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Modeling the effect of tat inhibitors on HIV latency
Accepted Manuscript
Modeling the Effect of Tat Inhibitors on HIV Latency. Luis U. Aguilera, Jesus ´ Rodr´ıguez-Gonzalez ´ PII: DOI: Reference:
S0022-5193(19)30159-6 https://doi.org/10.1016/j.jtbi.2019.04.018 YJTBI 9893
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Journal of Theoretical Biology
Received date: Revised date: Accepted date:
14 August 2018 7 February 2019 16 April 2019
Please cite this article as: Luis U. Aguilera, Jesus Modeling the Ef´ Rodr´ıguez-Gonzalez, ´ fect of Tat Inhibitors on HIV Latency., Journal of Theoretical Biology (2019), doi: https://doi.org/10.1016/j.jtbi.2019.04.018
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Highlights • Mathematical study to understand Tat-inhibitors as virus-suppressing
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agents.
• HIV-productive and latent cell phenotypes are described by stochastictransitions.
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• Competitive and non-competitive inhibitors produce reversible viral suppression.
• Didehydro-Cortistatin A (dCA) achieves a more permanent viral inhi-
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Modeling the Effect of Tat Inhibitors on HIV Latency. Luis U. Aguilera
, Jes´ us Rodr´ıguez-Gonz´alezb,
Department of Modeling of Biological Processes, COS Heidelberg / Bioquant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany. b Centro de Investigaci´ on y Estudios Avanzados del Instituto Polit´ecnico Nacional, Unidad Monterrey, Via del Conocimiento 201, Parque PIIT, CP 66600 Apodaca NL, M´exico.
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Abstract
Even in the presence of a successful combination therapy stalling the progress of AIDS, developing a cure for this disease is still an open question. One of the major steps towards a cure would be to be able to eradicate latent HIV
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reservoirs present in patients. During the last decade, multiple findings point to the dominant role of the viral protein Tat in the establishment of latency.
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Here we present a mathematical study to understand the potential role of Tat inhibitors as virus-suppressing agents. For this aim, we implemented
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a computational model that reproduces intracellular dynamics. Simulating an HIV-infected cell and its intracellular feedback we observed that remov-
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ing Tat protein from the system via inhibitors resulted in a temporary and reversible viral suppression. In contrast, we observed that compounds that
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interact with Tat protein and disrupt the integrated viral genome produced a more permanent viral suppression.
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Email address: [email protected] (Jes´ us Rodr´ıguez-Gonz´ alez) Present Address: Colorado State University.
Preprint submitted to Journal of Theoretical Biology
April 17, 2019
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Keywords: Viral suppression, Stochastic model, Tat circuit 1. Introduction
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Treating patients infected with the Human Immunodeficiency Virus (HIV)
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has strongly progressed during the last years. Although until today HIV in-
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fection cannot be eradicated in patients, Highly Active Antiretroviral Ther-
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apy (HAART) decreases viral loads during the infection and prevents clin-
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ical progression to the Acquired Immunodeficiency Syndrome (AIDS) [38].
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A major barrier to achieving HIV eradication is the existence of a reservoir
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of resting memory CD4+ T-lymphocytes (T4-cells) carrying latent provirus
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[7, 10]. HIV latency is a reversible non-virus-producing phenotype in an in-
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fected cell [21].
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It is not entirely clear what molecular processes dictate a latent or productive
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cell infection. Multiple mechanisms have been suggested to contribute to HIV
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latency [18, 20]. However, important findings point to the dominant role of
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the viral protein Tat in latency [30]. Tat is a transactivating regulatory pro-
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tein. Its activation is a key mechanism that promotes viral gene expression
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[4]. Thus, once Tat protein is produced, it enhances HIV gene expression by
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binding to the trans-activating response element (TAR), a stem-loop that is
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present in the 5 end of newly synthesized viral transcripts. Tat changes the
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effective transcription rate of the respective genes up to 100-fold over basal
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expression levels by recruiting the positive transcription elongation complex
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(P-TEFb) made of Cyclin T1 and CDK9 [27]. Since this process also accel-
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erates Tat transcription itself, it constitutes a positive feedback loop in the
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system. The absence of the Tat protein results in premature termination of
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transcription. Over-expression of Tat protein is sufficient to induce the pro-
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duction and spread of HIV from resting memory T4-cells [9]. The complete
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scheme of HIV gene expression is given in Fig. 1.
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Altogether, the cellular fate of individual cells is determined mainly by the
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number of molecules, e.g. of Tat protein present in the cell. Therefore,
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like other cellular events which involve low molecule numbers, cellular fate
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should be strongly affected by the stochasticity of discrete molecular events
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[2]. The central role of stochasticity in the processes carried out by the
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Tat protein was confirmed by studies conducted in the group of Weinberger.
