Modeling the molecular impact of SARS-CoV-2 infection on the renin-angiotensin system
MModeling the molecular impact of SARS-CoV-2 infectionon the renin-angiotensin system
Fabrizio Pucci, Philippe Bogaerts, Marianne Rooman ∗ Computational Biology and Bioinformatics,Universit´e Libre de Bruxelles, CP 165/61, Roosevelt Ave. 50, 1050 Brussels,BelgiumAugust 4, 2020
Abstract
SARS-CoV-2 coronavirus infection is mediated by the binding of its spike protein tothe angiotensin-converting enzyme 2 (ACE2), which plays a pivotal role in the renin-angiotensin system (RAS). The study of RAS dysregulation due to SARS-CoV-2 in-fection is fundamentally important for a better understanding of the pathogenic mech-anisms and risk factors associated with COVID-19 coronavirus disease, and to designeffective therapeutic strategies. In this context, we developed a mathematical model ofRAS based on data regarding protein and peptide concentrations; the model was testedon clinical data from healthy normotensive and hypertensive individuals. We then usedour model to analyze the impact of SARS-CoV-2 infection on RAS, which we modeledthrough a down-regulation of ACE2 as a function of viral load. We also used it topredict the effect of RAS-targeting drugs, such as RAS-blockers, human recombinantACE2, and angiotensin 1-7 peptide, on COVID-19 patients; the model predicted animprovement of the clinical outcome for some drugs and a worsening for others.
Introduction
Since December 2019, the world has been facing a global viral pandemic of the novel severeacute respiratory syndrome coronavirus 2, ‘SARS-CoV-2’; this pandemic has, to date, causedmillions of people to be infected and hundreds of thousands to die (Dong et al., 2020). Firstdetected in the city of Wuhan (China) (Chan et al., 2020; Huang et al., 2020; Chen et al.,2020b; Wu et al., 2020), SARS-CoV-2 spreads rapidly throughout the world. The coronavirusfamily, to which SARS-CoV-2 belongs, includes a number of viruses, such as SARS-CoVand MERS-CoV, that have been implicated in serious epidemics that cause acute respiratorydistress syndrome (ARDS). There is not yet consensus on the origin of the SARS-CoV-2(Andersen et al., 2020; Benvenuto et al., 2020; Zhang et al., 2020b; Zhou et al., 2020), but ∗ To whom the correspondence should be addressed: [email protected] a r X i v : . [ q - b i o . M N ] A ug he primary hypothesis is that it originated from bat ( Rhinolophus affinisor ) or pangolin(
Manis javanica ), since the genomes of these two viral species share high sequence identitywith SARS-CoV-2.Coronaviral genomes encode a series of structural proteins, one of which is the spikeglycoprotein or S-protein that protrudes from the membrane surface (Zhou et al., 2020).Similar to the SARS-CoV virus that was identified in 2003, the S-protein of SARS-CoV-2 hasbeen shown to bind to the angiotensin-converting enzyme 2 (
ACE2 ) so that it can be used asan entry receptor to the cell (Zhou et al., 2020; Hoffmann et al., 2020; Zhang et al., 2020a; Caoet al., 2020; Lu et al., 2020). This protein plays a pivotal role in the renin-angiotensin system(RAS) signaling pathway (Burrell et al., 2004) by cleaving angiotensin I and II peptides togenerate angiotensin 1–9 and the biologically active peptide angiotensin 1–7, respectively(Donoghue et al., 2000; Tipnis et al., 2000).
ACE2 is highly expressed in type II alveolarcells of lung, epithelial cells of oral mucosa, colon enterocytes, myocardial cells and kidneyproximal tubule cells. The protective role of ACE2 in severe ARDS is also widely recognized(Imai et al., 2005; Kuba et al., 2005). Indeed, it has been shown, both in vitro and in vivo mouse models, that a loss of
ACE2 expression causes increased production of angiotensin II,and that this contributes to lung failure (Kuba et al., 2005)It has already been established years ago that the SARS-CoV spike protein interfereswith RAS due to its binding to ACE2 (Li et al., 2003), thus causing ACE2 downregulation;this has opened up a number of interesting means of tackling SARS-CoV infection throughRAS modulation. Indeed, injection of a soluble form of recombinant human
ACE2 ( rhACE2 ,GSK2586881) into mice infected with SARS-CoV appears to have a double role (Kuba et al.,2005): it slows the viral infection by binding to the S-protein and rescues ACE2 activity, thuscausing angiotensin II reduction and protecting lung from severe failure. rhACE2 has been tested in phase II trials for its ability to ameliorate ARDS (Khan et al.,2017). Although rhACE2 treatment is well tolerated by patients and it offers a significantreduction in angiotensin II level, the clinical distress severity was not reduced in a recentpilot study (Khan et al., 2017). Further studies are needed to understand the biologicaldifferences between the responses of animal models and humans.Since SARS-CoV-2 also targets
ACE2 receptors when it infects cells, it is logical to hy-pothesize that rhACE2 might help reduce the severity of COVID-19 disease (Gheblawi et al.,2020). Indeed, it has been shown that rhACE2 inhibits SARS-CoV-2 infection in vitro , andthat this inhibition depends both on the initial quantity of the virus and on rhACE2 concen-tration (Monteil et al., 2020). Following these exciting results, a clinical trial with exogenoussubmission of rhACE2 recently started (NCT04287686, 2020). A number of other clinicaltrials are also underway that target the dysregulated RAS system to restore its function-ality (NCT04332666, 2020; NCT04335786, 2020; NCT04312009, 2020; NCT04311177, 2020;NCT04318418, 2020).Hypertension and cardiovascular disease have been shown to be risk factors in cases ofSARS-CoV-2 infection. This brings into question what might be the potential effects onCOVID-19 development of the RAS-targeting drugs that are used to treat hypertension andcardiovascular disease. RAS-targeting drugs fall into three categories: (i) angiotensin convert-ing enzyme inhibitors (ACE-I), (ii) angiotensin receptor blockers (ARB), and (iii) direct renininhibitors (DRI) (Fig. 1). Several recent studies on large patient cohorts (Reynolds et al.,2020; Mancia et al., 2020; Mehra et al., 2020) conclude that there is only weak correlationbetween treatment with drugs from these categories and any substantial increase in risk of2OVID-19 disease.Despite these interesting findings, there is not yet a detailed understanding of how SARS-CoV-2 infection leads to a dysregulation of RAS and, in severe cases, to ARDS. It is offundamental importance that we gain better insights into the perturbed RAS in order toproperly elucidate the pathogenic mechanisms and associated risk factors of SARS-CoV-2infection; this, in turn, will enable novel therapeutic strategies to be designed and tested sothat disease progression can be inhibited.
Results
The main objective of this paper is to investigate the effect of RAS-targeting drugs and SARS-CoV-2 infection, both individually and in combination, on RAS. We started by setting up thedynamical model describing RAS of healthy normotensive and hypertensive individuals. Therobustness and predictive power of our model was assessed by investigating the effects of threetypes of antihypertensive drugs: (i) ACE-I, (ii) ARB and (iii) DRI. This assessment includeda comparison of model simulations with patient clinical data. Following confirmation of modelrobustness and accuracy, ACE2 downregulation due to viral infection was introduced into themodel to quantitatively predict how RAS is perturbed in COVID-19.
Modeling the renin-angiotensin system
The RAS system has been widely studied (Paul et al., 2006; Raizada et al., 1993; Casariniet al., 2016). It plays a key role in the regulation of a large series of physiological systemsamong which the renal, lung and cardiovascular systems. Consequently, its dysregulation isrelated to multiple pathological conditions such as hypertension and ARDS, just to mentionsome of them (Ruiz-Ortega et al., 2001; de Man et al., 2012; Jia et al., 2018; te Riet et al.,2015; Kobori et al., 2007).There are two different types of RAS: the circulating RAS that is localized in the plasmaand is involved in the regulation of the cardiovascular system, and the tissue-localized systemsthat act intracellularly or interstitially within different organs in association with the systemicRAS or independently of it. Here we focus on the local RAS within the pulmonary circulationand model its network of biochemical reactions schematically depicted in Fig. 1.When the blood pressure decreases, the juxtaglomerular kidney cells that sense changesin renal perfusion pressure secret an aspartic protease protein called renin ( RE , EC 3.4.23.15).The activity of this enzyme, called plasma renin activity ( P RA ), is the common measure usedin clinical practice to set up diagnosis and treatment design of essential hypertension.The dynamics of the renin concentration can be modeled as: d [ RE ] dt = β − Log h re [ RE ] (1)where h re is renin’s half-life and β its production rate. The latter is not constant but dependson other elements of the RAS system which we will discuss later in the section. The role ofrenin is to cleave the N-terminus of a protein from the serine protease inhibitor family calledangiotensinogen ( AGT ) to form the decapeptide hormone angiotensin I (
AngI ). Assuming non-linear Michaelis-Menten kinetics, the dynamics of the angiotensinogen can be written as:3 ng IVAng 1-7Ang IIAng IAGT AT1R -AngII
ACE ACE2CHYMNEP
AT2R- AngII
AT1RAT2R
ARBDRI ACE-IRE
PRA
MAS -Ang 1-7
MAS
SARS-CoV-2
Figure 1: Schematic representation of the RAS system. In the unperturbed system, solubleproteins that are explicitly considered in the model are in grey blue, the peptides in lightblue and the peptide-bound membrane proteins in mid blue. The activities and enzymesconsidered only through reaction rates are in green. The feedback loop is indicated in blue.In the perturbed system, the drugs are in orange and SARS-CoV-2 in dark red. d [ AGT ] dt = k agt − k recat [ RE ][ AGT ][ AGT ] + K reM − Log h agt [ AGT ] (2)where k agt is AGT ’s production rate, h agt its half-life, k recat the turnover number of the enzymaticreaction and K reM the Michaelis constant. Although the substrate concentration [ AGT ] ∼ K reM and thus influences the reaction rate, the AGT concentration is much larger than the RE concentration which, as a consequence, impacts more on RAS regulation. Eq. (2) can thusbe linearly approximated as: d [ AGT ] dt = k agt − c re [ RE ] − Log h agt [ AGT ] (3)where the reaction rate c re relates the renin concentration to its activity.The AngI peptide is further cleaved by different enzymes: • The angiotensin-converting enzyme (
ACE , EC3.4.15.1), a zinc metalloproteinase locatedmainly in the capillaries of the lungs and in the endothelial cells. It catalyzes thetransformation of
AngI into the octapeptide angiotensin II (
AngII ). • Chymase (
CHY , EC 3.4.21.39), a serine protease that is mainly localized in blood vesselsand heart. It also catalyzes the transformation of
AngI into
AngII .4 Neprilysin (
NEP , EC3.4.24.11), another zinc metalloproteinase that is expressed in awide variety of tissues. It catalyzes the transformation of
AngI into the heptapeptidehormone angiotensin-(1-7) (
Ang1-7 ).The dynamics of
AngI can thus be described as: d [ AngI ] dt = c re [ RE ] − ( c ace + c chy + c nep ) [ AngI ] − Log h angI [ AngI ] (4)where c ace , c chy and c nep are the reaction rates associated with the corresponding enzymaticreactions. To get this relation, we started from the non-linear Michaelis-Menten kinetic term,which reads for ACE : [
ACE ][ AngI ] / ([ AngI ] + K aceM ). As the substrate concentration [AngI] ishere much lower than the Michaelis constant of the reaction ([ AngI ] << K aceM ), we droppedit from the denominator and considered the equilibrium concentrations of the ACE enzymefixed, so that the reaction term becomes linear in the concentration of the
AngI substrate.We made the same approximation for the reactions involving
CHY and
NEP and for all otherreactions described below.The role of
AngII in RAS is central since it has a vasoconstriction effect, enhances bloodpressure, and triggers inflammatory processes and fibrosis. In lung, the capillary blood ves-sels are among the sites that have the highest
ACE expression and production of
AngII . Itsdysregulation has frequently been related to a wide series of chronic and acute diseases suchas pulmonary fibrosis and ARDS.
