🧬 biology

Mathematical Modeling of HDV RNA, HBV DNA, and HBsAg Dynamics during Lonafarnib-Based Therapy: Insights from the LOWR HDV-1 Study

This study utilizes a mathematical model to characterize the distinct kinetic patterns of HDV RNA, HBV DNA, and HBsAg in coinfected patients treated with lonafarnib, revealing a 1.26-day HDV half-life, 94% initial treatment efficacy, and a mechanism where HDV suppression triggers a compensatory increase in HBV DNA production.

Original authors: Adquate Mhlanga, Louis Shekhtman, Rami Zakh, Sarah Duehren, Ashish Goyal, Alexander Churkin, Vladimir Reinharz, Danny Barash, Jeffrey Glenn, Ohad Etzion, Scott J. Cotler, Cihan Yurdaydin, Harel Dahari

Published 2026-06-12

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Adquate Mhlanga, Louis Shekhtman, Rami Zakh, Sarah Duehren, Ashish Goyal, Alexander Churkin, Vladimir Reinharz, Danny Barash, Jeffrey Glenn, Ohad Etzion, Scott J. Cotler, Cihan Yurdaydin, Harel Dahari

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

The Big Picture: Two Viruses, One Factory

Imagine the liver cells as a busy factory. In this study, the factory is infected by two different viruses: Hepatitis B (HBV) and Hepatitis D (HDV).

HBV is like the original factory owner. It builds its own products (HBV DNA) and also builds the "shipping containers" (a protein called HBsAg) needed to send viruses out.
HDV is a "hijacker." It cannot build its own shipping containers. It steals the containers built by HBV to send its own products (HDV RNA) out into the bloodstream.

The researchers wanted to understand what happens when you give a specific drug, Lonafarnib (LNF), to patients with both viruses. This drug is like a wrench thrown into the HDV assembly line—it stops HDV from packaging itself. Crucially, the drug does not touch the HBV factory owner directly.

The Experiment: Watching the Factory in Real-Time

The team looked at data from 15 patients who took this drug, either alone or mixed with other helpers (like Ritonavir or Interferon). They tracked three things over time:

HDV RNA: The hijacker's product.
HBV DNA: The owner's product.
HBsAg: The shipping containers.

They used a mathematical model (a computer simulation) to figure out exactly how the drug worked and why the viruses reacted the way they did.

Key Findings Explained with Analogies

1. The "Hijacker" Slows Down (HDV Kinetics)

When the drug was introduced, the HDV levels didn't drop instantly. There was a short pause (0–2 days), like a delivery truck waiting at the gate before it starts moving.

Once the drug kicked in, HDV levels dropped rapidly. The researchers found the drug was about 94% effective at stopping HDV production immediately.

The "Flat" vs. "Two-Step" Drop:
- Monotherapy (Drug alone): In many patients, the HDV levels dropped fast and then hit a "floor" (a plateau). It stopped going down. This is called a "flat partial response."
- Combination Therapy (Drug + Helper): When the drug was mixed with a helper (Ritonavir or Interferon), the HDV levels didn't just stop; they kept dropping slowly in a second phase. It was like the drug got stronger over time, eventually reaching nearly 99% effectiveness.

2. The "Owner" Gets a Boost (HBV Kinetics)

Here is the most surprising part. When the drug successfully suppressed the HDV hijacker, the HBV owner suddenly started producing more of its own product (HBV DNA).

The Analogy: Imagine the HDV hijacker was constantly bullying the HBV owner, telling him to "shut up and work less." When the drug kicked the hijacker out (or made it weak), the HBV owner felt relieved and started working overtime.
The Result: In about two-thirds of the patients, HBV DNA levels went up. The model showed that once HDV dropped below a certain "safety threshold," the HBV production rate jumped by a median of 4-fold.
The Exception: Patients who took the drug plus Interferon didn't see this spike. The Interferon acted like a security guard that kept the HBV owner in check even after the hijacker was gone.

3. The "Shipping Containers" Stayed Put (HBsAg)

While the viral levels (HDV and HBV DNA) were changing wildly, the level of HBsAg (the shipping containers) stayed exactly the same.

The Analogy: This suggests that the number of factory workers (infected liver cells) didn't change much. The drug stopped the production of new viruses, but it didn't kill off the workers who were already there. Since the workers stayed the same, the amount of containers they made stayed steady.

What the Math Tells Us

The researchers built a computer model that perfectly matched what they saw in the patients. This model helped them calculate specific numbers:

Half-life: The HDV virus in the blood is very short-lived; it disappears in about 1.26 days if not constantly replenished.
The "Threshold": There is a specific level of HDV in the blood. As long as HDV is above this level, it keeps HBV suppressed. Once the drug pushes HDV below this level, HBV wakes up and starts multiplying again.

Summary

The paper concludes that Lonafarnib is a very effective tool for stopping the HDV hijacker. However, because HDV naturally suppresses HBV, stopping HDV can accidentally wake up HBV, causing it to produce more virus.

Monotherapy stops HDV but often hits a wall, and HBV might wake up.
Combination therapy (adding a helper drug) keeps the pressure on HDV, preventing it from plateauing, and in some cases (with Interferon), prevents HBV from waking up.

