Kinetic modeling of antibody response following inactivated vaccine administrationInactivated vaccines represent a conventional approach in vaccine production. The term “inactivated vaccines” encompasses both the traditional method of rendering original pathogens non-infectious, as well as other approaches utilizing non-replicating forms of antigens for antigen delivery. This definition also extends to genetically modified inactivated vaccines produced through gene recombinant techniques. However, conventional inactivated vaccines encounter notable challenges in the development of RNA virus vaccines. Instability of RNA viruses during replication cycles poses a significant obstacle, leading to an increased presence of defective viral genomes (DVGs) with each passage. Eventually, this results in the complete loss of viral replication activity35. Nonetheless, genetically engineered vaccines have been industrially developed to combat RNA virus infections, such as the AstraZeneca vaccine for COVID-1936. Optimal efficacy for most inactivated vaccines often necessitates booster doses, and our simulation aims to elucidate the underlying mechanisms involved.As depicted in Fig. 2, the concentration changes subsequent to the initial dose are indicated by solid lines, while dashed lines represent the concentration changes of different substances following the second dose. Sustaining elevated levels of IgG within the body holds paramount importance in preventing reinfection owing to its notably slower decay rate in comparison to IgM. It is evident that the initial rise in IgG levels following the first dose is limited (as denoted by the green solid line), whereas there is a substantial increase in IgM levels (as indicated by the red solid line). This phenomenon primarily arises due to the initial scarcity of IgG within the body at the time of vaccination. Consequently, a small quantity of IgG is derived from the conversion of IgM, accompanied by the self-amplification of IgG through antigen binding. Simultaneously, IgM undergoes rapid proliferation, but experiences swift decay once antigen-like substances become depleted. The proliferation of IgM ceases when it is no longer stimulated by antigens, leading to a rapid decline. During this process, a fraction of IgM continues to transform into IgG.At the 50th time unit, administering the second dose leads to a notably distinct pattern. IgG experiences a rapid surge, with its concentration swiftly escalating to a higher level (> 2e5). Correspondingly, IgM levels also rise (as indicated by the red dashed line). This phenomenon arises from the presence of a certain level of IgG attained after the initial vaccination. The substantial increase in IgG content during the second dose primarily stems from the proliferation process of IgG itself, stimulated by antigens, as elucidated in Reaction 10 outlined in the methods section. By administering booster doses, IgG levels can attain a considerable threshold, thereby prolonging the protective effect and duration beyond that achieved by a single dose. Hence, multiple-dose administration strategies are commonly employed for vaccines37. Notably, Fig. 2 not only describes the kinetic changes of antibodies but also specifically depicts the dynamics of IgG-antigen and IgM-antigen complexes. These antigen-antibody complexes play a crucial role in the immune response. They not only participate directly in antibody regeneration through feedback regulation but also serve as a direct indicator of the intensity of patient symptoms. Symptoms resulting from viral infections or vaccine administration, such as fever, are positively correlated with the concentration of antigen-antibody complexes rather than the concentrations of viruses or antibodies alone. Therefore, when assessing vaccine side effects, it is indispensable to consider changes in the concentration of antigen-antibody complexes induced by the vaccine. Figure 2 illustrates that the blue curve represents the concentration changes of IgM-antigen complexes, with their peaks exceeding 2e5 in both doses, while the concentration of IgG-antigen complexes also exhibits a noticeable increase after the second dose (as denoted by the purple dashed line). Additionally, inactivated vaccines may have a potential drawback when antigen structures undergo changes after treatment with high temperatures or chemical reagents. Such alterations can lead to modifications in antigenic determinants, akin to the effect of antigenic drift, potentially resulting in a significant decline in vaccine efficacy38,39.Fig. 2Antibody dynamics after 2 doses of inactivated vaccines. First dose is injected at the initial time unit, second dose is injected at 50th time unit. Both injection dosages of antigen substances are 106.The results of parameter fitting using Adenovirus-Based COVID-19 vaccines in different age groups are presented in Fig. 3. Figure 3 demonstrates that the experimental data exhibit a strong concordance with the simulation results for both younger and older age groups. The data indicate that a booster vaccination strategy significantly enhances IgG levels. Furthermore, antibody concentrations in the younger cohort are marginally elevated compared to those in the older cohort. Distinct differences in curve trajectories between the two age groups are evident and can be further elucidated through the parameter fitting results presented below.Fig. 3(a) IgG level fit to the clinical data