AngII effects are mediated by two G-protein coupled receptors (GPCR) called angiotensinII type 1 (
AT1R ) and type 2 (
AT2R ). In addition, it can be cleaved by different enzymes.For example,
ACE2 generates
Ang1-7 peptides and aminopeptidase A (
APA , EC 3.4. 11.7)generates other peptides such as angiotensin III (
AngIII ) which is further cleaved to
AngIV .In our model, we skipped all details about the enzymatic reactions
AngII - AngIII - AngIV andkept only a single equation for their transformation. The dynamics of
AngII and
AngIV canthus be written as: d [ AngII ] dt = ( c ace + c chy ) [ AngI ] − ( c ace + c angIV + c at r + c at r ) [ AngII ] − Log h angII [ AngII ] (5) d [ AngIV ] dt = c angIV [ AngII ] − Log h angIV [ AngIV ] (6)where h angII and h angIV are the half-lives of the peptides and c ace , c angIV , c at r and c at r therates of the enzymatic reactions.The dynamics of the peptide-bound form of the GPCRs are expressed as: d [ AT1R-AngII ] dt = c at r [ AngII ] − Log h at r [ AT1R-AngII ] (7) d [ AT2R-AngII ] dt = c at r [ AngII ] − Log h at r [ AT2R-AngII ] (8)5here [
AT1R-AngII ] and [
AT1R-AngII ] are the concentrations of the bound forms of the re-ceptors, and h at r and h at r their half-lives.Until now, we have modeled the ACE / AngII / AT1R regulatory axis of the RAS system.Since the last two decades, it became clear that there is another RAS axis that acts as acounterregulator of the first axis (Sim˜oes e Silva et al., 2013). The key role of this second axisis played by the
Ang1-7 peptide that is mainly produced from
AngII by the
ACE2 enzyme andbinds to the transmembrane GPCR called
MAS . However,
Ang1-7 can also be obtained as anenzymatic product from
AngI via the catalytic activity of
NEP and, to a lesser extent, from
Ang1-9 via
ACE and
NEP . We overlooked the
Ang1-9 -related enzymatic reactions in our model,as they contribute less to
Ang1-7 formation (Raizada et al., 1993; Casarini et al., 2016). Thedynamical equations for the
Ang1-7 peptide and the
MAS -bound receptor are as follows: d [ Ang1-7 ] dt = c nep [ AngI ] + c ace [ AngII ] − c mas [ Ang1-7 ] − Log h ang − [ Ang1-7 ] (9) d [ MAS-Ang1-7 ] dt = c mas [ Ang1-7 ] − Log h mas [ MAS-Ang1-7 ] (10)Let us now go back to Eq. (1) in which we simply expressed the renin production as abaseline term β . To describe the autoregulatory nature of the RAS system, this term hasto depend on the production of other species, thus introducing a feedback regulation. It isknown that this feedback depends on AT1R bound to
AngII . Following other models (Leeteet al., 2018; Leete and Layton, 2019), we expressed β as: β = β + (cid:32) [ AT1R-AngII ] N [ AT1R-AngII ] (cid:33) δ − (11)where β is a constant parameter to be identified and [ AT1R-AngII ] N the equilibrium concen-tration for healthy normotensive humans. δ is a positive number that we fixed to 0.8 (Leeteet al., 2018).Technical details on the procedure used to solve the model and on model stability aregiven in the Materials and Methods section. Modeling blood pressure and antihypertensive RAS-blocker effects
Blood pressure is well known to be increased by the concentration of
AngII bound to
AT1R .It has also been described to be decreased by the concentration of
MAS bound to
Ang1-7 andof
AT2R bound to
AngII , but the precise mechanism is not yet known (Povlsen et al., 2020;Santos et al., 2003; Carey, 2017). Therefore, we did not introduce in our model a feedbackbetween these concentrations and renin production, as we did for
AT1R-AngII , and modeledthe blood pressure (DBP) simply from the
AT1R-AngII concentration:
DBP = P + P [ AT1R-AngII ] (12)We chose to fix the two parameters P and P to mimic the diastolic blood pressure (DBP)rather than the systolic one. We thus fixed DBP equal to 80 mmHg for normotensive indi-viduals and to 110 mmHg for hypertensive individuals. Hence, P + P [ AT1R-AngII ] N = 806mHg and P + P [ AT1R-AngII ] H = 110 mmHg, where the N and H superscripts denoteconcentration in normotensive and hypertensive individuals and the 0 subscript, equilibriumconcentrations.Since dysregulated RAS with high levels of AngII are related to essential hypertension, awide range of RAS-targeting drugs have been developed in the last fourty years (Zaman et al.,2002). They can be classified in three different categories based on their pharamacologicaltarget (Williams, 2016): • Angiotensin-converting enzyme inhibitors (ACE-I) that bind to
ACE and thus inhibitthe formation of angiotensin II and the associated vasoconstriction and inflammatorycascades. Examples of this type of drugs are enalapril, lisinopril and captopril. • Angiotensin receptor blockers (ARB) that block the binding of
AngII to AT1R and thusact in antagonism with
AngII . Examples are candesartan, losartan and valsartan. • Direct renin inhibitors (DRI) that act on renin and thus inihibit the conversion of
AGT to AngI . Examples are aliskiren, enalkiren and remikiren.We modeled the action of these three types of drugs by modifying the reaction ratesassociated to their targets as: c ace −→ c ace × (1 − γ ACE-I ) c at r −→ c at r × (1 − γ ARB ) c re −→ c re × (1 − γ DRI ) (13)where γ ACE-I , γ ARB and γ DRI are parameters describing the drug activity.
Model predictions and clinical data on RAS-blocker drugs
The effect of enalapril, an ACE-I type drug, on plasma
ACE activity and on plasma levels of
AngI and
AngII , has been measured in normotensive individuals who received a single oraldose of 20 mg (Nussberger et al., 1992). To compare these data with model predictions, we firstfitted the γ ACE-I parameter introduced in Eq. (13) to the
ACE activity values during enalapriladministration divided by the pre-treatment activity (measured by an antibody-trapping as-say). Once γ ACE-I was set, we used our model to predict the dynamical response of RAS tothis inhibitor drug. The time-dependent values of
AngI and
AngII concentrations, normalizedby their concentration at time 0, are shown in Figs 2.a-b both for our model predictions andexperimental enalapril data; there is very good agreement between the two curves, withoutany further parameter fitting. The excellent correspondence between model prediction andexperimental data is also clear from the root mean square deviation (rmsd) between modelprediction and experimental data on all time points following drug administration, as shownin Table 1.Our model, thus, captures the known dynamics of
ACE inhibition, ( i.e. , increased
AngI levels and decreased
AngII levels); this has the effect of lowering the concentration of
AngII bound to
AT1R and, thus, also lowers the blood pressure (Eq. (12)).To study the effect of ARB antihypertensive drugs on RAS, we considered data from (Maz-zolai et al., 1999), which measures the effects of different types of AT1R blocking moleculeson plasma levels of
AngII in normotensive individuals. Specifically, the study participants7
AngI(t) / AngI(0) AngII(t) / AngII(0) h predexp (a) (b) -
10 10 20 30 40 500.20.40.60.81.0 (h)
ACE/ACE(0)
ACE-I (h)
AngI / AngI(0) AngII / AngII(0) -
10 10 20 30 40 50246810 -
10 10 20 30 40 500.20.40.60.81.0 (h) exp pred exp pred -
10 10 20 30 40 500.20.40.60.81.0 (h)
ACE/ACE(0)
ACE-I (h)
AngI / AngI(0) AngII / AngII(0) -
10 10 20 30 40 50246810 -
10 10 20 30 40 500.20.40.60.81.0 (h) exp pred exp pred
DBP (c) (d)
DBP
Pucci et al.
Page 7 of 20 • Angiotensin receptor blockers (ARB) that block the binding of
AngII to AT1R and thus act in antagonism with
AngII . Examples are candesartan, losartanand valsartan. • Direct renin inhibitors (DRI) that act on renin and thus inihibit the conver-sion of
AGT to AngI . Examples are aliskiren, enalkiren and remikiren.We modeled the action of these three types of drugs by modifying the reactionrates associated to their targets as: c ace ! c ace ⇥ (1 ACE-I ) c at r ! c at r ⇥ (1 ARB ) c re ! c re ⇥ (1 DRI ) (13)where ACE-I , ARB and DRI are parameters describing the drug activity.
