Competitive exclusion by autologous antibodies can prevent broad HIV-1 antibodies from arising

Significance

Broadly neutralizing antibodies against HIV have recently been discovered, but their highly mutated nature and late emergence in infection make it difficult to infer how they arose. As a step to understanding their development, we investigate antibody–virus coevolution, using a mathematical model. Here we find that broadly neutralizing antibodies in principle may arise earlier and be less mutated, but that competition between broad responses and initial autologous antibody responses delays their emergence. It may be possible to reduce this competition and elicit broadly neutralizing antibodies earlier than previously thought by using a vaccine with diverse viral strains.

Abstract

The past decade has seen the discovery of numerous broad and potent monoclonal antibodies against HIV type 1 (HIV-1). Eliciting these antibodies via vaccination appears to be remarkably difficult, not least because they arise late in infection and are highly mutated relative to germline antibody sequences. Here, using a computational model, we show that broad antibodies could in fact emerge earlier and be less mutated, but that they may be prevented from doing so as a result of competitive exclusion by the autologous antibody response. We further find that this competitive exclusion is weaker in infections founded by multiple distinct strains, with broadly neutralizing antibodies emerging earlier than in infections founded by a single strain. Our computational model simulates coevolving multitype virus and antibody populations. Broadly neutralizing antibodies may therefore be easier for the adaptive immune system to generate than previously thought. If less mutated broad antibodies exist, it may be possible to elicit them with a vaccine containing a mixture of diverse virus strains.

A major challenge to developing an HIV type 1 (HIV-1) vaccine is the difficulty of eliciting an immune response that can neutralize the large diversity of viral strains circulating in the human population. The discovery of broad and potent neutralizing monoclonal antibodies against HIV-1 in humans has renewed hopes for an effective HIV vaccine (1–4). Termed broadly neutralizing antibodies (BnAbs), they are found some years into chronic infection and typically neutralize a large fraction of a diverse panel of HIV-1 strains in vitro (5). The B-cell lineages that produce these antibodies constitute on the order of 0.1% of the host’s B-cell population (6–8), and their presence does not seem to reduce viral load or decrease transmission in the individuals in which they are found (9). However, passive immunization with BnAbs has been shown to block infections of simian immunodeficiency virus (SIV) and simian-HIV-1 in nonhuman primates (10; see ref. 11 for a review). In addition, passive infusion with BnAbs leads to rapid, although transient, suppression of viral load in macaques chronically infected with simian-HIV-1 (12, 13). These studies suggest that if a vaccine can elicit BnAbs to a sufficiently high level before exposure to HIV-1, the transmitted virus may be neutralized before it becomes established in the host.

Attempts to elicit BnAbs have so far been unsuccessful (1–3, 14–16). One reason is the antibodies are highly mutated relative to their germline ancestor (Fig. 1A), and it is a challenge to develop a vaccine that can induce antibodies mutated to such an extent (3). However, several recent lines of research indicate that high levels of mutation may not be necessary for breadth. First, the extent of mutation is correlated with the length of infection (Fig. 1B), and as all broad antibodies to date have been found late into chronic infection, the high level of mutation may be a result of the passage of time. This is supported by a study that found high levels of somatic mutation in antibodies associated with chronic infections, regardless of whether the antibodies were broadly neutralizing (17). Second, B cells with long heavy chain complementarity determining region 3 loops, a property associated with neutralizing breadth, have been found to exist in the naive B-cell population (18). This suggests the potential for broad HIV-1 antibodies to be generated with few somatic mutations. Last, cross-clade neutralizing responses have been found in HIV-1-infected infants as early as 11–15 mo postinfection (19). That an infant immune response is capable of producing antibodies de novo that neutralize HIV-1 strains distinct from the founder strain within a relatively short period further supports the idea that B cells need not undergo substantial amounts of affinity maturation and mutation to produce BnAbs.

Fig. 1.

Levels of somatic mutation in HIV-1 antibodies. (A) Number of mutations in the heavy chain variable gene (V_H) in antibodies developed against pandemic H1N1 influenza (pH1N1; blue, data from ref. 40) compared with BnAbs against HIV-1 (green, data from ref. 4). (B) The number of mutations on V_H for antibodies in the CH103 BnAb lineage in a patient over three years (data from ref. 8). The length of V_H is ∼300 base pairs, and the number of mutations is relative to the closest germline gene, as determined by the international ImMunoGeneTics (IMGT) information system alignments (41).