for the 18–55 (two doses) age group. (b) IgG level fit to the clinical data for the 56–69 (two doses) age group.From Table 5, it can be observed that the value of k1 for older recipients is significantly higher than that of younger individuals. This indicates that antibodies exhibited stronger antigen affinity in older individuals, which aligns with biological principles. This is because older individuals have a greater abundance of antibodies in their bodies, resulting in significantly higher antigen affinity or neutralization capacity of IgG following subsequent vaccination compared to younger individuals. However, younger infected individuals exhibit higher germinal center activity, indicating a stronger stimulus for antibody regeneration, as reflected by a larger value of k3. This ensures rapid proliferation of antibodies.This result also highlights the differential strategies employed by different age groups during the viral infection process. Due to fewer exposures to pathogens, younger individuals have a lower concentration or probability of high-affinity binding antibodies in their bodies. However, due to the enhanced activity of Th cells, the stimulation of B cells in germinal centers leads to a strong capacity for antibody regeneration, thereby generating a large quantity of protective antibodies. In contrast, older individuals, despite having less regenerative capacity in germinal centers compared to younger individuals, possess a higher concentration of high-affinity binding antibodies due to historical exposure to various pathogens. Although their proliferation rate is slower, their antibodies have higher initial values and better binding activity, enabling them to combat microbial infections through this mechanism.Table 5 Estimated parameter value based on two clinical groups with different age.Kinetic modeling of antibody response following mRNA vaccine administrationWith the increasing comprehension of immunological mechanisms and the advancements in mRNA preparation and packaging technologies, significant progress has been made in the development of mRNA vaccines. Pfizer’s BNT162b2 and Moderna’s mRNA-1273 serve as notable examples that have exhibited superior efficacy compared to traditional vaccines in clinical trials40,41. The merits of mRNA vaccines stem from their ability to maintain the original antigenic structure due to the absence of inactivation processes, thereby mitigating the risk of antigenic drift42. Adverse reactions associated with mRNA vaccines are often less pronounced, owing to the gradual process of antibody synthesis following mRNA administration, which results in lower concentrations of antigen-antibody complexes observed in the model. The concentration changes of IgM-antigen complexes are specifically depicted by the blue curve in Fig. 4. It is evident from Fig. 4 that the peak concentrations of IgM-antigen complexes induced by the two doses are significantly smaller when compared to those elicited by traditional inactivated vaccines. Analogous to inactivated vaccines, the IgG levels after two doses of mRNA vaccines exhibit substantial elevation as compared to those following a single dose, signifying that multiple doses remain the optimal vaccination strategy for mRNA vaccines. It is important to note that both the final IgG concentration of inactivated vaccines and mRNA vaccines are closely correlated with the vaccination dosage. Excessive vaccination dosages can give rise to an excessive accumulation of antigen-antibody complexes, resulting in severe vaccine side effects. Insufficient vaccination dosages are inadequate to induce a sufficient IgG concentration, leading to decreased efficacy of protection and shortened duration of immunity. The determination of the optimal vaccination dosage can be achieved more scientifically through mathematical models. However, it should be emphasized that both inactivated vaccines and mRNA vaccines necessitate a specific vaccination dosage, which poses short-term production challenges and constraints on their widespread implementation. For highly contagious respiratory viruses, surpassing the natural infection rate through vaccination is crucial for disease prevention, which imparts limitations on the future development of vaccines43,44. Additionally, due to mRNA’s rapid degradation rate in comparison to proteins, mRNA vaccines encounter the drawback of storage difficulties, which introduces inconveniences during their utilization45. Another significant concern is the potential occurrence of myocarditis. To enable the entry of mRNA into cells for the translation of corresponding antigenic substances, carriers are utilized. These carriers, distinct from the spike protein of the original virus, have the capacity to indiscriminately infect all cells, including non-epithelial tissues and cells with minimal expression of ACE2 receptors. Consequently, there exists the possibility of infecting cardiomyocytes, and during the process of eliminating infected cells subsequent to antibody production, damage to cardiomyocytes can occur46.Fig. 4Antibody dynamics after 2 doses of mRNA vaccines. First dose is injected at the initial time unit, second dose is injected at 50th time unit. Both injection dosages of mRNA are 106.As the clinical data for mRNA vaccines are divided into different individuals, parameter fitting can be performed separately for each individual. The parameter fitting results for all 39 individuals are