Modeling CoViD-19 infection
Since
ACE2 is the entry point of SARS-CoV-2 [19], it is downregulated upon in-fection, and this impacts substantially on the local and systemic RAS systems. Inorder to model the downregulation e↵ect due to the virus, we modified the
ACE2 rate with the function CoV as: c ace ! c ace ⇥ (1 CoV ( C t )) (14)This function depends on the virus cycle threshold value C t , which is inverselyrelated to the viral load [69]. Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulationof the RAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio, defined as the ratio between the partial pressure of arterialoxygen (PaO2) and the fraction of inspired oxygen. This quantity plays a key rolein the assessment of ARDS patients [34, 35]. The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDS are characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg, respectively.ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 con-centrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by com-paring the baseline RAS with the same system in which ACE2 is knocked out. Inthe former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50mmHg.
Pucci et al.
Page 7 of 20 • Angiotensin receptor blockers (ARB) that block the binding of
AngII to AT1R and thus act in antagonism with
AngII . Examples are candesartan, losartanand valsartan. • Direct renin inhibitors (DRI) that act on renin and thus inihibit the conver-sion of
AGT to AngI . Examples are aliskiren, enalkiren and remikiren.We modeled the action of these three types of drugs by modifying the reactionrates associated to their targets as: c ace ! c ace ⇥ (1 ACE-I ) c at r ! c at r ⇥ (1 ARB ) c re ! c re ⇥ (1 DRI ) (13)where ACE-I , ARB and DRI are parameters describing the drug activity.
Modeling CoViD-19 infection
Since
ACE2 is the entry point of SARS-CoV-2 [19], it is downregulated upon in-fection, and this impacts substantially on the local and systemic RAS systems. Inorder to model the downregulation e↵ect due to the virus, we modified the
ACE2 rate with the function CoV as: c ace ! c ace ⇥ (1 CoV ( C t )) (14)This function depends on the virus cycle threshold value C t , which is inverselyrelated to the viral load [69]. Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulationof the RAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio, defined as the ratio between the partial pressure of arterialoxygen (PaO2) and the fraction of inspired oxygen. This quantity plays a key rolein the assessment of ARDS patients [34, 35]. The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDS are characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg, respectively.ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 con-centrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by com-paring the baseline RAS with the same system in which ACE2 is knocked out. Inthe former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50mmHg.
Pucci et al.
Page 7 of 20 • Angiotensin receptor blockers (ARB) that block the binding of
AngII to AT1R and thus act in antagonism with
AngII . Examples are candesartan, losartanand valsartan. • Direct renin inhibitors (DRI) that act on renin and thus inihibit the conver-sion of
AGT to AngI . Examples are aliskiren, enalkiren and remikiren.We modeled the action of these three types of drugs by modifying the reactionrates associated to their targets as: c ace ! c ace ⇥ (1 ACE-I ) c at r ! c at r ⇥ (1 ARB ) c re ! c re ⇥ (1 DRI ) (13)where ACE-I , ARB and DRI are parameters describing the drug activity.
Modeling CoViD-19 infection
Since
ACE2 is the entry point of SARS-CoV-2 [19], it is downregulated upon in-fection, and this impacts substantially on the local and systemic RAS systems. Inorder to model the downregulation e↵ect due to the virus, we modified the
ACE2 rate with the function CoV as: c ace ! c ace ⇥ (1 CoV ( C t )) (14)This function depends on the virus cycle threshold value C t , which is inverselyrelated to the viral load [69]. Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulationof the RAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio, defined as the ratio between the partial pressure of arterialoxygen (PaO2) and the fraction of inspired oxygen. This quantity plays a key rolein the assessment of ARDS patients [34, 35]. The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDS are characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg, respectively.ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 con-centrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by com-paring the baseline RAS with the same system in which ACE2 is knocked out. Inthe former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50mmHg. -
10 10 20 30 40 50246810 predexp -
10 10 20 30 40 500.20.40.60.81.0
Figure 2: Dynamical response of RAS to ACE-I (enalapril) administration. Comparison be-tween the computational prediction (green) and the experimental data (brown) of normalized
AngI (a) and
AngII (b) as a function of time (in hours) after the single dose administration.Continuum lines are obtained through data interpolation. (c) Predicted DBP as a function of γ ACE-I values (green line) and measured DBP averaged over more than ten ACE-I types asa function of the dosage divided by the maximal dosage (brown points). (d) Predicted effectof the combination of ACE-I and ARB on the DPB values.received a single 50 mg dose of losartan, 80 mg of valsartan or 150 mg of irbesartan. Firstwe fitted the γ ARB parameter (defined in Eq. (13)) to the in vitro ability of the administereddrug to induce the AngII receptor blockade, as measured by an AT1R radioreceptor bindingassay (Mazzolai et al., 1999). We then used our model to predict the time-dependent
AngI level, which was normalized by its concentration prior to drug administration. The resultswere evaluated through the rmsd between experimental and predicted values of
AngI / AngI at different time points after drug administration. The results, which are detailed in Table 1,clearly show that our model accurately predicts the RAS response to ARBs.We also studied the effect of DRI-type drugs using experimental data that describe PRA activity and RE , AngI and
AngII concentrations, when different doses of aliskiren were admin-istered orally to normotensive individuals (Nussberger et al., 2002). We used the
PRA activitydata to fit the γ DRI parameter (introduced in Eq. (13)) and we used our model to calculatethe normalized
AngI and
AngII levels as a function of time. Here also, the results from ourmodel and the experimental concentration data agree very well, as shown in Table 1.8rugs Class Dose [
AngI ](t)/[
AngI ] [ AngII ](t)/[
AngII ] Np Ref.(mg) rmsd (range) rmsd (range)Enalapril ACE-I 20 1.31 [1.0-9.2] 0.09 [0.2-1.0] 5 (Nussberger et al., 1992)Losartan ARB 50 0.61 [1.0-2.1] - 3 (Mazzolai et al., 1999)Valsartan ARB 850 0.83 [1.0-2.2] - 3 (Mazzolai et al., 1999)Irbesartan ARB 150 0.97 [1.0-4.4] - 3 (Mazzolai et al., 1999)Aliskiren DRI 40 0.13 [0.4-1.1] 0.14 [0.5-1.0] 6 (Nussberger et al., 2002)Aliskiren DRI 80 0.15 [0.4-1.0] 0.16 [0.4-1.0] 6 (Nussberger et al., 2002)Aliskiren DRI 160 0.26 [0.2-1.0] 0.20 [0.3-1.0] 6 (Nussberger et al., 2002)Aliskiren DRI 640 0.29 [0.1-1.0] 0.29 [0.1-1.0] 6 (Nussberger et al., 2002)
Mean 0.57 0.18
Table 1: Comparison between model predictions and experimental values of
AngI and
AngII levels normalized by their value before the administration of the drugs. Range is the intervalof experimental values and rmsd is the root mean square deviation between experimental andpredicted values, computed over all time points; Np is the number of time points.In summary, the rmsd between predicted and experimental values of normalized
AngI and
AngII levels, averaged over all tested drugs, dosages, and a total of 38 time points, is 0.57and 0.18, respectively (Table 1). These values should be compared with average experimentalvalues of 1.7 and 0.5 respectively, demonstrating excellent agreement between experimentaldata and model predictions.It should be noted that all reported experimental data have been obtained after adminis-tration of single doses of RAS-targeting drugs. However, for hypertensive patients receivinglong-term treatment, the expression of some enzymes involved in the RAS system could beeither up- or down-regulated; we will return to this point in the Discussion section.Finally, we compared model predictions against clinical data from large cohorts of patientsdescribing the effect of ACE-I and ARB drug administration on blood pressure (Heran et al.,2008; Doulton et al., 2005). We first analyzed the response to ACE-I drugs alone. We plottedin Fig 2.c predicted DBP values as a function of γ ACE-I , as well as measured DBP valuesaveraged over more than ten ACE-I drug types as a function of the normalized dosage (Heranet al., 2008). For this, we fixed γ ACE-I = 0 . γ ACE-I and dosage. Note that it would have been possible to introduce ad-ditional parameters to define a non-linear relationship between these two quantities and, thus,obtain a better fit. Despite these simplifications, chosen to limit the number of parametersto fit, the model curve shows a reasonable fit to the experimental data.We then studied the effect of the combined administration of the two drugs, ARB andACE-I, on blood pressure, plotting the predicted DBP values as a function of both γ ACE-I and γ ARB (see Fig. 2.d). We found that combined administration of ARB and ACE-I reducesDBP by 4 mmHg when compared with ARB monotherapy, and by 12 mmHg when comparedwith ACE-I monotherapy. These predictions should be compared with clinical DBP valuesof 3 mmHg for combined administration compared to either monotherapy (Doulton et al.,2005). Thus, our model again provides an excellent prediction of experimental clinical data;further improvements to the model’s predictive strength might be possible by fixing the γ ARB value at the maximum dose to be slightly lower than the corresponding γ ACE-I value.9 odeling SARS-CoV-2 infection and ARDS severity
Since
ACE2 is the entry point of SARS-CoV-2 (Li et al., 2003), it is downregulated uponinfection, and this impacts substantially on the local and systemic RAS systems. In order tomodel the downregulation effect due to the virus, we modified the
ACE2 reaction rate withthe function γ CoV : c ace −→ c ace × (1 − γ CoV ( C t )) (14)We chose γ CoV to be a sigmoid function of the cycle threshold value C t , which is inverselyrelated to the viral load (Borg et al., 2003): γ CoV = 11 + e aC t − b (15)where a and b are positive real numbers. C t values of 31.5, 27.6, and 23.8 correspond to mild,moderate and severe disease, respectively, and C t >
40 to undetected viral infection (Zhenget al., 2020). We thus chose the inflection point of the sigmoid at C t = 31 . γ CoV > .