The study provides a mathematical "blueprint" showing exactly how these two viruses interact and how different drug combinations change the rules of the game inside the human body.

Technical Summary: Mathematical Modeling of HDV RNA, HBV DNA, and HBsAg Dynamics during Lonafarnib-Based Therapy

Problem Statement
Hepatitis D virus (HDV) requires the hepatitis B virus (HBV) envelope to replicate, creating a complex coinfection dynamic where HDV often suppresses HBV replication. While previous mathematical models have explored HBV/HDV coinfection, many were either too simplistic to capture specific therapeutic responses or too complex (incorporating intracellular dynamics) to be fitted to clinical patient data. There was a need for a robust, semi-mechanistic model capable of simultaneously characterizing the kinetics of serum HDV RNA, HBV DNA, and hepatitis B surface antigen (HBsAg) in response to anti-HDV therapies, specifically to understand how suppressing HDV affects HBV dynamics.

Methodology
The authors analyzed data from the LOWR HDV-1 study, a Phase 2 pilot trial involving 15 patients with chronic HBV/HDV coinfection treated with lonafarnib (LNF), a prenylation inhibitor that disrupts HDV assembly but does not directly inhibit HBV. The study included LNF monotherapy and combination therapies with ritonavir (RTV) or pegylated interferon-α (PEG-IFN𝛼).

The authors developed a new mathematical model consisting of three ordinary differential equations (ODEs) describing the dynamics of serum HDV RNA ( $D$ ), HBV DNA ( $B$ ), and HBsAg ( $H$ ). Key features of the model include:

Constant Infected Cell Population: The model assumes a constant number of co-infected hepatocytes ( $I_0$ ) during therapy, justified by the stability of HBsAg levels.
HDV-Dependent HBV Production: The production rate of HBV DNA is modeled as dependent on HDV RNA levels. Specifically, it follows a function where HBV production is suppressed when HDV RNA is high and increases as HDV RNA declines below a specific threshold ( $\kappa$ ).
Time-Dependent Efficacy: Treatment efficacy ( $\epsilon$ ) in blocking HDV RNA production is modeled as increasing over time ( $g$ ), reflecting in vitro findings that LNF progressively increases non-infectious HDV genomes.
Pharmacological Delay: A delay parameter ( $\tau$ ) accounts for the time between drug administration and the onset of measurable antiviral activity.

Parameter estimation was performed using a nonlinear mixed-effects (NLME) population approach via Monolix software, utilizing data from 15 patients across five treatment groups. The model was fitted to viral kinetic data up to the point of HDV breakthrough or the end of treatment.

Key Results

HDV Kinetics: The model successfully reproduced three distinct kinetic patterns observed in patients:
- Flat Partial Response (FPR): An initial decline followed by a plateau, observed primarily in monotherapy patients.
- Biphasic Decline: A rapid first phase followed by a slower second phase, observed primarily in combination therapy patients.
- Monophasic Decline: Followed by viral breakthrough.
  The model estimated an HDV RNA half-life of 1.26 days [95% CI: 1.05–1.47] and a first-phase treatment efficacy of 94% [95% CI: 89%–97%] in blocking HDV RNA production. The second phase of decline in biphasic responders was attributed to a time-dependent increase in efficacy, reaching a maximum of ~99%.
HBV Dynamics: The model explained the observed increase in serum HBV DNA in 9 of 15 patients as a consequence of HDV suppression. As HDV RNA levels dropped below a patient-specific threshold ( $\kappa$ , estimated at a median of 2.78 log10 IU/mL), the inhibitory pressure on HBV was lifted, resulting in a median 4-fold increase in HBV DNA production rate.
HBsAg Stability: The model confirmed that HBsAg levels remained stable throughout treatment, supporting the assumption of a constant population of HBsAg-producing cells.
Treatment Comparisons: Combination therapy (LNF + RTV or PEG-IFN𝛼) was significantly associated with biphasic HDV decline patterns compared to monotherapy. The parameter $g$ (time-dependent efficacy) was significantly higher in the combination therapy group.
Model Extensions: An extended model distinguishing between infectious and non-infectious HDV particles was tested. The authors found that varying the assumed ratio of infectious to non-infectious particles had minimal impact on parameter estimates, suggesting that total HDV RNA measurements are sufficient for the current modeling framework.

Significance and Claims
The paper claims that this study provides the first mathematical model to simultaneously characterize serum HDV RNA, HBV DNA, and HBsAg kinetics during anti-HDV therapy. The authors state that their model offers a quantitative framework to:

Explain the interplay between HDV suppression and the subsequent rebound of HBV DNA.
Differentiate the kinetic outcomes of monotherapy versus combination therapy.
Provide a basis for understanding why different regimens produce distinct viral kinetic patterns.

The authors conclude that the model serves as a "good starting point" to improve the understanding of HDV suppression and associated HBV dynamics. They explicitly note limitations, including the assumption of a constant infected cell population, the inability to capture viral breakthroughs within the current model structure, and the semi-mechanistic nature of the time-dependent efficacy parameter ( $g$ ), which does not model underlying intracellular mechanisms. The authors emphasize that further studies are needed to delineate the molecular interplay between HDV and HBV.