presented in figures in the supplementary materials, and the individual parameter fitting results are summarized in supplementary Table 1. These 39 individuals are divided into two groups, with 10 individuals having previously been infected with COVID-19 before receiving the vaccine (individuals 5, 15, 17, 19, 20, 22, 29, 32, 35, and 42) and the remaining 29 individuals having not been infected before vaccination. The parameter fitting results for both groups are presented in Table 6.As shown in Table 6, it is displayed that the k1 value for vaccinated individuals with a history of infection is significantly greater than that for uninfected vaccine recipients, indicating that their antibodies exhibit stronger antigen affinity. This is consistent with immunological principles, as the initial infection process selects for high binding antibodies. Therefore, after subsequent vaccination, their IgG antigen affinity or neutralization ability is significantly higher than that of uninfected individuals. k2 and k3 values are also significantly increased, which is consistent with immunological principles, as the initial infection brings about an increase in T-cell immunity, which manifests in two ways. The increase in the number and activity of helper T cells will enhance the capacity of germinal centers to produce antibodies, leading to an increase in the k3 value. Meanwhile, the increase in cytotoxic T cells will lead to an increase in the clearance rate of antigen-antibody complexes, resulting in an increase in the k2 value.The most distinctive feature of our model is that it can explicitly represent the properties of antibodies, i.e., the antigen-binding activity k1. By fitting data from different individuals, we can identify which individuals produce antibodies with stronger binding affinity, and these antibodies can be further sequenced by experimental researchers for the production of ultra-potent spectral neutralizing antibodies. Moreover, based on these fitted parameters, we can calculate the changes in IgG concentration for different individuals in the future, as well as the trend in IgG concentration changes for the population. Furthermore, we can conduct further dose optimization and vaccination timing optimization to achieve optimal antibody maintenance.Table 6 Estimated parameter value based on two clinical group (10 people with pre-infection and 29 people without pre-infection).Kinetic modeling of antibody response following attentuated vaccine administrationThe concept of utilizing attenuated vaccines has recently emerged as a potential immunization strategy. Attenuated vaccines involve the administration of viruses with reduced replicability to stimulate antibody-mediated immunity in hosts. Recent advancements in our understanding of viruses, particularly defective viruses, have shed light on the existence of various genotypes within a single viral strain that exhibit decreased replication activity and milder symptoms47,48,49. In the context of COVID-19, many asymptomatic cases have been attributed to infections with defective viruses. Consequently, some scholars have proposed and implemented the use of attenuated viruses as natural vaccines50. Different approaches are employed to reduce viral activity, such as introducing rare codons in the host to hinder translation efficiency51,52 or utilizing defective viruses50,53. The characteristics of the antibody response elicited by attenuated vaccines are depicted in Fig. 5. From Fig. 5, it is evident that the administration of attenuated vaccines induces a substantial increase in IgG levels (represented by the solid green line), surpassing the effects of mRNA and inactivated vaccines after two doses. Importantly, the immune response triggered by attenuated vaccines maintains a balanced intensity, as indicated by relatively low levels of antigen-antibody complexes. The peak concentration of IgG-antigen complexes (represented by the dashed purple line) is approximately 2.5e5, while the peak concentration of IgM-antigen complexes (represented by the dashed blue line) is around 1.5e5. The advantages of attenuated vaccines can be summarized as follows: Firstly, a high level of IgG can be achieved without the need for multiple doses. Unlike traditional vaccine regimens, the antibody response induced by attenuated vaccines exhibits kinetics similar to those observed during natural viral infections. This is attributed to the low viral inoculum, which allows for sufficient time for viral replication and the subsequent conversion from IgM to IgG. As a result, a significant increase in IgG levels can often be achieved with a single low-dose infection caused by attenuated viruses. Secondly, attenuated vaccines require minimal vaccine dosage. Due to the inherent replicability of the virus, only a small amount of attenuated virus is needed to stimulate an adequate level of antibodies, and the final antibody levels are not significantly influenced by the vaccine dosage. This greatly reduces production costs and usage requirements. Thirdly, attenuated vaccines exhibit good transmissibility. Since attenuated vaccines consist of live viruses, they possess similar infectivity to the original virus. Consequently, unvaccinated individuals can acquire the virus from vaccinated individuals, further accelerating the achievement of herd immunity. Lastly, attenuated vaccines closely resemble the original virus, containing antigenic epitopes that more accurately