99 for C t >
40. Using these relations, we identified the values of the parameters a and b . They are reported in Table 5, and the sigmoid is represented in Fig. 3.a.To model ARDS severity and how the lungs of SARS-CoV-2 infected patients evolvein response to RAS dysregulation, we introduced a phenomenological relation to estimatethe PaO2/FiO2 ratio, defined as the ratio between the partial pressure of arterial oxygen(
PaO2 ) and the fraction of inspired oxygen (
FiO2 ). This quantity plays a key role in theassessment of ARDS patients (Villar et al., 2013; Ware and Matthay, 2000). The normal rangeof
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDS are characterizedby
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg, respectively.ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 concentrations:
PaO2/FiO2 = A + A (cid:32) − [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] (cid:33) (16)where A and A are two parameters that we identified on the basis of our model by comparingthe baseline RAS with the same system in which ACE2 is knocked out. In the former case wefixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50 mmHg.
RAS in COVID-19
It is known that
ACE2 is the cellular receptor of the spike glycoprotein of SARS-CoV-2 (Zhouet al., 2020; Hoffmann et al., 2020; Zhang et al., 2020a; Cao et al., 2020; Lu et al., 2020), andthat it triggers the entry of SARS-COV-2 into the host cell. Although
ACE2 is expressed in avariety of tissues (Chen et al., 2020a; Xu et al., 2020; Sungnak et al., 2020), it is expressedmainly in the alveolar epithelial cells of the lung, in the gastrointestinal tract and in thekidney proximal tubular cells.Here, we used our model to predict how the RAS system is perturbed by the SARS-CoV-2 virus. Simulation results for different
AngII and
Ang1-7 concentrations, and for thephysiological value of
PaO2/FiO2 , are presented in Figs 3.b-d and in Table 2.We observe that the
AngII level increases with increasing viral load, with a much strongerincrease for hypertensive than for normotensive patients. The
AngII level is predicted to10ninfected Mild Moderate Severe C t AngII ] (fmol/ml) 28 32 36 38[
Ang1-7 ] (fmol/ml) 36 21 5 1
PaO2/FiO2 (mmHg) 450 300 145 98DBP (mmHg) 80 81 82 82Hypertensive[
AngII ] (fmol/ml) 156 186 221 231[
Ang1-7 ] (fmol/ml) 92 55 15 2
PaO2/FiO2 (mmHg) 450 292 115 60DBP (mmHg) 110 117 125 128Table 2: Prediction of biochemical and clinical features of SARS-CoV-2 infected patients.increase by approximately 15% for patients with moderate and severe COVID-19 (Table 2);this prediction is in very good agreement with the experimental value of 16% found in (Liuet al., 2020a), but in poorer agreement with the value of 35% resulting from a study of only12 patients (Liu et al., 2020b).We also observe that our model predicts a severe reduction of the
Ang1-7 level, due to
ACE2 downregulation; this reduction is the same for hypertensive and normotensive patients.The overall result of the model is that the RAS system becomes imbalanced upon SARS-CoV-2 infection, with the harmful
AngII axis upregulated and the counteracting
Ang1-7 axisseverely downregulated. This imbalance can be related to multiple clinical manifestations ofCOVID-19. More specifically, increased
AngII levels cause hyperinflammation which, in turn,increases plasma proinflammatory cytokine levels (in particular, IL-6) (Merad and Martin,2020; Satou et al., 2018). In addition, thrombotic events are observed, since
AngII pro-motes the expression of plasminogen activator inhibitor-1 (PAI-1) and tissue-factors (TFs)(Vaughan et al., 1995; Vaughan, 2005).
Ang1-7 , which normally counteracts these variouseffects (Sim˜oes e Silva et al., 2013), is downregulated by SARS-CoV-2 infection, such that theCOVID-19 clinical manifestations become increasingly severe as the disease develops.Moreover, our model predicts severe ARDS with
PaO2/FiO2 <
100 mmHg for normoten-sive and hypertensive patients whose C t values are smaller than 24.1 and 27.0, respectively.Our model predicts moderate ARDS, characterized by a PaO2/FiO2 ratio in the range100-200 mmHg, for normotensive and hypertensive patients having 24 . < C t < . . < C t < .
7, respectively, and mild ARDS, characterized by a
PaO2/FiO2 ratio in therange 200-300 mmHg for normotensive and hypertensive patients having 29 . < C t < . . < C t < .
6, respectively.Our modelling approach suggests a weak relationship between hypertension and ARDSseverity resulting from SARS-CoV-2 infection. The mean value of the
PaO2/FiO2 ratio overthe entire C t range is approximately 20 mmHg lower for hypertensive than for normotensivepatients. Indeed, the large difference in AngII levels between normotensive and hypertensivepatients is partially compensated by the absence of any difference in
Ang1-7 levels.11 a) (b)(c) CoV ( C t C t C t AngII / AngII(0)Ang1-7 / Ang1-7(0)
20 25 30 35 400.20.40.60.81.0 C t (d) Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulation of theRAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio,defined as the ratio between the partial pressure of arterial oxygen (PaO2) and the fraction ofinspired oxygen. This quantity plays a key role in the assessment of ARDS patients [34, 35].The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDSare characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg,respectively. ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 concentrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by comparing thebaseline RAS with the same system in which ACE2 is knocked out. In the former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50 mmHg.
Solving the RAS model xx should this part not be in the Results section? With the paragraph of Philippe ? xxThe mathematical model of the RAS system described in Eqs (1)-(11) is a system ofordinary di↵erential equations (ODEs), which are linear except for the feedback loop of Eq.(11). We collected from the literature the values of the equilibrium concentrations of allproteins and peptides for both normotensive and hypertensive humans (Table 1), exceptrenin and
MAS bound to
Ang1-7 . From these values, we fixed the parameters that appear inthe phenomenological relations (12) and (15) for DBP and PaO2/FiO2 (2).We also got the values of the half-life of all proteins and peptides but
MAS ; we assumed thelatter to be equal to that of the other membrane receptors (Table 2). Moreover, we estimatedthe value of reaction rate c re from [32, 33].Using these concentration and parameter values, we solved the system of 9 ODEs (1)-(11)at the stationary state to identify the unknown parameters and concentrations. However,these equations have 12 unknowns: k agt , , c ace , c ace , c angIV , c at r , c at r , c mas , c chy , c nep ,[ RE ] and [ MAS-Ang1-7 ]. We had thus to assume three additional relations to be able to solvethe system. These are: c mas = c at r (16) c chy = 0 (17) c nep = 0 (18)Since no quantitative data related to the MAS receptor can be found in the literature, wehypothesized the first relation assuming
MAS and
AT2R to be equally expressed and the a nityof
Ang1-7 for
MAS to be similar to the a nity of
AngII for
AT2R [46]. Moreover, we assumed c chy = 0 and c nep = 0, but carefully discussed the e↵ect of non-vanishing values in theDiscussion section.Imposing these three additional relations, we solved the system of 9 ODEs (1)-(11) at thestationary state. The values obtained for [ RE ] and [ MAS-Ang1-7 ], k agt , , c ace , c ace , c angIV , c at r and c at r for normotensive and hypertensive humans are given in Table 1.7
20 25 30 35 401.01.11.21.31.41.5
Normo
Hyper
25 30 35 400.00.20.40.60.81.0
Normo
Hyper
Normo
Hyper
25 30 35 400100200300400
Figure 3: Simulated response of the RAS system to viral infection. (a) γ CoV function used tomodel the effect of the infection as a function of C t , the cycle threshold of the virus. (b)-(d)Predictions obtained from our model for the normalized levels of AngII and
Ang1-7 , andfor the physiological
PaO2/FiO2 value, as a function of C t , for normotensive (blue) andhypertensive (red) individuals. Impact of RAS-modulating drugs on COVID-19 severity
We analyzed the effect of administering a selection of drugs to normotensive and hyperten-sive patients who were infected with the SARS-CoV-2 virus. More specifically, we consideredRAS-blocking drugs that are already commonly used to treat hypertension, as well as drugsthat are currently undergoing clinical trials in the context of COVID-19, such as rhACE2 andAng1-7. • Antihypertensive RAS-blocking drugs. We combined the effect of each of the three RAS-blocking ACE-I, ARB and DRI drugs, which were modeled by the enzyme-inhibiting γ func-tions (introduced in Eq. (13)), with the ACE2 -inhibiting C t -dependent γ CoV function (definedin Eq. (15)), which mimics SARS-CoV-2 infection. The
PaO2/FiO2 values predicted byour model are presented in Fig. 4.Our model predicts that administration of ACE-I and DRI drugs protect from the adverseeffects of ARDS, especially for hypertensive patients, while ARB drugs are predicted to worsenARDS severity, especially for normotensive patients.12odel predictions for ACE inhibitors are in agreement with clinical data, which indicatethat treatment with ACE inhibitors is associated with better survival among COVID-19patients (Mehra et al., 2020; Ssentongo et al., 2020). Indeed, only 3% of non-survivingCOVID-19 patients that were monitored were treated with ACE-I drugs compared to 9% ofsurviving COVID-19 patients (Mehra et al., 2020). Moreover, in a meta-analysis (Ssentongoet al., 2020), hypertensive patients treated with ACE-I drugs were associated with a reducedmortality of 35% when compared to patients who were not treated with ACE-I drugs. Inanother clinical analysis (Khera et al., 2020), older patients who were treated with ACE-Idrugs had a 40% lower risk of hospitalization than those who were not treated with ACE-Idrugs.No data are currently available to validate our model prediction that COVID-19 diseaseattenuation due to ACE-I drug treatment is stronger in hypertensive than in normotensivepatients. Furthermore, no data are currently available to validate our model prediction thatDRI and ACE-I drug treatments cause similar levels of COVID-19 disease attenuation.In contrast to DRI and ACE-I drugs, our model predicts that ARB drug treatment wors-ens COVID-19 disease severity, with the effect being stronger for normotensive compared tohypertensive patients. Here, the agreement between model predictions and clinical data isless clear, with some clinical data in agreement with our model prediction (Mehra et al., 2020;Khera et al., 2020), while other clinical data suggest that ARB drug treatment does not af-fect hospitalization risk (Khera et al., 2020) or mortality (Ssentongo et al., 2020; Baral et al.,2020). This lack of agreement must be further investigated with additional clinical data.Moreover, we performed a quantitative prediction of the drug effects on disease severityby calculating RAS peptide concentrations,
PaO2/FiO2 values and DPB of for moderateCOVID-19 patients. Results are presented in Table 3.Administration of ACE-I drugs, modeled by γ ACE − I = 0 .
