Massinissa Beldjenna1, Dr. J. G. Coen van Hasselt1, Tingjie Guo1
1System Pharmacology and Pharmacy, Leiden Academic Centre for Drug Research (LACDR), Leiden University
Introduction and objectives: Lytic viruses, such as oncolytic viruses and bacteriophages, follow complex replication dynamics in codependence with their host cells [1, 2]. It can be modeled with a delay differential equation model (DDE) with four key parameters [3, 4]: (i) adsorption rate f, the rate at which free viruses bind to a target host, (ii) burst size ß, the number of viruses released per cell lysis, (iii) eclipse period ? and (iv) latent period t, the delays from adsorption to first intracellular replication and to cell lysis respectively. Single-cell experimental studies have shown cellular variability in latent period, eclipse period [5] and burst size [6]. Yet, those parameters are traditionally modeled as fixed values for the whole cell population [7]. Distribution of the latent period has been previously addressed using distributed delay differential equation (DDDE) [7, 8] or transit compartments (TC) [9] models. Yet, the benefits of these methods have not been evaluated to warrant the associated increase in model complexity. Moreover, distribution characteristics for other parameters are missing in current viral dynamic models, despite being observed experimentally [5, 6, 10]. Here, we systematically assessed the relevance of distributed methods in the context of viral dynamic models. We developed a comprehensive modeling framework, aiming specifically to: (i) determine which parameter distributions impact population dynamics, (ii) quantify how difference in distribution can influence predictions, and (iii) compare this approach with simpler model structures to inform model building in viral PD. Methods: We implemented a viral dynamic model as an extension of Campbell’s viral dynamics model [3], with logistic growth of the host cell, saturable adsorption rate [11], delayed lysis, and burst size as a function of eclipse and latent periods as observed experimentally [10]. To account for cell-level variability, we introduced distributions: (i) t and ? are distributed around mean values t0 and ?0, (ii) For given t and ?, ß is distributed around a mean value ß0(t,?) [10], (iii) At given time t, f is distributed around a mean value f0(t) (saturation) [11]. We investigated normal, lognormal and gamma distributions for all four viral parameters, within a range of relative standard deviations (rsd = 10 to 50%) observed experimentally [5, 12, 13]. We compared resulting simulated profiles of viruses and host cells, using a Monte Carlo approach to cover typical ranges of all parameters (with 100 combinations). We compared our model to the non-distributed DDE model and to the TC model [14] to quantify improvement in predictions. The number of transit compartments and transit rate were chosen to have the same mean latent period and same standard deviation as the distributed model [15]. The differential equations were solved using the Euler method for distributed delay differential equations. The model was implemented in Python, using standard libraries scipy and numpy. Results: We found that only distribution of the latent period and its influence on burst size impacted population dynamics. The distribution shape influenced little predicted dynamics (< 8% difference for rsd = 50%, highest variability previously observed [12]). However, neglecting the distribution of latent period did introduce bias in the model prediction: (i) setting t to “time to first observed lysis”, as is standard practice [9, 16], resulted in high error for all standard deviations (25% to 58% error for rsd = 10% to 50%); (ii) setting t to the mean of its distribution introduced small bias up to 20% variability (< 8% error). However, the error remained substantial for high variability (32% for rsd = 50%). As such, for moderate variability (rsd = 20%, observed for ? and T7-phages [5, 13]), the distributed model can be decently approximated by the non-distributed DDE model. As for the TC model, it performed slightly worse than the DDE model for all standard deviations (14% and 38% error for rsd = 20% and 50% respectively). Conclusion: We successfully evaluated the impact of cellular variability on viral dynamics, to help better inform model selection for different use cases in viral dynamics. Both DDE models, when using mean latent period, and TC models proved to be adequate approximations of the distributed model for moderate latent period variability [5, 13]. If the latent period variance is expected to be large, a full DDDE model is warranted.
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Reference: PAGE 33 (2025) Abstr 11340 [www.page-meeting.org/?abstract=11340]
Poster: Methodology - New Modelling Approaches