represent the original virus and a diverse range of antigenic epitopes. This results in a superior immune response. Although mRNA vaccines have demonstrated promising antigenic determinants, their expression primarily focuses on specific antigens rather than the entire virus. Specific antigens often exist in a free state, exposing fewer antigenic epitopes that are absent in their natural conformation. Antibodies induced by such epitopes are evidently insufficient to provide protection against real infections. However, it should be noted that the development of attenuated vaccines is still in its early stages, and these vaccines may pose significant risks to individuals with compromised immune function. The design of attenuated vaccines requires precise control over viral replicability, as excessive replication activity can lead to severe side effects, while insufficient replication activity may fail to stimulate an adequate concentration of protective antibodies.Fig. 5Antibody dynamics after attenuated virus vaccination. Only one injection is implemented at the initial time with an attenuated live virus.The impact of viral inoculum dose on the ratio of IgM to IgGThe correlation between IgM and IgG levels has been extensively investigated in the context of dengue fever virus, where initial attention was directed to this phenomenon. Primary dengue infection is associated with a considerable increase in IgM levels, while the rise in IgG concentrations is not prominent54,55. However, during secondary dengue infection, a substantial increase in IgG levels is observed, similar to the response seen after secondary vaccination. In contrast, for respiratory infectious diseases such as COVID-19, a significant elevation in IgG levels can generally be detected after the initial infection. The differences in these observations can be attributed to variations in viral inoculum dose. A high viral inoculum dose, akin to that of inactivated vaccine administration, promptly enhances IgM levels but due to the absence of an initial IgG reservoir, the initial IgG levels are negligible. Conversion from IgM to IgG is reliant on the inefficient process of isotype switching, resulting in limited IgG elevation during the initial infection. However, this scenario changes during secondary infections, as elucidated in Sect. 3.2. In the case of bloodborne infectious diseases like dengue fever, where the viral inoculum dose is higher, the dynamics of IgM and IgG resemble those of vaccine administration. Conversely, for respiratory infectious diseases like COVID-19, where the viral inoculum dose is low, ample time is provided for IgG conversion, extending the incubation period and leading to a higher IgG/IgM ratio post-infection56. As demonstrated in Fig. 6, an increase in viral inoculum dose from 1 to 100, compared to Fig. 5, results in a shorter incubation period and a significant rise in induced IgM levels (solid red line) along with a marked decrease in IgG levels (solid green line), leading to a highly significant reduction in the IgG/IgM ratio.Fig. 6Dosage effect on IgM/IgG ratio. Only one injection is implemented at the initial time with larger number of attenuated live viruses (100 in this case).Calculation of the protection time brought by vaccinationThe term “herd immunity” was a common concept discussed prior to the widespread administration of COVID-19 vaccines. The attainment of herd immunity is achievable by vaccinating a proportion of the population equivalent to 1–1/R0, where R0 refers to the basic reproduction number of the virus, thus resulting in the fundamental eradication of the infectious disease. This approach has been successful in eliminating highly transmissible diseases like smallpox. However, combating COVID-19 has proven to be a more complex issue as it has become increasingly recognized that antibodies can undergo decay and result in time-limited protection, in addition to viral mutation effects. Consequently, the theory of herd immunity may not be applicable for certain infectious diseases, since repeated infections become unavoidable for the majority of the population. Our previous research22 provided a detailed explanation of the reasons why certain vaccines, such as those for smallpox and mumps, provide lifelong protection, while others, such as the hepatitis B vaccine, offer protection for over a decade, and vaccines like the COVID-19 and influenza vaccines confer shorter-term protection, typically within a year.The study of the duration of vaccine-induced protection is analogous to the study of the duration of naturally acquired immunity, both of which require the calculation of critical threshold levels of IgG. However, it should be noted that the critical thresholds differ for different antibody isotypes, with high-affinity antibodies having much lower thresholds compared to low-affinity antibodies. Once the host’s antibody kinetic parameters have been determined, our model can be used to calculate the duration of vaccine-induced protection. Our calculation methodology involves simulating viral invasion at different time points by setting the viral quantity at a specific time to 1. We then observe the dynamic changes in the virus and antibody populations. If significant viral proliferation and peak concentrations of antigen-antibody complexes occur during subsequent time points, it indicates an infection. When the concentration is relatively low, as shown in Fig. 7a, the infection may