5, increases the
PaO2/FiO2 value by approximately 50 and 70 mmHg for normotensive and hypertensive patients, respec-tively. An equivalent administration of DRI drugs increases this ratio even more, by 70 and150 mmHg, while ARB administration decreases it by 140 and 30 mmHg for normotensiveand hypertensive patients, respectively.The opposite effect of ARBs administration compared to ACE-I and DRI drugs can beattributed to the substantial increase in
AngII concentration, which is only partially balancedby a relatively small increase in
Ang1-7 concentration, given that
ACE2 is downregulated inSARS-CoV-2 infection.Note that a number of ARB drugs, including valsartan and losartan, are currently beingtested in clinical trials, with the hope that they will rescue the RAS system in COVID-19 patients (NCT04335786, 2020; NCT04312009, 2020; NCT04311177, 2020). Our modelpredicts that this will not be the case.Finally, as shown in Table 3, the blood pressure is predicted to be unaffected by the ad-ministration of either ACE-I, ARB or DRI to normotensive COVID-19 patients, but to bereduced by approximately 10-20 mmHg by administration to hypertensive patients. • Other RAS-targeting drugs. We used our model to test the potential of other drugs thatare currently in clinical trials to restore the functional activity of the perturbed RAS systemupon viral infection. First, we modeled how the administration of an exogenous supplementof rhACE2 (GSK2586881) affects RAS by modifying the reaction rate c ace defined in Eq.(14). This rate already includes the function γ CoV that mimics SARS-CoV-2 infection, and we13 a) C t Pucci et al.
Page 7 of 20 • Angiotensin receptor blockers (ARB) that block the binding of
AngII to AT1R and thus act in antagonism with
AngII . Examples are candesartan, losartanand valsartan. • Direct renin inhibitors (DRI) that act on renin and thus inihibit the conver-sion of
AGT to AngI . Examples are aliskiren, enalkiren and remikiren.We modeled the action of these three types of drugs by modifying the reactionrates associated to their targets as: c ace ! c ace ⇥ (1 ACE-I ) c at r ! c at r ⇥ (1 ARB ) c re ! c re ⇥ (1 DRI ) (13)where ACE-I , ARB and DRI are parameters describing the drug activity.
Modeling CoViD-19 infection
Since
ACE2 is the entry point of SARS-CoV-2 [19], it is downregulated upon in-fection, and this impacts substantially on the local and systemic RAS systems. Inorder to model the downregulation e↵ect due to the virus, we modified the
ACE2 rate with the function CoV as: c ace ! c ace ⇥ (1 CoV ( C t )) (14)This function depends on the virus cycle threshold value C t , which is inverselyrelated to the viral load [69]. Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulationof the RAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio, defined as the ratio between the partial pressure of arterialoxygen (PaO2) and the fraction of inspired oxygen. This quantity plays a key rolein the assessment of ARDS patients [34, 35]. The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDS are characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg, respectively.ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 con-centrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by com-paring the baseline RAS with the same system in which ACE2 is knocked out. Inthe former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50mmHg. (b)(c)
Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulation of theRAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio,defined as the ratio between the partial pressure of arterial oxygen (PaO2) and the fraction ofinspired oxygen. This quantity plays a key role in the assessment of ARDS patients [34, 35].The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDSare characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg,respectively. ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 concentrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by comparing thebaseline RAS with the same system in which ACE2 is knocked out. In the former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50 mmHg.
Solving the RAS model xx should this part not be in the Results section? With the paragraph of Philippe ? xxThe mathematical model of the RAS system described in Eqs (1)-(11) is a system ofordinary di↵erential equations (ODEs), which are linear except for the feedback loop of Eq.(11). We collected from the literature the values of the equilibrium concentrations of allproteins and peptides for both normotensive and hypertensive humans (Table 1), exceptrenin and
MAS bound to
Ang1-7 . From these values, we fixed the parameters that appear inthe phenomenological relations (12) and (15) for DBP and PaO2/FiO2 (2).We also got the values of the half-life of all proteins and peptides but
MAS ; we assumed thelatter to be equal to that of the other membrane receptors (Table 2). Moreover, we estimatedthe value of reaction rate c re from [32, 33].Using these concentration and parameter values, we solved the system of 9 ODEs (1)-(11)at the stationary state to identify the unknown parameters and concentrations. However,these equations have 12 unknowns: k agt , , c ace , c ace , c angIV , c at r , c at r , c mas , c chy , c nep ,[ RE ] and [ MAS-Ang1-7 ]. We had thus to assume three additional relations to be able to solvethe system. These are: c mas = c at r (16) c chy = 0 (17) c nep = 0 (18)Since no quantitative data related to the MAS receptor can be found in the literature, wehypothesized the first relation assuming
MAS and
AT2R to be equally expressed and the a nityof
Ang1-7 for
MAS to be similar to the a nity of
AngII for
AT2R [46]. Moreover, we assumed c chy = 0 and c nep = 0, but carefully discussed the e↵ect of non-vanishing values in theDiscussion section.Imposing these three additional relations, we solved the system of 9 ODEs (1)-(11) at thestationary state. The values obtained for [ RE ] and [ MAS-Ang1-7 ], k agt , , c ace , c ace , c angIV , c at r and c at r for normotensive and hypertensive humans are given in Table 1.7 Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulation of theRAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio,defined as the ratio between the partial pressure of arterial oxygen (PaO2) and the fraction ofinspired oxygen. This quantity plays a key role in the assessment of ARDS patients [34, 35].The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDSare characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg,respectively. ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 concentrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by comparing thebaseline RAS with the same system in which ACE2 is knocked out. In the former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50 mmHg.
Solving the RAS model xx should this part not be in the Results section? With the paragraph of Philippe ? xxThe mathematical model of the RAS system described in Eqs (1)-(11) is a system ofordinary di↵erential equations (ODEs), which are linear except for the feedback loop of Eq.(11). We collected from the literature the values of the equilibrium concentrations of allproteins and peptides for both normotensive and hypertensive humans (Table 1), exceptrenin and
MAS bound to
Ang1-7 . From these values, we fixed the parameters that appear inthe phenomenological relations (12) and (15) for DBP and PaO2/FiO2 (2).We also got the values of the half-life of all proteins and peptides but
MAS ; we assumed thelatter to be equal to that of the other membrane receptors (Table 2). Moreover, we estimatedthe value of reaction rate c re from [32, 33].Using these concentration and parameter values, we solved the system of 9 ODEs (1)-(11)at the stationary state to identify the unknown parameters and concentrations. However,these equations have 12 unknowns: k agt , , c ace , c ace , c angIV , c at r , c at r , c mas , c chy , c nep ,[ RE ] and [ MAS-Ang1-7 ]. We had thus to assume three additional relations to be able to solvethe system. These are: c mas = c at r (16) c chy = 0 (17) c nep = 0 (18)Since no quantitative data related to the MAS receptor can be found in the literature, wehypothesized the first relation assuming
MAS and
AT2R to be equally expressed and the a nityof
Ang1-7 for
MAS to be similar to the a nity of
AngII for
AT2R [46]. Moreover, we assumed c chy = 0 and c nep = 0, but carefully discussed the e↵ect of non-vanishing values in theDiscussion section.Imposing these three additional relations, we solved the system of 9 ODEs (1)-(11) at thestationary state. The values obtained for [ RE ] and [ MAS-Ang1-7 ], k agt , , c ace , c ace , c angIV , c at r and c at r for normotensive and hypertensive humans are given in Table 1.7 C t Pucci et al.
Page 7 of 20 • Angiotensin receptor blockers (ARB) that block the binding of
AngII to AT1R and thus act in antagonism with
AngII . Examples are candesartan, losartanand valsartan. • Direct renin inhibitors (DRI) that act on renin and thus inihibit the conver-sion of
AGT to AngI . Examples are aliskiren, enalkiren and remikiren.We modeled the action of these three types of drugs by modifying the reactionrates associated to their targets as: c ace ! c ace ⇥ (1 ACE-I ) c at r ! c at r ⇥ (1 ARB ) c re ! c re ⇥ (1 DRI ) (13)where ACE-I , ARB and DRI are parameters describing the drug activity.
Modeling CoViD-19 infection
Since
ACE2 is the entry point of SARS-CoV-2 [19], it is downregulated upon in-fection, and this impacts substantially on the local and systemic RAS systems. Inorder to model the downregulation e↵ect due to the virus, we modified the
ACE2 rate with the function CoV as: c ace ! c ace ⇥ (1 CoV ( C t )) (14)This function depends on the virus cycle threshold value C t , which is inverselyrelated to the viral load [69]. Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulationof the RAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio, defined as the ratio between the partial pressure of arterialoxygen (PaO2) and the fraction of inspired oxygen. This quantity plays a key rolein the assessment of ARDS patients [34, 35]. The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDS are characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg, respectively.ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 con-centrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by com-paring the baseline RAS with the same system in which ACE2 is knocked out. Inthe former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50mmHg.
Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulation of theRAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio,defined as the ratio between the partial pressure of arterial oxygen (PaO2) and the fraction ofinspired oxygen. This quantity plays a key role in the assessment of ARDS patients [34, 35].The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDSare characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg,respectively. ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 concentrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by comparing thebaseline RAS with the same system in which ACE2 is knocked out. In the former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50 mmHg.
