Development of mathematical models for the analysis of hepatitis delta virus viral dynamics

Modelling HDV kinetics under the entry inhibitor bulevirtide suggests the existence of two HDV-infected cell populations

Background & Aims

Bulevirtide (BLV) was approved for the treatment of compensated chronic hepatitis D virus (HDV) infection in Europe in 2020. However, research into the effects of the entry inhibitor BLV on HDV-host dynamics is in its infancy.

Methods

Eighteen patients with HDV under nucleos(t)ide analogue treatment for hepatitis B, with compensated cirrhosis and clinically significant portal hypertension, received BLV 2 mg/day. HDV RNA, alanine aminotransferase (ALT), and hepatitis B surface antigen (HBsAg) were measured at baseline, weeks 4, 8 and every 8 weeks thereafter. A mathematical model was developed to account for HDV, HBsAg and ALT dynamics during BLV treatment.

Results

Median baseline HDV RNA, HBsAg, and ALT were 4.9 log IU/ml [IQR: 4.4-5.8], 3.7 log IU/ml [IQR: 3.4-3.9] and 106 U/L [IQR: 81-142], respectively. During therapy, patients fit into four main HDV kinetic patterns: monophasic (n = 2), biphasic (n = 10), flat-partial response (n = 4), and non-responder (n = 2). ALT normalization was achieved in 14 (78%) patients at a median of 8 weeks (range: 4-16). HBsAg remained at pre-treatment levels. Assuming that BLV completely (∼100%) blocks HDV entry, modeling indicated that two HDV-infected cell populations exist: fast HDV clearing (median t1/2 = 13 days) and slow HDV clearing (median t1/2 = 44 days), where the slow HDV-clearing population consisted of ∼1% of total HDV-infected cells, which could explain why most patients exhibited a non-monophasic pattern of HDV decline. Moreover, modeling explained ALT normalization without a change in HBsAg based on a non-cytolytic loss of HDV from infected cells, resulting in HDV-free HBsAg-producing cells that release ALT upon death at a substantially lower rate compared to HDV-infected cells.

Conclusion

The entry inhibitor BLV provides a unique opportunity to understand HDV, HBsAg, ALT, and host dynamics.

Impact and implications

Mathematical modeling of hepatitis D virus (HDV) treatment with the entry inhibitor bulevirtide (BLV) provides a novel window into the dynamics of HDV RNA and alanine aminotransferase. Kinetic data from patients treated with BLV monotherapy can be explained by hepatocyte populations with different basal HDV clearance rates and non-cytolytic clearance of infected cells. While further studies are needed to test and refine the kinetic characterization described here, this study provides a new perspective on viral dynamics, which could inform evolving treatment strategies for HDV.

Modeling the Interplay between HDV and HBV in Chronic HDV/HBV Patients

Hepatitis D virus is an infectious subviral agent that can only propagate in people infected with hepatitis B virus. In this study, we modified and further developed a recent model for early hepatitis D virus and hepatitis B virus kinetics to better reproduce hepatitis D virus and hepatitis B virus kinetics measured in infected patients during anti-hepatitis D virus treatment. The analytical solutions were provided to highlight the new features of the modified model. The improved model offered significantly better prospects for modeling hepatitis D virus and hepatitis B virus interactions.

A Mathematical Model for early HBV and -HDV Kinetics during Anti-HDV Treatment

Hepatitis delta virus (HDV) is an infectious subviral agent that can only propagate in people infected with hepatitis B virus (HBV). HDV/HBV infection is considered to be the most severe form of chronic viral hepatitis. In this contribution, a mathematical model for the interplay between HDV and HBV under anti-HDV treatment is presented. Previous models were not designed to account for the observation that HBV rises when HDV declines with HDV-specific therapy. In the simple model presented here, HDV and HBV kinetics are coupled, giving rise to an improved viral kinetic model that simulates the early interplay of HDV and HBV during anti-HDV therapy.