be asymptomatic or mild. When the concentration is higher, as shown in Fig. 7b, it corresponds to symptomatic infection. Figure 7a,b represent calculated diagrams illustrating the duration of protection for all infections and the duration of protection specifically against symptomatic infections following vaccination, respectively.In Fig. 7a, the actual viral invasion occurs at 200 time units, with viral proliferation and antibody elevation observed in the red region on the right after a long incubation period. At this point, the concentration of IgG-antigen complexes increases only slightly, which can be considered a case of asymptomatic infection. The critical time unit, marked as the 200th time unit, is the threshold before which viral infection barely leads to any viral proliferation due to rapid neutralization by high concentrations of IgG. Beyond this critical point, the virus demonstrates varying degrees of proliferation, and the later the invasion occurs, the lower the IgG concentration, resulting in more pronounced viral proliferation. As shown in Fig. 7b, when viral invasion occurs at the 400th time unit, significant viral proliferation, antibody elevation, and antigen-antibody complex elevation are observed. The concentration of antigen-antibody complexes exceeds 1e5, which can be considered the critical concentration for symptomatic infection. Therefore, viral invasions occurring before the 400th time unit do not lead to symptomatic infections, while those occurring thereafter consistently result in symptomatic infections. It can be observed that the duration of protection against symptomatic infections conferred by the vaccine is significantly longer than the duration of protection against all infections.An interesting phenomenon is that after vaccination or natural infection, to prevent the recurrence of severe infections, moderate exposure to the virus is advisable rather than achieving complete self-protection. Early exposure to the virus without significant symptoms, as shown in Fig. 7a, can lead to a re-elevation of IgG antibody levels, thus providing more durable subsequent protection. Complete avoidance of virus exposure may result in more pronounced clinical symptoms upon encountering the virus at a later stage, as demonstrated in Fig. 7b. The later the viral invasion occurs, the higher the peak concentration of antigen-antibody complexes, leading to more pronounced symptoms. For this reason, long periods of excessive self-protection, such as habitual mask-wearing, are not recommended.Fig. 7(a) An illustration of protection time calculation toward asymptomatic infection. First dose is injected at the initial time unit, second dose is injected at 50th time unit. Both injection dosages of antigen substances are 106. Single live virus invaded at 200th time unit. The protection duration and subsequent infection curve are both marked in this figure. (b) An illustration of protection time calculation toward symptomatic infection. First dose is injected at the initial time unit, second dose is injected at 50th time unit. Both injection dosages of antigen substances are 106. Single live virus invaded at 400th time unit. The protection duration and subsequent infection curve are both marked in this figure.Four suggestions in vaccine designIn the preceding sections, we expounded upon diverse mathematical models pertaining to vaccine administration. Drawing upon these models, we now proffer four recommendations for prospective vaccine design. Although the systematic overview and theoretical summarization of these approaches are yet to be accomplished, numerous scientists have endeavored to undertake and implement them.Enhancing the T-cell immunogenicity of the antigenThe T-cell immunogenicity of antigens is a critical factor in eliciting antibody production, yet it is often overlooked in vaccine design. Indeed, the T-cell immunogenicity of antigens provides the basis for host recognition of self and foreign components. When antibodies strongly bind to self-antigenic substances due to the low T-cell immunogenicity of self-antigens, they cannot undergo extensive proliferation with the aid of T cells. Consequently, they are rapidly eliminated by the immune system, forming the basis for clonal deletion28. The T-cell immunogenicity of antigens arises from the peptide sequences derived from antigen degradation, called primary sequences. Through bioinformatics techniques, scientists can now quantitatively analyze the T-cell immunogenicity of antigens57,58,59,60. Pathogenic microorganisms capable of causing acute infections, such as SARS-CoV-2, have primary sequences of antigens with highly potent T-cell immunogenicity. This is reflected in our model by larger values of k3 and k10. For the development of vaccines against this type of pathogenic microorganisms, the immunogenicity of helper T-cells is often not the primary consideration.Nevertheless, in the case of chronic infections such as HIV, where the T-cell immunogenicity of the antigen is low, it is necessary to moderately enhance the T-cell immunogenicity of the antigen. In immunization, increasing the T-cell immunogenicity of the antigen, indicated by the values of k3 and k10, is crucial for boosting the level of neutralizing antibodies. As shown in Fig. 8a, the IgG antibody level (denoted by the purple dashed line) after secondary immunization with an antigen exhibiting strong T-cell immunogenicity is significantly higher than