Solving the RAS model xx should this part not be in the Results section? With the paragraph of Philippe ? xxThe mathematical model of the RAS system described in Eqs (1)-(11) is a system ofordinary di↵erential equations (ODEs), which are linear except for the feedback loop of Eq.(11). We collected from the literature the values of the equilibrium concentrations of allproteins and peptides for both normotensive and hypertensive humans (Table 1), exceptrenin and
MAS bound to
Ang1-7 . From these values, we fixed the parameters that appear inthe phenomenological relations (12) and (15) for DBP and PaO2/FiO2 (2).We also got the values of the half-life of all proteins and peptides but
MAS ; we assumed thelatter to be equal to that of the other membrane receptors (Table 2). Moreover, we estimatedthe value of reaction rate c re from [32, 33].Using these concentration and parameter values, we solved the system of 9 ODEs (1)-(11)at the stationary state to identify the unknown parameters and concentrations. However,these equations have 12 unknowns: k agt , , c ace , c ace , c angIV , c at r , c at r , c mas , c chy , c nep ,[ RE ] and [ MAS-Ang1-7 ]. We had thus to assume three additional relations to be able to solvethe system. These are: c mas = c at r (16) c chy = 0 (17) c nep = 0 (18)Since no quantitative data related to the MAS receptor can be found in the literature, wehypothesized the first relation assuming
MAS and
AT2R to be equally expressed and the a nityof
Ang1-7 for
MAS to be similar to the a nity of
AngII for
AT2R [46]. Moreover, we assumed c chy = 0 and c nep = 0, but carefully discussed the e↵ect of non-vanishing values in theDiscussion section.Imposing these three additional relations, we solved the system of 9 ODEs (1)-(11) at thestationary state. The values obtained for [ RE ] and [ MAS-Ang1-7 ], k agt , , c ace , c ace , c angIV , c at r and c at r for normotensive and hypertensive humans are given in Table 1.7 C t Pucci et al.
Page 7 of 20 • Angiotensin receptor blockers (ARB) that block the binding of
AngII to AT1R and thus act in antagonism with
AngII . Examples are candesartan, losartanand valsartan. • Direct renin inhibitors (DRI) that act on renin and thus inihibit the conver-sion of
AGT to AngI . Examples are aliskiren, enalkiren and remikiren.We modeled the action of these three types of drugs by modifying the reactionrates associated to their targets as: c ace ! c ace ⇥ (1 ACE-I ) c at r ! c at r ⇥ (1 ARB ) c re ! c re ⇥ (1 DRI ) (13)where ACE-I , ARB and DRI are parameters describing the drug activity.
Modeling CoViD-19 infection
Since
ACE2 is the entry point of SARS-CoV-2 [19], it is downregulated upon in-fection, and this impacts substantially on the local and systemic RAS systems. Inorder to model the downregulation e↵ect due to the virus, we modified the
ACE2 rate with the function CoV as: c ace ! c ace ⇥ (1 CoV ( C t )) (14)This function depends on the virus cycle threshold value C t , which is inverselyrelated to the viral load [69]. Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulationof the RAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio, defined as the ratio between the partial pressure of arterialoxygen (PaO2) and the fraction of inspired oxygen. This quantity plays a key rolein the assessment of ARDS patients [34, 35]. The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDS are characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg, respectively.ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 con-centrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by com-paring the baseline RAS with the same system in which ACE2 is knocked out. Inthe former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50mmHg.
Figure 4: Impact of different RAS-blocking drugs in normotensive (blue) and hypertensive(red) SARS-CoV-2 infected patients. Predicted
PaO2/FiO2 value as a function of the cycletreshold value C t and (a) γ ACE − I , (b) γ ARB and (c) γ DRI functions that model the adminis-tration of the corresponding drugs.
Drugs
No Drugs ACE-I ARB DRI rhACE2 Ang1-7Normotensive - Moderate Infection[
AngII ]/[
AngII ] Ang1-7 ]/[
Ang1-7 ] PaO2/FiO2 (mmHg) 145 188 0 216 337 278DBP (mmHg) 82 81 80 80 81 82Hypertensive - Moderate Infection[
AngII ]/[
AngII ] Ang1-7 ]/[
Ang1-7 ] PaO2/FiO2 (mmHg) 115 185 83 268 332 167DBP (mmHg) 125 114 101 102 115 125Table 3: Predicted effects on
AngII and
Ang1-7 levels,
PaO2/FiO2 and DBP upon drugadministration by normotensive and hypertensive COVID-19 patients. The drug adminis-trations are modeled by γ ACE − I , γ ARB , γ
DRI , γ rhACE = 0 . η Ang = 25 fmol/(ml min) andmoderate SARS-CoV-2 infection by γ CoV = 27 . γ rhACE2 associated with the effects of rhACE2 administration:14 ace −→ c ace × (1 + γ rhACE2 − γ CoV ( C t )) (17)Our model predicts an increase in PaO2/FiO2 following the administration of exogenous rhACE2 , thus predicting an alleviation of disease severity, as shown in Fig. 5 and Table 3.Specifically,
PaO2/FiO2 is predicted to increase by approximately 200 mmHg when γ rhACE2 is fixed to 0.5. Our model also predicts, as expected, a reduction in AngII level and an increasein
Ang1-7 level.These predictions are in agreement with both animal and in vitro studies (Kuba et al.,2005; Monteil et al., 2020), whereby rhACE2 is observed to alleviate virus-related ARDS sever-ity through a double action. First, by rhACE2 binding to the virus spike protein, interactionwith endogenous
ACE2 is prevented and infection is slowed down. Second, rhACE2 adminis-tration increases
ACE2 activity, thus causing a reduction in
AngII level and an increase in
Ang1-7 level; this protects the lung against severe failure.Current clinical trial data concerning the administration of different doses of rhACE2 (0.1,0.2, 0.4 and 0.8 mg/kg) to SARS-CoV infected patients at different time intervals (2, 4, and 18h), are only in partial agreement with our model predictions (Khan et al., 2017). Specifically,while clinical data followed the predicted decrease in [
AngII ] and the predicted increase in[
Ang1-7 ], there was no sustained increase in
PaO2/FiO2 compared with placebo. It has beensuggested that the drug concentrations used in these clinical trials were too low to have ameasurable effect on the respiratory system and that drug administration via infusion wouldhave been more sustained (Khan et al., 2017). More experimental and clinical data are clearlyneeded to further investigate the effect of rhACE2 on coronavirus-related ARDS.Another method of boosting the second RAS axis,
ACE2 / Ang1-7 / MAS , which is downreg-ulated by SARS-CoV-2 infection, is to administer
Ang1-7 peptides as a means of triggeringanti-inflammatory and anti-fibrotic mechanisms. We modeled
Ang1-7 peptide administrationby introducing a new parameter, the production rate η Ang , to the dynamical Eq. (9) of[ Ang1-7 ]; this allows the model to describe the exogenous
Ang1-7 level, which is added tothe endogenous
Ang1-7 baseline. As shown in Fig. 5.b and Table 3, our model predicts aclear alleviation of COVID-19 severity, with
PaO2/FiO2 increasing by 50 and 130 mmHgfor hypertensive and normotensive patients, respectively, upon administration of η Ang =25 fmol/(ml min) Ang1-7 in infusion. Note that the COVID-19 alleviation is significantlystronger in normotensive compared to hypertensive patients for the same drug concentrations;a slightly stronger concentration of
Ang1-7 must be administered to hypertensive patients foran equivalent effect.Our model predicts a quantitative reduction in ARDS severity in COVID-19 patients,in agreement with the known anti-inflammation and anti-fibrosis nature of
Ang1-7 . Modelpredictions nicely agree with data from animal studies without the need of any additionalfitting. For example, administration of
Ang1-7 by infusion to acid-injured rats suffering fromARDS increases baseline
Ang1-7 level by a factor 2.5, leading to an increase in
PaO2/FiO2 of approximately 70 mmHg (Zambelli et al., 2015). However, while the
PaO2/FiO2 valueincreases linearly in our model as a function of
Ang1-7 concentration, it reaches a plateauin rats; this suggests that our model is probably oversimplified, since
PaO2/FiO2 is not alinear function of
Ang1-7 concentration. Further work on this aspect of our model will bepossible when more data become available. 15 a) C t (b) Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulation of theRAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio,defined as the ratio between the partial pressure of arterial oxygen (PaO2) and the fraction ofinspired oxygen. This quantity plays a key role in the assessment of ARDS patients [34, 35].The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDSare characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg,respectively. ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 concentrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by comparing thebaseline RAS with the same system in which ACE2 is knocked out. In the former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50 mmHg.
Solving the RAS model xx should this part not be in the Results section? With the paragraph of Philippe ? xxThe mathematical model of the RAS system described in Eqs (1)-(11) is a system ofordinary di↵erential equations (ODEs), which are linear except for the feedback loop of Eq.(11). We collected from the literature the values of the equilibrium concentrations of allproteins and peptides for both normotensive and hypertensive humans (Table 1), exceptrenin and
MAS bound to
Ang1-7 . From these values, we fixed the parameters that appear inthe phenomenological relations (12) and (15) for DBP and PaO2/FiO2 (2).We also got the values of the half-life of all proteins and peptides but
MAS ; we assumed thelatter to be equal to that of the other membrane receptors (Table 2). Moreover, we estimatedthe value of reaction rate c re from [32, 33].Using these concentration and parameter values, we solved the system of 9 ODEs (1)-(11)at the stationary state to identify the unknown parameters and concentrations. However,these equations have 12 unknowns: k agt , , c ace , c ace , c angIV , c at r , c at r , c mas , c chy , c nep ,[ RE ] and [ MAS-Ang1-7 ]. We had thus to assume three additional relations to be able to solvethe system. These are: c mas = c at r (16) c chy = 0 (17) c nep = 0 (18)Since no quantitative data related to the MAS receptor can be found in the literature, wehypothesized the first relation assuming
MAS and
AT2R to be equally expressed and the a nityof
Ang1-7 for
MAS to be similar to the a nity of
AngII for
AT2R [46]. Moreover, we assumed c chy = 0 and c nep = 0, but carefully discussed the e↵ect of non-vanishing values in theDiscussion section.Imposing these three additional relations, we solved the system of 9 ODEs (1)-(11) at thestationary state. The values obtained for [ RE ] and [ MAS-Ang1-7 ], k agt , , c ace , c ace , c angIV , c at r and c at r for normotensive and hypertensive humans are given in Table 1.7 Monitoring the acute respiratory distress syndrome and its severity
To model how the lungs of the infected patients evolve in response to the modulation of theRAS system, we introduced a phenomenological relation to estimate the
PaO2/FiO2 ratio,defined as the ratio between the partial pressure of arterial oxygen (PaO2) and the fraction ofinspired oxygen. This quantity plays a key role in the assessment of ARDS patients [34, 35].The normal range of
PaO2/FiO2 is between 400 and 500 mmHg. Mild and moderate ARDSare characterized by
PaO2/FiO2 values in the range [200–300] mmHg and [100-200] mmHg,respectively. ARDS is severe for values below 100 mmHg.We predicted the
PaO2/FiO2 ratio as a function of the
AngII and
Ang1-7 concentrations:
PaO2/FiO2 = A + A ✓ [ AngII ][ AngII ] + [ Ang1-7 ][ Ang1-7 ] ◆ (15)where A and A are two parameters that we identified from our model by comparing thebaseline RAS with the same system in which ACE2 is knocked out. In the former we fixed
PaO2/FiO2 = 450 mmHg and in the latter
PaO2/FiO2 = 50 mmHg.