Intra- and Inter-cellular Modeling of Dynamic Interaction between Zika Virus and Its Naturally Occurring Defective Viral Genomes

Here, we examine in silico the infection dynamics and interactions of two Zika virus (ZIKV) genomes: one is the full-length ZIKV genome (wild type [WT]), and the other is one of the naturally occurring defective viral genomes (DVGs), which can replicate in the presence of the WT genome, appears under high-MOI (multiplicity of infection) passaging conditions, and carries a deletion encompassing part of the structural and NS1 protein-coding region. Ordinary differential equations (ODEs) were used to simulate the infection of cells by virus particles and the intracellular replication of the WT and DVG genomes that produce these particles. For each virus passage in Vero and C6/36 cell cultures, the rates of the simulated processes were fitted to two types of observations: virus titer data and the assembled haplotypes of the replicate passage samples. We studied the consistency of the model with the experimental data across all passages of infection in each cell type separately as well as the sensitivity of the model's parameters. We also determined which simulated processes of virus evolution are the most important for the adaptation of the WT and DVG interplay in these two disparate cell culture environments. Our results demonstrate that in the majority of passages, the rates of DVG production are higher inC6/36 cells than in Vero cells, which might result in tolerance and therefore drive the persistence of the mosquito vector in the context of ZIKV infection. Additionally, the model simulations showed a slower accumulation of infected cells under higher activation of the DVG-associated processes, which indicates a potential role of DVGs in virus attenuation. IMPORTANCE One of the ideas for lessening Zika pathogenicity is the addition of its natural or engineered defective virus genomes (DVGs) (have no pathogenicity) to the infection pool: a DVG is redirecting the wild-type (WT)-associated virus development resources toward its own maturation. The mathematical model presented here, attuned to the data from interplays between WT Zika viruses and their natural DVGs in mammalian and mosquito cells, provides evidence that the loss of uninfected cells is attenuated by the DVG development processes. This model enabled us to estimate the rates of virus development processes in the WT/DVG interplay, determine the key processes, and show that the key processes are faster in mosquito cells than in mammalian ones. In general, the presented model and its detailed study suggest in what important virus development processes the therapeutically efficient DVG might compete with the WT; this may help in assembling engineered DVGs for ZIKV and other flaviviruses.

Using the pandemic to decolonize nature: Interrogating pragmatic education

This article seeks to use Dewey’s interpretation of pragmatism and education as a model for how dominant notions of school exemplify a colonizing theory of nature. The article argues that Dewey sought to commodify nature as a tool for human progress. This aspect of Dewey’s beliefs is further demonstrated in the kind of schooling that is being implemented through globalization. The article draws on Indigenous concepts of the nature and the Earth, for decolonizing science instruction in an elementary classroom.

A multi-scale spatial model of hepatitis-B viral dynamics

Chronic hepatitis B viral infection (HBV) afflicts around 250 million individuals globally and few options for treatment exist. Once infected, the virus entrenches itself in the liver with a notoriously resilient colonisation of viral DNA (covalently-closed circular DNA, cccDNA). The majority of infections are cleared, yet we do not understand why 5% of adult immune responses fail leading to the chronic state with its collateral morbid effects such as cirrhosis and eventual hepatic carcinoma. The liver environment exhibits particularly complex spatial structures for metabolic processing and corresponding distributions of nutrients and transporters that may influence successful HBV entrenchment. We assembled a multi-scaled mathematical model of the fundamental hepatic processing unit, the sinusoid, into a whole-liver representation to investigate the impact of this intrinsic spatial heterogeneity on the HBV dynamic. Our results suggest HBV may be exploiting spatial aspects of the liver environment. We distributed increased HBV replication rates coincident with elevated levels of nutrients in the sinusoid entry point (the periportal region) in tandem with similar distributions of hepatocyte transporters key to HBV invasion (e.g., the sodium-taurocholate cotransporting polypeptide or NTCP), or immune system activity. According to our results, such co-alignment of spatial distributions may contribute to persistence of HBV infections, depending on spatial distributions and intensity of immune response as well. Moreover, inspired by previous HBV models and experimentalist suggestions of extra-hepatic HBV replication, we tested in our model influence of HBV blood replication and observe an overall nominal effect on persistent liver infection. Regardless, we confirm prior results showing a solo cccDNA is sufficient to re-infect an entire liver, with corresponding concerns for transplantation and treatment.