that achieved with an antigen displaying weak T-cell immunogenicity (denoted by the red dashed line). Figure 8b presents two commonly used methods to enhance the T-cell immunogenicity of antigens, both of which have been widely applied in practice. The prerequisite for these methods is to not disrupt the antigenic epitopes of the antigen. The first method involves molecular engineering, where antigens are artificially modified without altering their antigenic epitopes. This is achieved by introducing point mutations in internal or non-epitope regions to alter their primary sequences and maximize T-cell immunogenicity. With the advent of computational protein design technologies, this method has been used to reduce or increase the T-cell immunogenicity of target antigens61,62. Another approach is grafting the original antigen onto other proteins to enhance its T-cell immunogenicity. Many vaccines use other viral vectors for production, inadvertently leading to the fusion of the target antigen with other protein components. Composite antigens generated through fusion often exhibit stronger T-cell immunogenicity and greatly enhance the induction of neutralizing antibodies. Encouraging results from the clinical trial of the HIV vaccine sv144 demonstrated that increasing the T-cell immunogenicity of antigens has the potential to overcome the challenges of HIV vaccines63,64. The RV144 trial, a randomized, double-blind phase 3 efficacy trial, employed a recombinant canarypox vector vaccine, ALVAC-HIV (vCP1521), expressing Env (clade E), group-specific antigen (Gag) (clade B), and protease (Pro) (clade B), along with an alum-adjuvanted AIDSVAX B/E and a bivalent HIV glycoprotein 120 (gp120) subunit vaccine. One inherent risk of this method is that the fusion antigens may introduce additional antigenic epitopes, thereby posing risks of inducing antibody responses against non-target antigenic epitopes.Fig. 8(a) Effect of T-cell immunogenicity on IgG induction. k3 and k10 are assigned to a smaller number (1.5) for the low T-cell immunogenicity group. They are assigned to a larger number (2.5) for its strong T-cell immunogenicity counterpart. (b) An illustration of approaches in improving Th-cell immonogenity. Two stragties are presented : rational design of antigen with conserved epitope structure and the design of polymer antigen with strong T-cell immonogenity segments.Directing the induction of high-affinity neutralizing antibodiesThe generation of high-affinity antibodies against targeted antigens represents a major challenge in vaccine development. A critical bottleneck in this process is the paucity of template antibodies in the IgM repertoire that display strong binding to vaccine antigens. This scarcity may be attributed to the high similarity between the antigenic epitopes of the vaccine antigen and self-antigens, resulting in the loss of highly binding antibodies to the target antigen due to clonal deletion. In the context of chronic infections such as HIV, only a small fraction of individuals are able to produce neutralizing antibodies65,66. To increase the production levels and probability of generating neutralizing antibodies, it is necessary to direct their induction through a targeted approach, as depicted in Fig. 9a. In a seminal study, Jardine et al. employed computational protein design techniques to induce mice to generate high concentrations of neutralizing antibodies against the classic HIV antigen, gp12067. This involved obtaining the crystal structure of the antibody-antigen complex and using computational protein design methods to introduce point mutations in the epitope region of the antigen to enhance antibody binding affinity. The mutated gp120 was then used as the vaccine for the first immunization, followed by a second immunization with the original vaccine. This approach yielded superior results compared to traditional two-dose immunization approaches. The simulated process of this method is depicted in Fig. 9b. During the simulation, two competitive antibody isotypes were utilized—one with strong binding affinity as a neutralizing antibody and another with weak binding affinity as a non-neutralizing antibody. At the outset, the level of neutralizing antibodies was extremely low at 1e−5, but exhibited high binding capability (k1 = 1e−5), while the initial level of non-neutralizing antibodies was higher at 1e3 but with lower binding affinity (k1 = 1e−-6). Through the employment of the directed induction approach, the binding affinity between antigen and antibody was enhanced to 5e−-5 due to the altered antigen in the first immunization. However, in the second immunization, when the original antigen was reintroduced, the binding affinity of the target antibodies reverted back to 1e−-5. As shown in Fig. 9b, the IgG levels induced by the new strategy (represented by the red dashed line) were significantly higher than those induced by the traditional method (represented by the yellow dashed line).An alternative and more direct strategy for stimulating the production of neutralizing antibodies involves the augmentation of initial antibody levels. This approach entails the utilization of gene editing techniques to introduce the genes encoding potent neutralizing antibodies into B cells. Subsequently, these genetically modified B cells are administered to the host in conjunction with vaccine administration, resulting in a rapid proliferation of neutralizing antibodies68,69,70. This