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They modeled the Tat-circuit and adjusting it to the experimental data they
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determined a monostable architecture, which after introducing stochasticity
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showed bimodal dynamics [37]. Subsequently, they proved that HIV expres-
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sion is dictated by the time that the Tat protein remains in the inactive
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(deacetylated) state, which is longer than the time that it remains in the
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active state (acetylated) [36]. Recently, the same group proved that the
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transition between a latent to a productive infection depends solely on the
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Tat circuit, independent of the cellular state [31].
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As previously stated, the biggest barrier to eradicating HIV infection is the 5
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persistence of HIV latent infected cells [33]. Two main strategies have been
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discussed for achieving a functional cure. The first one is known as the
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”shock and kill” strategy, and it involves the purge of latent reservoirs by up-
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regulating HIV expression in combination with antiviral therapy [26]. The
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second less explored approach involves the long-term control of the virus by
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achieving a permanent HIV suppression in the absence of HAART [8, 29]. So
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far, the shock and kill strategy is being actively studied and clinical studies
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have been discussed [22]. In contrast, the only example of permanent inhibi-
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tion is the use of the Tat inhibitor didehydro-cortistatin-A, a natural alkaloid
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that restricts viral reactivation probably by the establishment of epigenetic
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modifications at the viral promoter [24]. Permanent HIV suppression still
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faces multiple challenges; the most important is the finding of stronger and
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permanent virus-suppressing agents [11].
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Intense research has been done to develop specific compounds to affect the
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Tat-dependent transcription. Those compounds include specific Tat com-
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petitive inhibitors and indirect inhibitors to cell machinery used during the
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Tat-dependent transcription. However, the effect of those inhibitors in viral
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latency is not completely understood [25]. Little attention has been paid to
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understand the potential role of Tat inhibitors as virus-suppressing agents.
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To test our hypothesis, we developed a series of computational experiments
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that allowed us to simulate the temporal HIV infection in the presence of Tat
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inhibitors. Our simulation results showed that competitive, non-competitive
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and irreversible Tat inhibitors confer a dose-dependent viral inhibition and
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that removal of those inhibitors resulted in viral expression. Contrarily, by
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simulating the suggested mechanism of action of didehydro-cortistatin-A, we
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predicted a more permanent inhibition in the viral gene expression.
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2. Materials and Methods
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2.1. Model for intracellular HIV gene expression.
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To reproduce the overall dynamics of the intracellular HIV infection, we used
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the simple and tractable mathematical model developed by Razooky et al.
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[31]. In the model the dynamics of viral biomolecules are lumped in the
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following reactions: First, reaction (1) gives the viral promoter switching
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between active (LT RON ) and inactive (LT ROF F ) states. Subsequently, in
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reaction (2) a constant term represents the basal transcription rate of HIV
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which is given by the TATA-binding protein, NF-κB, Sp1 and RNAPII [27].
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Reaction (3) describes a complex formed by the viral promoter and Tat
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protein, transactivation is represented in reaction (4). Translation of Tat
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protein is shown in reaction (5), and finally, first order terms that represent
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the degradation of the mRN A and Tat are specified in reactions (6) and (7),
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respectively.
k
ON −−− −− * LT ROF F ) − LT RON ,
kOf f
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(1)
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k
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bind −− − −− * T at + LT RON − ) − − LT RON −T at ,
kunbind
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trans −→ LT RON −T at + mRN A, LT RON −T at −−
T at mRN A −− → mRN A + T at,
δ
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(5)
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mRN A −−m→ ∅,
(2)
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LT RON −−m→ mRN A + LT RON ,
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T at T at −− → ∅.
(7)
Model initial conditions are given in Table 1, and all the parameters in the
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reactions have ranges defined by experimental reports and are depicted in
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Table 2. The stochastic model dynamics were solved using the Gillespie’s
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algorithm [12] coded in COPASI [14].
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2.2. Tat dependent transcription inhibitors.
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To describe the mechanism of action from Tat inhibitors, we borrowed termi-
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nology from enzyme kinetics and defined three categories according to their 8
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mechanism of action [32]. Additionally, given the particular mechanism of
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action of didehydro-cortistatin-A, it was considered in an independent cate-
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gory. In the simulations, we considered inhibitor concentrations as constants.
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This can be justified by assuming a large inhibitor concentration so that the
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formation of complexes does not change the inhibitor dynamics [15]. The de-
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scription of additional reactions and mechanisms of action for Tat inhibitors
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are given as follows:
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Competitive Inhibitors (CI) compete with the LTR for the active site of the
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Tat. Examples of those inhibitors are oligonucleotides that mimic the TAR
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structure [19, 1, 39] (see Fig. 2A). The inhibition constant (IC), for those
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compounds, is reported to be of the order of 250nM. The effect of those
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compounds was incorporated in the model by adding a reversible reaction
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(8), that describes the binding of the CI to T at.