Here we demonstrate with simulations of coevolving virus and antibody populations a possible reason why less-mutated broad antibodies have not been observed and suggest a vaccine strategy to elicit them. We find that broad antibodies have a low chance of emerging early in infection, even if we assume they require only moderately more mutations than specific antibodies. This is because antibodies that target the founder strain competitively exclude broad antibodies in the initial stages of chronic infection. This competition is strongest when there is a single founder strain, as is often the case in natural HIV-1 infections (20, 21). When we remove this competition between broad and specific antibodies from our model, we find that broad antibodies arise earlier. We also demonstrate that this competitive exclusion is reduced in infections initialized with multiple strains.

Model

A schematic of the stochastic simulation model for the evolution of virus and antibody populations is shown in Fig. 2 (details in SI Appendix). Following refs. 22 and 23, we represent viruses and antibodies as strings of characters from an alphabet of size four (Fig. 2A, with colors corresponding to characters). An antibody is modeled as a single string, representing its binding site, and a virus is modeled as two strings, representing a variable epitope and a conserved epitope on the HIV envelope protein. With the exception of occasional mutations, the conserved epitope is common to all viruses. A similar approach has been used to model a malaria vaccine antigen (24). The binding between an epitope and an antibody is determined by the length of the longest common substring between their string representations (25, 26) in the absence of any occluding structures, a quantity we call the match length. This notion of match length endows the antibody repertoire with desirable properties such as variation in binding affinity and variation in mutational effects (SI Appendix).

Fig. 2.

Schematic of mathematical model. Strings are represented by blocks of color. (A) Each virus consists of a length 8 variable epitope and a length 8 conserved epitope. Each antibody is of length 8. The match length, the length of the longest common substring, is shown for the antibody against both variable and conserved epitope (rectangles). The match length is determined by comparing all possible alignments of the antibody string with the variable and conserved epitopes and taking the maximum. (B) Types of events in the model. At t₀, the virus population is homogeneous and one antibody matches the virus strain (indicated by rectangle). At t₁, this high-affinity antibody has increased in the population because of its selective advantage. At the same time, mutations have occurred on some virus strains. At t₂, the virus strains with mutations that confer escape from the antibody have increased in the population. Meanwhile, a mutation in the third antibody has occurred, allowing it to bind the conserved region.

Antibodies that match the conserved epitope correspond to BnAbs, as they recognize almost all viruses. Antibodies that match the variable epitope correspond to specific antibodies, and in the case where they match the variable epitope of the founder strain, they correspond to autologous antibodies. We intentionally keep the model simple and assume the variable and conserved epitopes occupy different locations. This formulation thus does not recapitulate the breadth development seen in some studies (8, 27), in which the broadly neutralizing antibody and its autologous precursor recognize the same region. The model in ref. 28 is an example of how such a scenario could be formulated.

The size of the virus and antibody populations are assumed to be constant in time. This fixed population size assumption is common in theoretical evolutionary biology and is also a reasonable approximation in the case of chronic HIV-1 infection. Indeed, after the acute stage of HIV-1 infection, the amount of virus in an individual stays approximately constant at the set point viral load. The fixed antibody population size reflects our belief that there is some carrying capacity for the number of B cells that can undergo affinity maturation in an infection, for example, due to selection by follicular T helper cells (29).

Coevolutionary Dynamics.

Antibodies replicate at a rate that increases with the fraction of circulating virus they match (Fig. 2B, time t₁). This reflects the affinity maturation process B cells undergo in germinal centers to increase their binding to a circulating virus (30). Viruses, in contrast, replicate at a rate that decreases with the fraction of circulating antibodies that match them (Fig. 2B, time t₂), reflecting the selective pressure for virus strains to accumulate mutations that evade antibody recognition (31, 32). The selection in both these processes relies on diversity in the virus and antibody strains. This is maintained in the model by a stochastic mutation process in which characters in the string representations are changed uniformly at random (Fig. 2B, time points t₁ and t₂).

Properties of Variable and Conserved Epitopes.

Conserved epitopes have been observed to be less immunogenic than variable epitopes, likely because of their lower accessibility resulting from occluding structures on the Env protein (1, 15, 31, 32). We encode this in our model in two ways. First, an antibody has a lower “match score” (a proxy for the binding energy) against a conserved epitope than against a variable epitope with the same match length (Fig. 3A). The exception to this is when the match is exact, as broad antibodies that precisely bind conserved epitopes have just as high a fitness as the best specific antibodies to variable epitopes (4, 33). Second, broad antibodies make up a smaller fraction of all possible antibody types. We achieve this by representing the conserved epitope by “00000000,” which has fewer antibodies that match it than the majority of string representations (Fig. 3B). A specific example is shown in Fig. 2A, where the variable epitope, comprising a variety of substrings along its length, offers more match possibilities than the conserved epitope, which comprises only substrings containing “0.”