Mathematical models of the interrelated dynamics of hepatitis D and B

The hepatitis delta virus (HDV) is a rarest form of viral hepatitis, but has the worst outcomes for patients.It is a subviral satellite dependent on coinfection with hepatitis B (HBV) to replicate within the host liver.To date, there has been little to no modeling effort for HDV. Deriving and analyzing such a mathematical model poses difficulty as it requires the inclusion of (HBV). Here we begin with a well-studied HBV model from the literature and expand it to incorporate HDV. We investigate two models, one with and one without infected hepatocyte replication. Additionally, we consider treatment by the drug lamivudine. Comparison of model simulations with experimental results of lamivudine treatment indicate that infected cell proliferation may play a significant role in chronic HDV infection. Our results also shed light on several questions surrounding HDV and illustrate the need for more data.

Understanding early serum hepatitis D virus and hepatitis B surface antigen kinetics during pegylated interferon-alpha therapy via mathematical modeling

There is little information on the early kinetics of hepatitis delta virus (HDV) and hepatitis B surface antigen (HBsAg) during interferon-α therapy. Here a mathematical model was developed and fitted to frequent HDV and HBsAg kinetic data from 10 patients during the first 28 weeks of pegylated-interferon-α2a (peg-IFN) therapy. Three patients achieved a complete virological response (CVR), defined as undetectable HDV 6 months after treatment stopped with loss of HBsAg and anti-HBsAg seroconversion. After initiation of therapy, a median delay of 9 days (interquartile range [IQR]: 5-15) was observed with no significant changes in HDV level. Thereafter, HDV declined in a biphasic manner, where a rapid first phase lasting for 25 days (IQR: 23-58) was followed by a slower or plateau second phase. The model predicts that the main effect of peg-IFN is to reduce HDV production/release with a median effectiveness of 96% (IQR: 93-99.8). Median serum HDV half-life (t1/2 ) was estimated as 2.9 days (IQR: 1.5-5.3) corresponding to a pretreatment production and clearance of about 10(10) (IQR: 10(9.7) -10(10.7) ) virions/day. None of the patients with flat second phase in HDV achieved CVR. HBsAg kinetics of decline paralleled the second phase of HDV decline consistent with HBsAg-productive-infected cells being the main source of production of HDV, with a median t1/2 of 135 days (IQR: 20-460). The interferon lambda-3 polymorphism (rs12979860) was not associated with kinetic parameters.

CONCLUSION

Modeling results provide insights into HDV-host dynamics, the relationship between serum HBsAg levels and HBsAg-infected cells, IFN's mode of action, and its effectiveness. The observation that a flat second phase in HDV and HBsAg kinetics was associated with failure to achieve CVR provides the basis to develop early stopping rules during peg-IFN treatment in HDV-infected patients.

Life cycle and pathogenesis of hepatitis D virus: A review

Hepatitis D virus (HDV) is a defective RNA virus which requires the help of hepatitis B virus (HBV) virus for its replication and assembly of new virions. HDV genome contains only one actively transcribed open reading frame which encodes for two isoforms of hepatitis delta antigen. Post-translational modifications of small and large delta antigens (S-HDAg and L-HDAg) involving phosphorylation and isoprenylation respectively confer these antigens their specific properties. S-HDAg is required for the initiation of the viral genome replication, whereas L-HDAg serves as a principal inhibitor of replication and is essential for the assembly of new virion particles. Immune mediation has usually been implicated in HDV-associated liver damage. The pathogenesis of HDV mainly involves interferon-α signaling inhibition, HDV-specific T-lymphocyte activation and cytokine responses, and tumor necrosis factor-alpha and nuclear factor kappa B signaling. Due to limited protein coding capacity, HDV makes use of host cellular proteins to accomplish their life cycle processes, including transcription, replication, post-transcriptional and translational modifications. This intimate host-pathogen interaction significantly alters cell proteome and is associated with an augmented expression of pro-inflammatory, growth and anti-apoptotic factors which explains severe necroinflammation and increased cell survival and an early progression to hepatocellular carcinoma in HDV patients. The understanding of the process of viral replication, HBV-HDV interactions, and etio-pathogenesis of the severe course of HDV infection is helpful in identifying the potential therapeutic targets in the virus life cycle for the prophylaxis and treatment of HDV infection and complications.

Genes alternations with exposure time of environmental factors

A theoretical model discussing the environmental factors (EFs) effect of exposure time on genes, which leads to human diseases, is presented using multi-logistic model. The advantages and limitations of this model are discussed in terms of its usefulness for simulating genetic samples. It has been shown that EFs affect genes with the same degree both at high exposure level, low exposure time and at low exposure level, high exposure time.