells are assumed to regenerate and equilibrate quickly relative to the rate at whichinfection events occur [30]. Thus, between infection events the homeostatic naive cell population dependson a slowly-decaying memory population. More explicitly, the four timescales in IIB model are chosen tosatisfy τ infec < /δ N < ∆ T (cid:28) /δ M .Over the course of an infection sequence, early infection events (e.g. before the 50th infection event) aresuccessfully cleared by the immune system, and the system returns to the health steady state. However, forlater infection events the system fails to recover and instead transitions to the chronic inflammation steady11tate, where it remains thereafter. This age-driven, history-dependent transition to chronic inflammation isqualitatively similar to “inflammaging.”Depending on the details of the infection sequence, the timing of the onset of chronic inflammation ishighly variable. Two instances of the transition to chronic inflammation, with different sequences of pathogenencounters generated from the same statistical distribution of pathogen frequencies, are displayed in Fig. 5aand Fig. 5b. The strengths of the adaptive (purple) and innate (green) responses during each infection eventare plotted in Fig. 5a and Fig. 5b, quantified by the average number of effector cells (cid:104) E (cid:105) and average numberof phagocytes (cid:104) N ∗ (cid:105) over the course of each infection, respectively. For the (cid:96) th infection, (cid:104) E (cid:105) ≡ T (cid:90) t (cid:96) +1 t (cid:96) | (cid:126)E ( t ) | d t, and (cid:104) N ∗ (cid:105) ≡ T (cid:90) t (cid:96) +1 t (cid:96) N ∗ ( t ) d t, (2)where | (cid:126)E ( t ) | ≡ (cid:80) S max i =1 E i ( t ), and t (cid:96) is the starting time of the (cid:96) th infection event. Once the system assumesthe chronic inflammation steady state, the heightened inflammatory response limits the activity of theadaptive response, and accordingly leads to the sharp transition behavior of the two trajectories observed inFig. 5a and 5b. Thus, the onset of chronic inflammation causes the innate response to strengthen while theadaptive response weakens.When averaged over an ensemble of infection sequences, variability in the timing of the sharp transitionfrom health to chronic inflammation smooths into the crossing displayed in Fig. 5c (though the actualdistribution of effector cells and phagocytes across infection sequences is bimodal, as seen in the inset ofFig. 5c). This crossing behavior is consistent with a longitudinal study of Swedish people, in which middle-aged people exhibited steady lymphocyte and neutrophil counts over the three-year span of the study, whileolder people ( >
85 years of age) exhibited significantly increased neutrophil counts and significantly decreasedlymphocyte counts over the same span [50]. In addition, people with an immune risk phenotype (IRP) (whichoften precedes immune decline and death) commonly possess a weakened adaptive immune repertoire andexperience inflammaging [23]. Taking (cid:104) E (cid:105) and (cid:104) N ∗ (cid:105) as proxies for adaptive and innate immune function,the age-dependent transition in the IIB model resembles the shift in immune function experienced by peoplewith an IRP.The number of infection events that are encountered before chronic inflammation is reached is plotted asa distribution across 10,000 randomly-generated infection sequences in Fig. 5d. The distribution in Fig. 5ddecays approximately exponentially for large numbers of infection events. Different choices of pathogenshape distributions result in different distributions of transition times that are qualitatively similar but ingeneral not exponentially distributed, as demonstrated in Fig. S1. Thus, the sequence of infection events isa significant driver of variability in the timing of the transition to chronic inflammation.To identify the relationship between an infection sequence and the transition from health to chronicinflammation, we examine the effect of accumulated pathogen exposures on the bulk immune state variables | M | ≡ (cid:80) S max i =1 M i and | N | ≡ (cid:80) S max i =1 N i ; see Fig. 5e. Over the course of an infection sequence, memorycells are generated in response to new pathogen encounters at a faster rate than their decay. When fewernovel pathogens are encountered, memory accumulation slows, since previously encountered pathogens arecleared more quickly and adaptive immune cells are stimulated for a shorter amount of time. As thememory cell repertoire grows, the naive cell population