Fig. 3.

Broad antibodies have a slight immunogenic disadvantage. (A) The match score, and hence selective advantage, of an antibody against the conserved epitope is lower than an antibody against the variable epitope for every value of substring match length. (B) The fraction of randomly selected antibodies that match a given epitope is lower for the conserved epitope than for the variable epitope. For the conserved epitope, these are the fraction of antibodies that match “00000000” of 10⁵ randomly generated antibodies. For the variable epitope, the fraction of antibodies of 10⁵ that match a randomly generated variable epitope was first calculated. We then averaged these fractions over 10 randomly generated variable epitopes.

We note that the frequency of broad antibodies, although lower than specific antibodies, is not more so than an order of magnitude for each match length. These assumptions put broad antibodies at an overall disadvantage with respect to specific antibodies.

In addition to a difference in immunogenicity, we also assume that the conserved epitope performs a functionally important role and the virus incurs a fitness cost if its conserved epitope deviates from the fixed configuration, “00000000.” This is motivated by the CD4 binding site, which is crucial for virus entry into a cell and is a target of several broadly neutralizing HIV-1 antibodies (34).

Parameterization.

Because our focus is on the role of coevolutionary dynamics in generating a broad antibody response, we do not model the full physiological dynamics that occur in HIV-1 infection. Our viral population reflects the combined dynamics of productively infected cells and free viral particles. The viral population size in our model corresponds to the number of free virions. The antibody population in our model reflects the combined dynamics of B cells and antibody molecules. In contrast to the viral population, however, the antibody population size in our model corresponds to the number of B cells, as antibody replication occurs at the level of B cells.

Where possible, we have used empirically measured parameters and order-of-magnitude estimates (Table 1). For parameters such as virus and antibody population sizes, however, the actual numbers are on the order of 10⁹ or higher (30, 35) and are computationally intractable to use. We therefore used values that are sufficiently large to capture interesting properties of the model while being efficient to simulate (SI Appendix, Table S1). Other parameters, such as the number of clonal B-cell populations that respond to HIV-1, are simply not known, and we made educated choices about them. We stress that because our parameters have been chosen this way, our goal is to gain qualitative insight, rather than quantitative predictions. Further rationale underlying our parameterization is detailed in the SI Appendix.

Table 1.

Replication and mutation rates

Parameter	Value in model	Empirically measured quantity
HIV generation time	2 d	1–2 d (35)
HIV mutation rate	10−2/virus/generation	10−5/base/generation 103 nucleotides in env (35)
Ab generation time	1 d	Germinal center B cells divide once every 6–14 h (29), but the fraction of time a B-cell spends in germinal center has not been measured
Ab mutation rate	10−1/ab/generation	10−3/base/generation order of 102 nucleotides (29)

Results

Dynamics of Natural Infection.

Three examples of coevolutionary dynamics under this model are shown in Fig. 4. Infections are founded by a virus strain consisting of a variable epitope (chosen at random) and a conserved epitope in the optimal (“00000000”) configuration. The initial antibody population consists of 100 copies each of 10 randomly chosen antibody strings. In our model, this corresponds to about a 10% chance that the initial B-cell population produces an antibody that reacts with the variable epitope of the founder strain (SI Appendix, Fig. S1C).

Fig. 4.

Examples of infection dynamics, with each column corresponding to one simulation. (A) An autologous antibody response occurs, with no broad antibody response. (B) A broad antibody response occurs after an initial autologous antibody response. (C) A broad antibody response occurs early in infection. In all three columns, the top panels show viral population dynamics, with each line a unique virus type (colored red to yellow in order of appearance). (Middle) Antibody population dynamics, with each line a unique antibody string (colored blue to green in order of appearance), and broad antibodies highlighted in purple. (Bottom) Fitness (normalized to lie in [0,1]) of each virus and antibody type that existed during the simulation. Colors correspond to the viral and antibody populations in the top and middle. For ease of visualization, the transparency of each fitness curve is in proportion to the integral of the corresponding virus or antibody population curve, i.e., the total area under the virus or antibody population size curve.