methodology bears resemblance to the use of convalescent blood from individuals who have recovered from specific acute infectious diseases for therapeutic purposes. However, it is crucial to recognize that this approach carries inherent risks, as the antibodies generated are not naturally derived from the host and have not undergone clonal selection and deletion processes. Consequently, there exists a potential for robust immune reactions against host tissues.Fig. 9(a) An illustration of induced neutralizing antibody production by mutated antigen. The mutated antigen is used as the vaccine in the first immunization. It was designed to increase the binding affinity with targeted neutralizing antibody. (b) Comparison between induced antibody production and traditional vaccination strategy. First dose is injected at the initial time unit, second dose is injected at 100th time unit. Both injection dosages of antigen substances are 106.Reduce the decay rate of IgGRecurrent viral infections in certain individuals often result from discrepant decay rates observed among distinct antibodies, alongside variations in immunocompetence attributed to factors such as age and overall health. The diverse decay rates experienced under the complex circumstances of self-antigenic stimulation deviate from conventional direct decay rates of antibodies. Prior investigations have identified the crucial role played by self-antigenic components in sustaining IgG levels. The presence of self-antigenic moieties impedes a simple exponential relationship governing antibody decay, leading to extended protective periods demonstrated by select antibodies. The paramount importance of self-antigens in maintaining antibody concentration is exemplified in Fig. 10. Case 1 presents the original profile of antibody fluctuations (indicated by the red dashed line). Enhancing the initial concentration of self-antigenic material (Case 2; increasing from 1e5 to 1e6) effectively decelerates the decline rate of antibodies (depicted by the yellow dashed line). Similarly, amplifying the binding affinity between antibodies and self-antigens (Case 3; increasing from 1e−8 to 5e−8) substantially retards antibody decay (shown as the blue dashed line). It is noteworthy that while manipulating self-antigenic components remains beyond our control, we can regulate antibody attributes. Each antibody variant corresponds to a unique self-antigenic moiety. Some antibodies exhibit robust self-antigenic moieties, which maintain relatively high concentrations and confer prolonged protection against secondary infections, underscoring their significance. Extending vaccine-induced protection durations entails not only enhancing antibody neutralization capacity but also inducing targeted slow-decay-rate antibody responses. It is critical to acknowledge that repetitive antigenic exposure merely amplifies existing antibody levels, without imparting alterations to antibody type and attributes. As a result, individuals experiencing recurrent infections continue to exhibit antibodies characterized by rapid decay rates, resulting in substantially abbreviated protective cycles relative to their counterparts. This realization emphasizes that repetitive vaccination does not necessarily represent the optimal strategy.Fig. 10IgG dynamics in different self-antigen scenarios. First dose is injected at the initial time unit, second dose is injected at 50th time unit. Both injection dosages of antigen substances are 106. It can be seen that all IgG would decline after the peak but with different decay speeds.Reduce the adverse effects of vaccineAll vaccines exhibit varying degrees of adverse reactions, and we shall refrain from delving into the specific adverse effects induced by different vaccines in this particular context. Instead, our focus is to introduce the concept that, within our model, adverse reactions can be evaluated based on the alterations in the concentrations of antigen-antibody complexes. Vaccines operate by stimulating the production of IgG, which inevitably leads to the formation of complexes with antigenic substances during the process of antibody synthesis. While these adverse reactions are unavoidable, the extent of adverse effects resulting from vaccines of different types and administration methods, at the same level of antibody induction, displays significant variations. Through systematic comparisons among inactivated vaccines, mRNA vaccines, and attenuated vaccines, we can draw preliminary conclusions. For individuals with normal immune function, when achieving equivalent levels of antibody induction, mRNA vaccines and attenuated vaccines demonstrate notably lower adverse effects compared to inactivated vaccines. In other words, at the same level of adverse reactions, antibodies induced by mRNA vaccines and attenuated vaccines are significantly higher than those induced by inactivated vaccines. This observation also elucidates why mRNA vaccines exhibit superior preventive capabilities against COVID-19 when compared to traditional vaccines. Furthermore, our model allows for the quantitative assessment of such adverse reactions, thereby facilitating better control over vaccine dosages. In the case of mRNA vaccines and inactivated vaccines, adverse reactions demonstrate a substantial positive correlation with the administered dosage. Our model provides a theoretical framework for optimizing vaccination strategies in future in-silico research.