shrinks according to the homeostatic constraints.Eventually, the immune system is unable to defend against novel pathogens because of the depleted naivecell population. Once this fragility is developed, chronic inflammation will be triggered when any novelpathogen is encountered. The disparate immunological outcomes of different individuals demonstrated in Fig. 5 are necessarilydetermined by the difference in their infection sequences, since the model equations in Table 2 are otherwisedeterministic. Until the transition to chronic inflammation, the system always returns to the health steadystate. In the health steady state most immune variables assume values that are independent of previouspathogen encounters; only the naive and memory cell populations occupy values that are potentially different12 ) c)b) Previous encounters with current pathogen shapeS ℓ before ℓ th infection CI onset none ≥ Infections T o t a l na i v e c e ll s | N | Authentic sequenceReliable protectionFull protectionFragile protection b d) Infection events A v e r age e ff e c t o r c e ll E A v e r age a c t i v a t ed neu t r oph il N * Infection events A v e r age e ff e c t o r c e ll E A v e r age a c t i v a t ed neu t r oph il N * A v e r age a c t i v a t ed phago cy t e s N * f r e q u e n c y d e n s i t y f r e q u e n c y d e n s i t y infection events
40 60 80 100
Infection events F r a c t i on o f hea l t h y i nd i v i dua l s HealthASD
40 60 80 10000.20.40.60.81 infection events f r a c t i o n o f i n d i v i d u a l s i n d i ff e r e n t s t e a d y s t a t e s healthSI a) b) c) e) infection events t o t a l n a i v e c e ll s t o t a l m e m o r y c e ll s a v e r a g e e ff e c t o r c e ll s p e r i n f e c t i o n a v e r a g e a c t i v a t e d p h a g o c y t e s p e r i n f e c t i o n t r i a l - a v e r a g e d e ff e c t o r c e ll s t r i a l - a v e r a g e d a c t i v a t e d p h a g o c y t e s a v e r a g e e ff e c t o r c e ll s p e r i n f e c t i o n a v e r a g e a c t i v a t e d p h a g o c y t e s p e r i n f e c t i o n d) Infection events T o t a l na i v e c e ll s | N | Authentic sequenceReliable protectionFull protectionFragile protection
Infection events P a t hogen s hape S CI .
05 0 . .
15 0 . Authentic sequence:Clustered sequence:Reliable protectionCyclic sequence:Full protectionIncomplete cyclic sequence:
Fragile protection
Reorder to form“synthetic” sequences Random sampling frompathogen frequency distribution
Infection events C ogna t e T c e ll s Figure 6:
Transition to chronic inflammation (CI) is driven by depletion of naive cells and lack ofprotection from memory cells. (a) The number of cognate T cells specific to a novel pathogen shape (equalto the sum of naive and memory cells) is the key indicator for whether an infection event will trigger the chronicinflammation steady state. Here, cognate T cell counts specific to an encountered pathogen P (cid:96) are plotted for eachinfection event (cid:96) across 20 infection sequences sampled from Eq. (1). The color of each point indicates the number oftimes that the encountered pathogen P (cid:96) has been previously encountered. The colored bands are generated from 1000infection sequences, and envelope the observed cognate cell counts. The large red circles in the lower-right cornermark the infections events that trigger chronic inflammation across all 1000 infection sequences, which occur whena novel pathogen is encountered after naive cells have been depleted below some threshold. A shorter time intervalbetween pathogen encounters of the same shape results in less memory cell decay and hence more cognate T cells,and this effect causes the shape of the colored bands. (b) We consider three synthetic reorderings of each “authentic”randomly generated pathogen sequence: the clustered sequence orders pathogens according to their prevalence; thecyclic sequence orders them to ensure immediate exposure to all pathogen types; and the incomplete cyclic sequenceinduces fragility by quickly depleting naive cells and then introducing a novel pathogen. (c) The authentic sequenceand three synthetic sequences transition to chronic inflammation (CI) at different times (black crosses). The pathogenshape distribution for this infection history (right histogram) is drawn from the theoretical shape distribution (blackline overlaid) given by Eq. (1). (d) The naive cell pool is depleted at different rates depending on how infection eventsare ordered. Naive cell counts and their variation across the 50 authentic sequences considered