Our simulations produce dynamics that are qualitatively consistent with natural infection. Initially, the founder strain dominates the virus population. Until there is an antibody that binds sufficiently well to the founder strain, the decrease in the founding virus population is solely the result of neutral mutation (Fig. 4). Once a reactive antibody is produced, it usually has a low fitness initially, but this fitness gradually increases, as seen in the stepwise increase of fitness traces in the lower panels of Fig. 4. This gradual increase in fitness occurs for both specific and broad antibodies. In response to the emergence of a neutralizing antibody, the founding virus population drops dramatically and is replaced by virus strains that are not recognized by the antibody (Figs. 4 A and B). Thereafter, the virus population consists of multiple distinct strains, and it is difficult for any single specific antibody to dominate the population. At this stage, because they target the conserved epitope, broad antibodies become selectively advantageous and can appear (Fig. 4B). The simulations are stochastic, and sometimes by chance, the first neutralizing response is a broad one (Fig. 4C).

Immunogenic Competition Suppresses Emergence of Broadly Neutralizing Antibody.

The dynamics in Fig. 4 provide only three instances of the stochastic computational model. To obtain a general pattern of broad antibody emergence, we ran the stochastic simulation multiple times with the same initial conditions and parameters. We saw that BnAbs tend to appear later in infection than autologous antibodies (Fig. 5). In fact, the phenomenon in Fig. 4C, in which a broad antibody arises early in infection, occurs infrequently. Whereas an autologous response emerged in 90% of simulations by day 60, a broad response occurred in only 25% of such cases.

Fig. 5.

Competition with autologous antibodies reduces the probability of a broad antibody. The cumulative probability that a broad antibody establishes during infection is compared between simulations of natural infections (blue) and simulations of a control (green), where the selective advantage for antibodies against the variable epitope is set to zero. For comparison, the cumulative probability of an autologous response (red) is also shown. A broad (autologous) antibody response is considered established if the fraction of antibodies that match the conserved (variable) epitope exceeds a quarter of the population. Probabilities are the fraction of 60 simulations that led to the autologous or broad response for both natural and control infections.

To check whether factors other than the lower immunogenicity of the conserved epitope cause broad antibodies to appear less readily than specific antibodies, we compared our simulations of natural infection with a control: simulations with the same parameterization but without selection for an autologous antibody response. Specifically, in the control, antibodies that match the variable epitope evolve neutrally; that is, they have no selective advantage. We found the probability of a broad antibody (within 120 d) increased to nearly 70% compared with 47% in the presence of competition with autologous antibodies (Fig. 5). If the initial autologous response does not play a role in the development of broad antibodies, we would expect the probability of observing a broad antibody to be the same with and without competition.

The emergence of a broad antibody is therefore delayed because of competitive exclusion by the autologous response. This mechanism is in addition to the inherent lower immunogenicity of conserved epitopes. The initial dynamics of HIV-1 infection itself may prevent early emergence of broad antibodies. Depending on the duration of this competitive exclusion in natural infection, the time at which broad antibodies are observed to arise may be much later than when they could have been generated by the adaptive immune system. In this period, circulating B cells will have accumulated more somatic mutations, giving the impression that high levels of mutation are required for neutralizing breadth.

Immunogenic Competition Can Be Diluted with a Diverse Founding Population.

A vaccination strategy that mimics a natural HIV-1 infection might not, therefore, be the fastest way of generating a broad antibody response. Instead, a vaccine should create conditions in an individual that give broad antibodies an immediate advantage over specific antibodies. Earlier, we demonstrated an extreme case of this, in which the specific antibodies have no selective advantage. However, vaccine constructs that present only a conserved epitope to the immune system have so far been unsuccessful (1, 36). A possible alternative to this approach is to dilute the advantage of any particular specific antibody by presenting the immune system with a set of distinct virus strains.

We simulated an infection founded by multiple distinct strains and, indeed, see an increase in the probability of a broad antibody arising as the number of founder strains increases (Fig. 6). Moreover, a broad response is more likely if the distinct strains are randomly chosen (Fig. 6B), rather than if they are closely related to a single strain (Fig. 6A). This suggests that natural infections with a single founder strain, where the initial diversity of virus strains is generated from single-mutant variants of the founder (21), are less conducive to a broad antibody response. Further, our model predicts that in natural infections with multiple founder strains, or conditions in which superinfection with diverse variants occurs early in infection, a broadly neutralizing response should tend to occur earlier than in the case of a single founder strain.

Fig. 6.

Increasing the number of distinct variable epitopes in the initial viral population increases the probability that a broad antibody establishes. (A) The initial variable epitopes differ by a single substitution. (B) The initial variable epitopes are chosen uniformly at random from all possible string representations. All simulations are initiated with a virus population divided equally among the distinct epitopes. As before, a broad antibody response is considered established if it exceeds a quarter of the total antibody population. Probabilities are based on 30 simulations per data point. Error bars show one sample proportion SE.

