[Paper Review] Mathematical model of SARS-Cov-2 propagation versus ACE2 fits COVID-19 lethality across age and sex and predicts that of SARS, supporting possible therapy

Ugo Bastolla|arXiv (Cornell University)|Apr 15, 2020

COVID-19 epidemiological studies4 citations

TL;DR

This study proposes a mathematical model linking SARS-CoV-2 lethality to ACE2 receptor levels, showing that higher ACE2 correlates with lower fatality due to reduced viral propagation speed in a non-monotonic regime. The model fits COVID-19 case fatality rates across age and sex with R² > 0.9 and predicts SARS lethality using spike protein binding rate ratios, challenging fears that ARBs worsen infection and identifying ACE2 and Ang-II as prognostic markers.

ABSTRACT

The fatality rate of Covid-19 escalates with age and is larger in men than women. I show that these variations correlate strongly with the level of the viral receptor protein ACE2 in rat lungs, which is consistent with the still limited and apparently contradictory data on human ACE2. Surprisingly, lower levels of the receptor correlate with higher fatality. However, a previous mathematical model predicts that the speed of viral progression in the organism has a maximum and then declines with the receptor level. Moreover, many manifestations of severe CoViD-19, such as severe lung injury, exacerbated inflammatory response and thrombotic problems may derive from increased Angiotensin II (Ang-II) level that results from degradation of ACE2 by the virus. I present here a mathematical model based on the influence of ACE2 on viral propagation and disease severity. The model fits Covid-19 fatality rate across age and sex with high accuracy ($r^2>0.9$) under the hypothesis that SARS-CoV-2 infections are in the dynamical regimes in which increased receptor slows down viral propagation. Moreover, rescaling the model parameters by the ratio of the binding rates of the spike proteins of SARS-CoV and SARS-CoV-2 allows predicting the fatality rate of SARS-CoV across age and sex, thus linking the molecular and epidemiological levels. The presented model opposes the fear that angiotensin receptor blockers (ARB), suggested as a therapy against the most adverse effects of CoViD-19, may favour viral propagation, and suggests that Ang-II and ACE2 are candidate prognostic factors for detecting population that needs stronger protection.

Motivation & Objective

• To explain the age- and sex-dependent variation in COVID-19 fatality rates using biological mechanisms.
• To test the hypothesis that ACE2 levels influence viral propagation speed non-monotonically, leading to reduced lethality at higher receptor levels.
• To predict SARS-CoV fatality rates using rescaled parameters from SARS-CoV-2 model, linking molecular and epidemiological scales.
• To evaluate the clinical implications of ACE2 degradation and Ang-II accumulation in severe COVID-19.
• To assess the safety of angiotensin receptor blockers (ARBs) in the context of ACE2 downregulation by SARS-CoV-2.

Proposed method

• Develops a mathematical model of viral propagation speed as a non-monotonic function of ACE2 receptor levels, based on a pre-existing viral infection model.
• Fits the model to observed case fatality rates (CFR) across six age-sex groups in Italy, Spain, and Germany using rescaled ridge regression with regularization.
• Uses Gaussian distribution of ACE2 levels across age and sex to model population-level CFR, with fitting parameters a, b, and c.
• Applies rescaling of SARS-CoV-2 model parameters by the ratio of spike protein on-rate constants (k_on) between SARS-CoV-2 and SARS-CoV to predict SARS lethality.
• Employs bootstrap resampling to estimate uncertainty in fitting parameters and selects c to yield 50% relative error on a and b.
• Incorporates the renin-angiotensin system (RAS) dynamics, where ACE2 degradation increases Ang-II, driving inflammation and thrombosis.

Experimental results

Research questions

• RQ1 Why does COVID-19 fatality increase with age and show a male bias, despite higher ACE2 levels in older females?
• RQ2 How can higher ACE2 levels correlate with lower lethality, given ACE2's role as a viral receptor?
• RQ3 Can a mathematical model of viral propagation speed explain the observed CFR patterns across age and sex?
• RQ4 Does the model predict the fatality rate of the 2003 SARS outbreak using SARS-CoV-2 parameters and spike protein binding rate ratios?
• RQ5 Is there a risk that ARBs, used to treat severe COVID-19, could enhance viral propagation due to ACE2 upregulation?

Key findings

• The model fits observed SARS-CoV-2 case fatality rates across age and sex with R² > 0.9, supporting the hypothesis that higher ACE2 levels slow viral propagation.
• ACE2 levels in rat lungs decrease with age and are higher in females, correlating with lower fatality in older women compared to men.
• The model predicts the 2003 SARS case fatality rate across age and sex using rescaled SARS-CoV-2 parameters and the ratio of spike protein on-rate constants (k_on_SARS-2/k_on_SARS ≈ 1.35).
• The rescaling of parameters yields a predicted lethality profile that matches observed SARS CFR, validating the model's cross-viral applicability.
• The model suggests that ACE2 and Ang-II levels are candidate prognostic factors for identifying high-risk populations.
• The findings counter concerns that ARBs might worsen infection, as higher ACE2 levels are associated with reduced viral spread and lower lethality.