in panel (a) are shownfor the three synthetic sequences. Error bars for the timing of chronic inflammation are 50% confidence intervals. after each infection event. Therefore different infection sequences lead to differences in memory and naivecell populations, which in turn are directly responsible for the transition to chronic inflammation.13n Fig. 6a, the number of cognate T cells (the sum of pathogen-specific naive and memory cells N S (cid:96) + M S (cid:96) )at the beginning of each infection event (cid:96) are plotted for 1000 infection sequences, each consisting of 100infection events sampled from the pathogen shape distribution Eq. (1). Due to the accumulation of immunememory, the number of cognate T cells specific to a pathogen shape will be greater if that pathogen hasbeen previously encountered. To demonstrate this, the colored points in Fig. 6a encode the number of timesthat a pathogen shape S (cid:96) was encountered in the (cid:96) − To probe the variability in the timing of the transition to chronic inflammation, we examine threesynthetic infection sequences that are reorderings of an “authentic” infection sequence sampled from Eq. (1).These sequences, showcased schematically in Fig. 6b and detailed in the text below, deliberately structurethe order of pathogen encounters to induce different levels of fragility towards novel pathogen shapes. Thesynthetic and authentic infection sequences affect the rate of memory cell accumulation and naive cell loss,and in turn, alter the timing of the onset of chronic inflammation. An example authentic sequence, alongwith its corresponding synthetic sequences, is illustrated in Fig. 6c. In Fig. 6d naive cell statistics of 50authentic infection sequences are compared with the statistics generated by their synthetic counterparts.In the clustered synthetic ordering (Fig. 6b-d, orange), the infection sequence is ordered so that themost common pathogens are encountered first and the rarest pathogens are encountered last. In this case,pathogens are immediately reencountered so memory cells do not significantly decay between infections, andthe accumulated immune memory causes an accelerated immune response that generates fewer memory cells.Therefore, this reordering is a lower bound for the naive cell loss rate. Indeed, the clustered sequence leadsto the slowest loss of naive cells among the authentic and synthetic sequences in Fig. 6d. The clusteredsequence provides reliable protection that delays the transition to chronic inflammation until infection 89,compared with the authentic sequence that transitions after infection 66, as shown in Fig. 6c.In the cyclic synthetic ordering (Fig. 6b-d, yellow) infections are ordered so that all available pathogentypes are encountered as early as possible: in this ordering each pathogen type is encountered once beforeany pathogen is encountered for the second time, then each pathogen type is encountered twice before anypathogen is encountered for the third time, and so on. Constantly encountering new pathogen types drivesthe accumulation of memory cells and in turn naive cell loss at an accelerated rate. Thus the cyclic sequenceyields an upper bound for the naive cell loss rate, as in Fig. 6d. At the same time, since this syntheticsequence is structured to front-load every pathogen type that can be encountered early in the infectionhistory, the generated memory cells eventually provide full protection against each pathogen type, and thechronic inflammation state never occurs, as in Fig. 6c. Thus, broad exposure to pathogens early in anindividual’s infection life history can provide adaptive-mediated protection from chronic inflammation in theIIB model.Lastly, the incomplete cyclic synthetic ordering (Fig. 6b-d, purple) is similar in construction to the cyclicordering, except that one rare pathogen is intentionally omitted from the initial pathogen cycles. Then, thispathogen is presented at a later time to trigger chronic inflammation. The incomplete cyclic ordering inducesa fragile immune response: naive cells deplete nearly as quickly as for the cyclic ordering, and incomplete14
20 40 60 80 1000100200300400500600 a)b) increasinganti-inflammation(smaller p )increasing pathogenclearance (larger p ) increasing anti-inflammation (smaller p )increasing pathogenclearance (larger p ) infection event f r e q u e n c y d e n s i t y c u m u l a t i v e p a t h o g e n l o a d = d u r i n g e a c h i n f e c t i o n Figure 7:
Effector cells are subject to a trade-off between clearing pathogens and suppressing inflam-mation. (a) The onset of chronic inflammation (histograms as in Fig. 6d) is delayed for lower values of p , i.e. whenthe anti-inflammatory role of effector cells is increased. (b) The cumulative pathogen load L (cid:96) over the course of eachinfection event (averaged over 1000 infection sequences) is larger for smaller values of p . The drop in L (cid:96) after the 60thinfection event for p = 0 . δ N , δ M , R , and θ N were modified to ensure that the timescales of infection clearance and homeostatic response were separated enoughfor us to use the adaptive programming method, as described in Table S1 of the Supplementary Information. Thesimulations in panel (b) are generated with the parameters given in Table 3. .immune memory coverage causes vulnerability to novel pathogens. Thus, the onset of chronic inflammationis accelerated in the incomplete cyclic ordering, with the onset occurring during the 48th infection in Fig. 6c.The clustered and cyclic synthetic immune histories demonstrate how some pathogen sequences candelay the onset of chronic inflammation, either by prolonging the abundance of naive cells or by quicklyacquiring full immune memory coverage across all pathogen shapes. In contrast, the incomplete cyclicsequence demonstrates how pathogen sequences can induce immune fragility, by quickly depleting naive cellswhile remaining vulnerable to novel pathogens; alternatively, the incomplete cyclic sequence shows how theintroduction of a new pathogen species, either through mutation or migration to a new environment, canbreak existing memory coverage and lead to immune fragility.15 .6. The adaptive immune response is subject to a trade-off between pathogen clearance and suppressinginflammation In the original adaptive immune model by Stromberg and Carlson [30], the sole function of effectorcells was to clear pathogens. However, the diverse repertoire of effector T cells— including helper T cells,cytotoxic T cells, and regulatory T cells— can additionally exhibit anti-inflammatory functions [13, 17,52]. Incorporating these features in the IIB model leads to a trade-off between pathogen clearance andinflammation suppression that can be explored quantitatively.Specifically, in the IIB model a proportion p of effector cells are allocated to pathogen clearance (aresponsibility of cytotoxic T cells with the aid of helper T cells [53]), while a proportion 1 − p of effector cellsare allocated to the production of anti-inflammatory cytokines (a responsibility of regulatory T cells [52]).These dual functions are presented schematically in Fig. 1 and explicitly in Table 2.For smaller values of p , effector cells are increasingly used to combat inflammation, which delays theonset of chronic inflammation as demonstrated in Fig. 7a. On the other hand, at smaller values of p moreresources are allocated to combat inflammation, so the diminished innate response slows the rate of pathogenclearance. This is quantified in Fig. 7b, which plots an ensemble average (across 1000 infection sequences)of the cumulative pathogen load L (cid:96) for each infection event: for the (cid:96) th infection, L (cid:96) ≡ (cid:90) t (cid:96) +1 t (cid:96) P S (cid:96) ( t ) d t, (3)where S (cid:96) is the pathogen shape and t (cid:96) the starting time of the (cid:96) th infection event. This measure wasoriginally introduced in Stromberg and Carlson [30] where it was called the “loss function,” and we similarlyuse it here as a proxy for the damage the pathogen inflicts during each infection event. In Fig. 7b, smallervalues of p lead to greater cumulative pathogen load for each infection event and vice versa.Note that for p as large as 0 . L (cid:96) for (cid:96) (cid:38)
60 due to the onset of the chronicinflammation steady state in a larger proportion of individuals. Once the chronic inflammation state isreached, the non-zero activated phagocyte population N ∗ rapidly responds to infection events, efficientlyclears pathogens, and returns to the chronic inflammation steady state. In this sense, the onset of chronicinflammation acts as a protective mechanism that shields the immune response from future pathogen en-counters and minimizes the damage that pathogen inflicts. Interpreted biologically, it is advantageous fororganisms to minimize cumulative pathogen load while also avoiding the early onset of chronic inflammation.Evolutionarily, these two opposing selection forces should lead to an intermediate optimal p in which effectorcells allocate resources both to pathogen clearance and innate suppression.