Solving the RAS model xx should this part not be in the Results section? With the paragraph of Philippe ? xxThe mathematical model of the RAS system described in Eqs (1)-(11) is a system ofordinary di↵erential equations (ODEs), which are linear except for the feedback loop of Eq.(11). We collected from the literature the values of the equilibrium concentrations of allproteins and peptides for both normotensive and hypertensive humans (Table 1), exceptrenin and
MAS bound to
Ang1-7 . From these values, we fixed the parameters that appear inthe phenomenological relations (12) and (15) for DBP and PaO2/FiO2 (2).We also got the values of the half-life of all proteins and peptides but
MAS ; we assumed thelatter to be equal to that of the other membrane receptors (Table 2). Moreover, we estimatedthe value of reaction rate c re from [32, 33].Using these concentration and parameter values, we solved the system of 9 ODEs (1)-(11)at the stationary state to identify the unknown parameters and concentrations. However,these equations have 12 unknowns: k agt , , c ace , c ace , c angIV , c at r , c at r , c mas , c chy , c nep ,[ RE ] and [ MAS-Ang1-7 ]. We had thus to assume three additional relations to be able to solvethe system. These are: c mas = c at r (16) c chy = 0 (17) c nep = 0 (18)Since no quantitative data related to the MAS receptor can be found in the literature, wehypothesized the first relation assuming
MAS and
AT2R to be equally expressed and the a nityof
Ang1-7 for
MAS to be similar to the a nity of
AngII for
AT2R [46]. Moreover, we assumed c chy = 0 and c nep = 0, but carefully discussed the e↵ect of non-vanishing values in theDiscussion section.Imposing these three additional relations, we solved the system of 9 ODEs (1)-(11) at thestationary state. The values obtained for [ RE ] and [ MAS-Ang1-7 ], k agt , , c ace , c ace , c angIV , c at r and c at r for normotensive and hypertensive humans are given in Table 1.7 C t Pucci et al.
Page 15 of 20 rhACE2 (GSK2586881). We modeled its e↵ect on the RAS system by modifyingthe c ace coe cient defined in Eq. (14) which already mimics the SARS-CoV-2infection, as: c ace ! c ace ⇥ (1 + rhACE2 CoV ( C t )) (20)We thus introduced a new gamma function rhACE2 associated to the e↵ect ofrhACE2 administration.The predictions of our model are shown in Fig. 5 and Table 5. We observe anincrease of the PaO2/FiO2 value upon intake of exogenous rhACE2 , and thus aweakening of the disease severity. The increase of
PaO2/FiO2 is of about 200mmHg when rhACE2 varies in the interval [0-0.5]. We also observe a reduction ofthe AngII level and an increase of the
Ang1-7 level.These predictions are in agreement with animal and in vitro studies [18, 27],where rhACE2 administration has led to an improvement of the disease conditionthrough a double action. First, its binding to the S-protein of the virus xx S or S1 ?xx prevents interaction with endogenous ACE2 and slows down the viral infection.Second, rhACE2 administration increases the
ACE2 activity, thus causing a reductionof the
AngII level and an increase of the
Ang1-7 level, which results in the protectionof the lung from severe failure.However, our predictions and the data described above do not agree with clinicaltrials clinical data [20] regarding the administration of rhACE2 at di↵erent doses(0.1 mg/kg, 0.2 mg/kg, 0.4 mg/kg and 0.8 mg/kg) and intervals (2, 4, and 18 h)to CoViD patients are less positive. A drop in [
ANGII ] and an increase in [
ANG1-7 ]was found, similar to what we found, but no sustained increase of
PaO2/FiO2 wasobserved for these patients compared with placebo, in contrast with what happensfrom animal model, . However there is the possibility that drug concentrationswere not enough substained and that maybe only trough its continuous infusionscould reach a more e↵ective result [20]. More experimental data are needed tofurther investigate e↵ect of rhACE2 on ARDS and preturbed RAS system due tothe SARS-CoV-2 infection.Another way to maintain an high level of the
ACE2 / Ang1-7 / MasR negativecounter-regulation in CoViD is to administrate the
Ang1-7 peptide to trigger anti-inflammatory and antifibrotic mechanisms. In our computation we model this ad-ministration introducing the parameter ⌘ describing the endogenously Ang1-7 quan-tity that is added to the normal baseline quantity. We can see the results of thecomputation in Fig 5.b and in Table XXX where a clear improvement of the dis-ease severity is observed with an increase
PaO2/FiO2 between 70 and 140 mmHgfor hypertensive and normotensve patients respectivley and for administration ininfusion of 25 fmol/ml that means almost doubling the control values
Ang1-7 Notethat the improvement is significantly more pronounced in normotensive patientsthan in hypertensive ones for equal drug concentrations and to reach the same ef-fects the
Ang1-7 concentration administrated to hypertensive patients have to beslightly increased.In agreement with clinical data on human ARDS and with the anti-inflammationand anti-fibrosis nature of
Ang1-7 , our results predict quantitatively an improvenent
Current clinical trial data concerning the administration of di↵erent doses of rhACE2 (0.1, 0.2, 0.4 and 0.8 mg/kg) to SARS-CoV infected patients at di↵erent time intervals(2, 4, and 18 h), are only in partial agreement with our model predictions [20]. Specif-ically, while clinical data followed the predicted decrease in [
AngII ] and the predictedincrease in [
Ang1-7 ], there was no sustained increase in
PaO2/FiO2 compared withplacebo. It has been suggested that the drug concentrations used in these clinical tri-als were too low to have a measurable e↵ect on the respiratory system and that drugadministration via infusion would have been more sustained [20]. More experimen-tal and clinical data are clearly needed to further investigate the e↵ect of rhACE2 oncoronavirus-related ARDS.Another method of boosting the second RAS axis,
ACE2 / Ang1-7 / MAS , which isdownregulated by SARS-CoV-2 infection, is to administer
Ang1-7 peptides as a meansof triggering anti-inflammatory and anti-fibrotic mechanisms. We modeled
Ang1-7 peptide administration by introducing a new parameter, ⌘ Ang , to dynamical equation(9) of [ Ang1-7 ]; this allowed the model to describe the exogenous
Ang1-7 level, which isadded to the endogenous
Ang1-7 baseline. As shown in Fig. 5.b and Table 5, our modelpredicts a clear alleviation of COVID-19 severity, with
PaO2/FiO2 increasing by 50and 130 mmHg for hypertensive and normotensive patients, respectively, upon admin-istration of ⌘ Ang =25 fmol/(ml min) Ang1-7 in infusion. Note that the COVID-19alleviation is significantly stronger in normotensive compared to hypertensive patientsfor the same drug concentrations; a slightly stronger concentration of
Ang1-7 must beadministered to hypertensive patients for an equivalent e↵ect.Our model predicts a quantitative reduction in ARDS severity in COVID-19 pa-tients, in agreement with the known anti-inflammation and anti-fibrosis nature of
Ang1-7 . Model predictions nicely agree with data from animal studies without theneed of any additional fitting. For example, administration of
Ang1-7 by infusionto acid-injured rats su↵ering from ARDS increases baseline
Ang1-7 level by a factor2.5, leading to an increase in
PaO2/FiO2 of approximately 70 mmHg [77]. However,while the
PaO2/FiO2 value increases linearly in our model as a function of
Ang1-7 concentration, it reaches a plateau in rats; this suggests that our model is probablyoversimplified, since
PaO2/FiO2 is not a linear function of
Ang1-7 concentration.Further work on this aspect of our model will be possible when more data becomeavailable.
The spike protein of SARS-CoV-2 interferes with the RAS system by binding to the
ACE2 receptor, a key element of RAS. Despite recent progress in understanding theCOVID-perturbed RAS system and how its functionality can be restored, more workis urgently needed in the context of the current COVID-19 pandemic.We here present a simple computational approach to modeling RAS system evolu-tion in the context of SARS-CoV-2 infection. Inspired by a number of existing RASmodels [41, 42, 52, 59], we searched the literature for measured half-lives and con-centrations of angiotensin peptides and their receptors in healthy normotensive andhypertensive individuals, and then identified the unknown production and reactionrate parameters from the model. As an initial test of our model, we compared its18
Figure 5: Impact on the
PaO2/FiO2 value of the administration of rhACE2 and
Ang1-7 in normotensive (blue) and hypertensive (red) SARS-CoV-2 infected patients. (a) Predicted
PaO2/FiO2 values as a function of C t and γ rhACE2 (b) Predicted PaO2/FiO2 values asa function of C t and η Ang , the increase in the level of Ang1-7 due to its administration ininfusion.