We note the decline in probability when there are about 10 distinct founder strains (Fig. 6B). This is an artifact of the model when using 10 initial antibody lineages and about 10 viral strains. The decline in the probability of a broad response is because when there are around 10 founder strains, there is a high probability that exactly one of the 10 initial antibodies recognizes one of the founder strains. This gives a slight selective advantage to that single initial antibody and leads to a mild competitive exclusion of a broad response. With a larger number of founder strains, the probability that a single initial antibody has a selective advantage over the other antibodies is low, and this mild competitive exclusion becomes negligible.

Discussion

The high level of mutation in BnAbs remains a major obstacle to developing an antibody-based HIV-1 vaccine. Here we suggest that this high level of mutation may be an artifact of the delayed emergence of broad antibodies, a delay resulting from competitive exclusion by autologous antibodies.

We further show that one way to increase the probability of a broad response is to present the immune system with virus strains bearing distinct variable epitopes, but sharing a common conserved epitope. This dilutes the selective advantage of a specific antibody response relative to an antibody against the conserved epitope. Although the native HIV-1 envelope protein is not the two-epitope object we model here, this idea could be applied by selecting a set of highly diverse HIV-1 strains. An example of such a set is the 12-virus global reference set of HIV-1 that was statistically demonstrated to represent the spectrum of serum neutralizing activity from a large panel of global circulating strains (37).

In contrast to the results here, a recent study based on modeling and experiment recommends vaccination with viral variants in series, rather than in a mixture, to achieve cross-reactive antibodies against HIV-1 (28). The study found that sequential vaccination focuses the immune response toward a conserved region, whereas vaccination with a mixture increases the chance of B-cell apoptosis in the germinal centers, and is therefore less effective. As a result of substantial differences in modeling assumptions between the work here and that in ref. 28, however, it is difficult to directly compare the results. Crucially, the model here includes a coevolving viral population, whereas the model in ref. 28 does not (there are three viral strains, but no viral evolution).

Our results provide a proof of principle that a broadly neutralizing antibody response against HIV-1 can be elicited to arise earlier than in natural infections. However, critical questions need to be addressed before a vaccine based on this principle can be realized. First, it is unclear how to design a vaccine that triggers adaptive immune dynamics similar to a real infection. Our predictions are based on simulations of infections seeded with multiple strains. We do not simulate a vaccine scenario. This was intentional: Although factors such as adjuvants, vectors for virus delivery, and whether viral DNA or protein is presented are known to affect the strength of the immune response, they are insufficiently understood to be modeled meaningfully here. Thus, even with a well-chosen mixture of HIV-1 variants, a multistrain vaccine may not work as our model predicts because the immune system does not respond to the vaccine as it would to an infection. This might be why a study that compared the immune responses between a vaccine composed of a mixture of multiple strains of HIV-1 and one based on a single strain did not find them to be dramatically different (38).

Another question is whether broad antibodies require high levels of somatic mutation. We have assumed here that antibodies do not a priori require a large number of mutations to have neutralizing breadth against HIV-1. Although this is supported by recent studies (17–19) and is the scenario in which an antibody-based HIV-1 vaccine is most likely to succeed, all BnAbs discovered to date are more mutated than is typical. If each mutation is indeed necessary for breadth, then the delay in the observed emergence of BnAbs would be solely a result of waiting for the requisite mutations to occur, and not a result of competitive exclusion.

A further issue is that competition between B cells that target different epitopes is still not well understood. In the case in which B cells target the same epitope, B cells with higher affinity have a greater selective advantage and preferentially proliferate. This is the form of competition we have adopted in our model. However, an experiment carried out in mice suggests that when B cells target distinct epitopes, they do not directly compete with each other (39): When one epitope is shielded from the immune response, the response to the other epitope is largely unchanged.

These questions need to be addressed, regardless of the antibody-based vaccine strategy. For example, one current strategy for rational HIV-1 vaccine design is to induce the same set of mutations as those found in infections producing broad antibodies (3, 8). This relies on accurately mapping the developmental pathway for known broad antibodies (identifying necessary mutations) and reproducing the pathway in a vaccine protocol (eliciting an adaptive immune response comparable to that in real infections).

Traditional vaccine design is based on the premise that infection is protective, and a vaccine should thus mimic a natural infection. Our results suggests a vaccine should instead present the host with multiple diverse strains. In the case of HIV-1, with the exception of i.v. and blood transfusion transmissions, this is a highly nonnatural scenario.