4. Discussion
Though immunosenescence affects every aging individual, the mechanisms through which it develops arenot yet fully understood. In this paper we demonstrate through quantitative modeling how physiologicalmarkers of immunosenescence can arise from the accumulated effect of pathogen encounters. In particular,clonal expansion and homeostatic maintenance lead to an increase in memory cells and a decrease in naivecells, which are qualitatively consistent with their clinically-observed abundances [28]. Accumulated memorycells protect the immune system against previously-encountered pathogens, but the shrinkage in the naivecell pool renders the immune system vulnerable to novel pathogens and is the key indicator of immunesystem fragility. While a similar mechanism was demonstrated in the model by Stromberg and Carlson [30],in their study the overspecialized immune repertoire led to increased cumulative pathogen load. In the IIBmodel, the acquired immune fragility is characterized by a transition to a chronic inflammatory state, andthe timing of this transition is highly variable and depends on the infection history.In addition to this mechanism of imbalanced immunological space, several other immune functions varywith age and could play a role in the development of immunosenescence. For example, clinical studiesobserved that the average cytotoxicity of natural killer cells decreases with age [54, 55], cell signaling betweenimmune cells can become impaired with age [56], and thymus involution leads to decreased T cell productionwith age [57, 58]. The current formulation of the IIB model exhibits an inflammaging-like behavior withouttaking these additional factors into account. However, in future work physiological parameters of the model16ould be used as a proxy for these observed behaviors: for example, the decreased cytotoxicity of naturalkiller cells (which are innate) could be incorporated by decreasing k pn with age, the impaired cell signaling inT cells (which are adaptive) could be achieved by decreasing γ with age, or the reduced thymus output couldbe modeled by decreasing θ N with age. The calculated immune outcomes that result from these modificationscould shed light on the relative contributions to immunosenescence from memory-induced fragility in theadaptive response, an impaired innate response, and an impaired adaptive response. The chronic inflammation steady state has two physiological interpretations. First, the runaway tissuedamage caused by the sustained inflammatory response may cause death in the host, as was implied byReynolds et al . when they called this steady state “aseptic death.” Second, if the sustained inflammatoryresponse is relatively minor, the chronic inflammation state can be interpreted as “inflammaging,” a chroniclow-grade inflammation that is common among the elderly [24]. In this paper we choose this second inter-pretation and construe the transition to the chronic inflammation state as inflammaging. Accordingly, themechanisms of the IIB model that induce this transition might inform the biological mechanisms that theyemulate.For example, recent work has suggested that the development of inflammaging might be a result ofimmune system remodeling: as immunosenescence lessens the efficacy of the adaptive immune response,the body relies on inflammaging for protection against pathogens via the innate immune response [28].Similarly, the adaptive response in the IIB model is subject to a trade-off between clearing pathogens andsuppressing inflammation. In part based on recent work demonstrating that the adaptive response can act tosuppress a hazardous innate response [17], recent theories suggest that this suppression might have been theevolutionary driver that promoted the development of an adaptive immune response [16]. Similarly, in theIIB model when pathogens are introduced to a system in the chronic inflammation state, they are clearedalmost immediately since the inflammatory response is already primed.Evolutionarily, the innate immune response preceded the creation of the adaptive response [59]. This isconsistent with the taxonomic complexity of organisms, in which invertebrates possess only an innate responsewhile vertebrates possess the additional capacity for pathogen-specific immune memory [60]. Additionally,adaptive immune components are dependent on innate cells— for example, the activation of an adaptiveresponse through antigen presentation relies on dendritic cells. The evolutionary drivers of the adaptiveimmune response could be explored with immune models that quantify the added benefit of possessing anadaptive immune system.
The efficiency of the human immune system changes in a non-monotonic manner as one ages: it is weak ininfancy and dependent on maternal antibodies; then it grows stronger as the innate and adaptive responsesmature and as immune memory is accumulated; and finally it plummets in the elderly [61]. As people age,effector T cell levels drop, chronic inflammation builds [23, 62], and immune outcomes among the elderlybecome extremely variable [62].In this work we present a potential mechanism for these clinically-observed aging trends, driven by over-specialization of the adaptive immune repertoire. The accumulation of memory cells initially strengthensthe immune response against previously-encountered pathogens. Eventually, memory cells become overspe-cialized and restrict the growth of naive cells, rendering aged individuals vulnerable to rare pathogen types.In the IIB model the onset of the chronic inflammation state is variable, and dependent on the history ofprevious pathogen encounters. The age-dependent immune system efficiency observed in the IIB model isconsistent with the previously mentioned clinically-observed immune behaviors.