Discussion
The spike protein of SARS-CoV-2 interferes with the RAS system by binding to the
ACE2 re-ceptor, a key element of RAS. Despite recent progress in understanding the COVID-perturbedRAS system and how its functionality can be restored, more work is urgently needed in thecontext of the current COVID-19 pandemic.We here present a simple computational approach to modeling RAS system evolutionin the context of SARS-CoV-2 infection. Inspired by a number of existing RAS models(Leete et al., 2018; Leete and Layton, 2019; Versypt et al., 2017; Hallow et al., 2014), wesearched the literature for measured half-lives and concentrations of angiotensin peptides andtheir receptors in healthy normotensive and hypertensive individuals, and then identified theunknown production and reaction rate parameters from the model. As an initial test, wecompared our model predictions of how the administration of RAS-blocking drugs wouldaffect
Ang peptide concentrations and blood pressure with relevant experimental data; wefound good quantitative agreement between our model and experimental data, without theneed for further parameter fitting. We then modeled the effect of SARS-CoV-2 infection onthe RAS system through the downregulation of
ACE2 , which we related to the SARS-CoV-2viral load.A focal point of our work was to investigate how a series of RAS-targeting drugs affectedCOVID-19 patients. We found that the administration of two antihypertensive drugs, ACE-Iand DRI, tended to reduce the severity of COVID-19, while ARB drugs worsened it. Clinicaldata generally supports the model’s predictions for the administration of ACE-I drugs, butthey are either absent or partially contradict the model’s prediction for DRI and ARB ad-ministration. Additionally, we modeled a potential treatment that is currently under clinicaltrial in COVID-19 patients: administration of rhACE2 or Ang1-7 by drug infusion. Our modelpredicts improved clinical outcomes in these cases, in agreement with a series of experimentaldata on animal models.It is important to note that, despite its simplicity, our model has excellent accuracy inreproducing clinical and experimental data on the perturbed RAS system. Furthermore, the16odel’s predictions of changes in COVID-19 severity due to drug administration are blindpredictions, without the fitting of any additional parameters.Many challenges remain in our current understanding of RAS perturbation in COVID-19patients. Importantly, more data regarding angiotensin peptide concentrations upon SARS-CoV-2 infection are urgently needed, since currently available data are often inconsistentor conflicting so that reliable comparisons between model predictions and experimental datacannot be made. Even in healthy individuals, angiotensin peptide levels can vary substantiallydue to their low circulating concentrations, the experimental techniques used to measure them,and interpatient variability.When developing our model we chose not to consider two enzymes that are active in theRAS system through the cancellation of their reaction rates:
CHY and
NEP (see Eqs (18)-(19)).The
CHY enzyme is expressed in mast cells present in interstitial lung connective tissues, andit cleaves
AngI to form
AngII . The addition of this enzymatic reaction in the model would notreally influence the predictions since it would essentially be a reparametrization of
ACE activityand of ACE-I action. It might, nevertheless, be interesting to add the
CHY enzymatic reaction,which yields
ACE -independent synthesis of
AngII and has been suggested (although debated)to be upregulated in the case of long-term ACE-I administration (Chester and Borland, 2000);this would enable an explanation of why ACE-I fails to inhibit
AngII formation after sometime (Chester and Borland, 2000; Athyros et al., 2007).The
NEP enzyme is expressed in a wide range of tissues, being particularly abundant inkidney, and it cleaves
AngI to form
Ang1-7 . It influences the counterregulatory RAS axisthrough its connection to
Ang1-7 levels, thus affecting COVID-19 severity. However,
NEP ’srole is far from clear and the literature contains contradictory findings. Experimental datafrom rats with ARDS suggest that
NEP is severely downregulated in both plasma and lungtissues (Hashimoto et al., 2010). Note that
NEP also cleaves natriuretic peptides, whichhave both anti-inflammatory and anti-fibrotic effects (Bayes-Genis et al., 2016). Therefore,the combined administration of
NEP -inhibiting and ARB drugs has been suggested to treatSARS-CoV-2 infected patients (Acanfora et al., 2020).Our future work will include building more complexity into our model by explicitly con-sidering the communication between local and systemic RAS systems (Raizada et al., 1993;Casarini et al., 2016), and by including the interaction between RAS and the immune system(Crowley and Rudemiller, 2017). This model extension is necessary for an improved quanti-tative understanding of RAS system dysregulation upon a variety of perturbations, includingSARS-CoV-2 infection.In summary, our model and its predictions provide a valuable and robust framework for in silico testing of hypotheses regarding COVID-19 pathogenic mechanisms and the effect ofdrugs therapies that are aimed at restoring RAS functionality. Our work also opens a broaderdiscussion on the role of the full RAS system in COVID-19, a topic that has received littleattention to date, perhaps due to the current focus on the
ACE2 enzyme which, although veryimportant as directly targeted by the virus, constitutes only one part of a much more complexsystem. 17 aterials and Methods
Solving the RAS model
The mathematical model of the RAS system described in Eqs (1)-(11) is a system of ordinarydifferential equations (ODEs), which are linear except for the feedback loop of Eq. (11).We collected from the literature the values of the equilibrium concentrations of all pro-teins and peptides except renin and
MAS bound to
Ang1-7 , for normotensive and hypertensivehumans (Table 4). From these values, we fixed the parameters that appear in the phenomeno-logical relations (12) and (16) for DBP and
PaO2/FiO2 (Table 5). We also collected thevalues of the half-life of all proteins and peptides but
MAS ; we assumed the latter to be equalto that of the other membrane receptors (Table 5). Moreover, we estimated the value ofreaction rate c re from (Versypt et al., 2017; Streatfeild-James et al., 1998).Using these concentration and parameter values, we solved the system of nine ODEs (Eqs(1) and (3)-(10)) at the stationary state to identify the unknown parameters and concentra-tions. However, these equations have 12 unknowns: k agt , β , c ace , c ace , c angIV , c at r , c at r , c mas , c chy , c nep , [ RE ] and [ MAS-Ang1-7 ] . We had thus to assume three additional relations,which are: c mas = c at r (18) c chy = 0 (19) c nep = 0 (20)Since no quantitative data related to the MAS receptor can be found in the literature, wehypothesized the first relation assuming
MAS and
AT2R to be equally expressed and the affinityof
Ang1-7 for
MAS to be similar to the affinity of
AngII for
AT2R (Santos et al., 2003). Moreover,we assumed c chy = 0 and c nep = 0, but discussed the effect of non-vanishing values in theDiscussion section.By imposing these three additional relations, we solved the system of 9 ODEs at thestationary state. The values obtained for [ RE ] and [ MAS-Ang1-7 ] , k agt , β , c ace , c ace , c angIV , c at r and c at r for normotensive and hypertensive humans are given in Table 4. Stability of the RAS model
The system of nine ODEs (Eqs (1) and (3)-(10)) can be summarized in the form: dx ( t ) dt = f ( x ( t ) , θ ) (21)where x ( t ) is the vector containing the nine state variables, i.e. the concentrations of allproteins and peptides at time t , θ is the vector with all the production, kinetic and half-live parameters, and f represents the vector that corresponds to the right-hand sides of Eqs(1) and (3)-(10). In order to analyze the stability of the two steady states x N and x H fornormotensive and hypertensive individuals, respectively, we computed the eigenvalues of theJacobian matrix: J ( x ) = ∂f ( x, θ ) ∂x (cid:12)(cid:12)(cid:12) x = x (22)18arameter Unit Normotensive Hypertensive Reference[ AGT ] fmol/ml 6 × × (Katsurada et al., 2007)[ AngI ] fmol/ml 70 110 (Chappell, 2016)(Pendergrass et al., 2008)[ AngII ] fmol/ml 28 156 (Chappell, 2016)(Pendergrass et al., 2008)[ Ang1-7 ] fmol/ml 36 92 (Chappell, 2016)(Pendergrass et al., 2008)(Sullivan et al., 2015)[ AngIV ] fmol/ml 1 1 (Nussberger et al., 1986)[ AT1R-AngII ] fmol/ml 15 85 (Leete et al., 2018)[ AT2R-AngII ] fmol/ml 5 27 (Leete et al., 2018)[ RE ] fmol/ml 9.43 25.25 Solved[ MAS-Ang1-7 ] fmol/ml 6.43 15.92 Solved k agt fmol/(ml min) 881.82 1198.22 Solved β fmol/(ml min) 0.54 2.21 Solved c ace c ace c angIV c at r c at r x stands for either x N or x H .In both the normotensive and hypertensive cases, seven strictly negative real values wereobtained, together with two complex conjugate eigenvalues with strictly negative real parts.Both steady-states x N and x H are therefore stable. The nonzero imaginary parts of thetwo complex conjugate eigenvalues are responsible of some damped oscillations in transientresponses to parameter changes, but the overshoots are limited. It is interesting to note thatthe imaginary part is more than three times lower in the hypertensive case, hence leading tomore damped responses in comparison with the normotensive case.To quantify the state variable transients and the aforementioned overshoots, we simulatedstep responses corresponding to 10% increase in the normal baseline for renin production β .We observe some damped oscillations during the transient phase of the normotensive case,with very limited overshoots, e.g. RE concentration. In the hypertensive case, theimaginary part of the complex conjugate eigenvalues is so low that the overshoots becomealmost undetectable (0.025%). Data availability
The code used to generate all the results of this paper freely is available on GitHub(https://github.com/3BioCompBio/RASinCOVID).19arameter Unit Values Reference h agt min 600 (Hallow et al., 2014) h ang − min 0.5 (Hallow et al., 2014) h angI min 0.5 (Hallow et al., 2014) h angII min 0.5 (Hallow et al., 2014) h angIV min 0.5 (Hallow et al., 2014) h at r min 12 (Hallow et al., 2014) h at r min 12 (Hallow et al., 2014) h re min 12 (Hallow et al., 2014) h mas min 12 - c re A mmHg 450 Fitted A mmHg 267 Fitted P mmHg 73.6 Fitted P mmHg ml/fmol 0.43 Fitted a - 0.53 Fitted b - 16.7 FittedTable 5: Half-lives of the species involved in RAS and other parameters of the model. ’Fitted’means fitted on experimental data. Acknowledgements
We thank Dr. Filippo Annoni and Prof. Fabio Taccone for enlightening discussions. FP andMR are Scientific Collaborator and Research Director, respectively, at the F.R.S.-FNRS Fundfor Scientific Research.
Conflict of Interest
The authors declare that they have no conflict of interest.
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