Lastly, the shape space formulation of the adaptive immune response produces results that are quali-tatively similar to the clinically-observed behaviors of immune imprinting [63] and the decreased efficacyof vaccines in the elderly [55]. Immune imprinting occurs when individuals exhibit sustained memory tothe pathogens they were exposed to early in their life. In the IIB model naive cells are more abundant atthe beginning of an infection sequence, and as memory cells accumulate over time, homeostatic pressures17rive down the population of naive cells. Thus, during the first several infection events the larger naive cellpool will induce a stronger adaptive response and therefore generate a stronger memory for encounteredpathogens. On the contrary, near the end of an infection sequence the diminished naive pool will induce aweaker adaptive response to a novel pathogen, and generate a weaker immune memory. If we interpret vacci-nation as an exposure to a novel pathogen, then the clinically-observed characteristics of immune imprintingand vaccination in the elderly are qualitatively captured by the IIB model.
5. Conclusion
The progression towards immunosenescence is a dynamical process influenced by a lifetime of pathogenencounters, physiological alterations, genetic factors, and general lifestyle choices. This blend of factorsmakes it difficult to isolate and identify the most relevant causative agents of immunosenescence. Therefore,mathematical models hold great utility in their ability to probe the causes of immunosenescence.In this paper we developed the IIB model, which incorporates the structure of the innate and adaptiveimmune branches, and exhibits behaviors that are qualitatively consistent with clinically-observed phenom-ena. We found that repeated pathogen encounters cause the overspecialization of memory cells and thedepletion of naive cells, and over time these effects render the immune system vulnerable to novel pathogens.By describing immune dynamics with a mathematical model, we demonstrated how feedbacks between theinnate and adaptive immune responses could give rise to variable immune courses and outcomes. Goingforward, experimental studies combined with quantitative immune models will continue to illuminate themechanisms of immunosenescence.
6. Acknowledgements
We thank Andrea Graham, Micaela Martinez, and members of the Aging and Adaptation in InfectiousDiseases working group at the Santa Fe Institute for thoughtful discussions regarding the formulation of theIIB model. This publication is based on work supported by the Santa Fe Institute through the Complex Time:Adaptation, Aging, Arrow of Time research theme, which is funded by the James S. McDonnell Foundation(Grant No. 220020491); by the National Science Foundation Graduate Research Fellowship under Grant No.1650114; and by the David and Lucile Packard Foundation and the Institute for Collaborative Biotechnologiesthrough grant W911NF-09-0001 from the U.S. Army Research Office; and by funding from the Chancellor’sOffice of UCLA. 18 eferences [1] T. T. Yoshikawa, Important infections in elderly persons, Western Journal of Medicine 135 (6) (1981)441.[2] T. C. Eickhoff, I. L. Sherman, R. E. Serfling, Observations on excess mortality associated with epidemicinfluenza, Jama 176 (9) (1961) 776–782.[3] K. E. Powell, L. S. Farer, The rising age of the tuberculosis patient: a sign of success and failure, TheJournal of Infectious Diseases 142 (6) (1980) 946–948.[4] L. H. Miller, P. A. Brunell, Zoster, reinfection or activation of latent virus?: Observations on theantibody response, The American Journal of Medicine 49 (4) (1970) 480–483.[5] T. T. Yoshikawa, Perspective: aging and infectious diseases: past, present, and future, Journal ofInfectious Diseases 176 (4) (1997) 1053–1057.[6] Clinical features of COVID-19 in elderly patients: A comparison with young and middle-aged patients,Journal of Infection 80 (6) (2020) e14 – e18.[7] United Nations Department of Economic and Social Affairs, Population Division, World populationprospects 2019: Ten key findings. (2019).URL https://population.un.org/wpp/Publications/Files/WPP2019_10KeyFindings.pdfhttps://population.un.org/wpp/Publications/Files/WPP2019_10KeyFindings.pdf