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k
bCI −− −− * CI + T at − ) − CI/T at.
kubCI
(8)
Non-Competitive Inhibitors (NCI) reversibly bind to elements that are indis-
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pensable for Tat-dependent transcription but not the active site. Examples
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of NCI include Flavopiridol and its derivatives that bind and inactivate the
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cellular factor P-TEFb that is indispensable on the Tat-dependent transcrip-
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tion, with IC value of 10nM [6, 3], 6BIOder with an IC value of 40nM [17, 13],
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and Tat peptide inhibitors with IC ranging from 0.1 to 3.5 µM [34]. A graph-
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ical representation for the mechanism of action of these compounds is given
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in Fig. 2B. The effect of those compounds was incorporated in the model
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by adding reversible reaction (9), describing the binding of the NCI to the
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complex LT RON −T at and reversible reaction (10) that represents the binding
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of the NCI to T at. k
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bN CI −− −− −− * N CI + LT RON −T at − ) − N CI/LT RON −T at ,
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k
2bN CI −− −− −− −− * N CI + T at − ) − N CI/T at.
k2ubN CI
(9)
(10)
Irreversible Inhibitors (II) exert their action by forming an irreversible com-
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plex that promotes proteosomal degradation. Examples include Triptolide
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(a natural diterpenoid epoxide) with IC ranging from 0.32 - 1.6 nM [35], and
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dominant negative mutants of Cycling T1 that promote Tat protein degra-
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dation [16] (see Fig. 2C). The effect of these compounds was incorporated
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in the model by adding reaction (11) that describes the inactivation of T at
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by binding the II, and reaction (12) that describes the degradation of the
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complex.
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k
bII II + T at −− → II/T at,
δII/T at
II/T at −−−−→ ∅.
(11)
(12)
Didehydro-cortistatin-A (dCA) is a natural alkaloid that dramatically re10
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stricts viral reactivation promoting a state of permanent latency. dCA mech-
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anism of action is not fully understood, but it has been shown that it binds
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specifically to the Tat protein. Additionally, it has been suggested that it
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promotes the establishment of epigenetic modifications at the viral promoter
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[23]. This compound has a IC ranging from 0.7 pM to 2.6 nM [25, 24] (see
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Fig. 2D). The effect of dCA was incorporated into the model by adding a
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reaction (13), describing the irreversible binding of the dCA to the complex
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LT RON −T at .
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k
dCA −→ dCA/LT RON −T at . dCA + LT RON −T at −−
(13)
3. Results
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To reproduce the latent-productive decision at single-cell resolution stochas-
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tic dynamics were taken into account. Here we performed multiple stochastic
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simulations using the Direct Method from Gillespie [12] and the intracellular
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model (reactions (1) to (7)) obtaining trajectories that represent the dynam-
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ics of T at in one infected cell. In our simulations, we used the dynamics of
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T at to define a threshold to differentiate latent and virus-producing states.
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This threshold was assumed to be similar to the one used by Razooky et
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al. [31]. Latency is characterized by low expression of viral gene products,
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and for that reason, a low concentration of T at (T at < 100 Molecules/Cell)
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was used to define the latent state. In contrast, the virus-producing state
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is characterized by the active expression of viral gene products. For this, 11
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we assumed the virus-productiing state if T at reached values larger than
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100 Molecules/Cell. The simulation results showed cellular activation prob-
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abilistically reactivates latent virus starting in the initial condition (latent
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state) and then - with increasing time - stochastically changing to the virus-
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productive state, see Fig. 3.
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To understand the effect of Tat inhibitors in the HIV intracellular dynam-
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ics, we performed a set of simulations where the inhibitors were introduced
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in two approaches. The first one represents the effect of having a constant
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inhibitor in the system, and the second one represents the effect of applying
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the inhibitor for an intermediate time of 8 days and then removing it for
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the rest of the total simulation time. For those experiments, we used the
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intracellular model (reactions (1) to (7)), and we observed the effect of the
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different classes of inhibitors. Modeling the inhibitors in the system requires
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binding and unbinding constants that were initially adjusted to obtain the
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latent state. All simulations were performed using parameters values given
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in Table 2. To model the effect of CI in the system, we introduced reaction
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(8). We observed that CI applied at a constant concentration delays Tat
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expression, but when it is removed, the Tat expression recovers a dynamics
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similar to a system without inhibitor, see Fig. 4A. Subsequently, we studied
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the effect of NCI, and we found that a constant application of NCI reduced
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most transitions to the virus-producing state. Removing NCI restores Tat
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expression, see Fig. 4B. Then, we analyzed the effect of II in the system
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through the introduction of reactions (11) and (12). Our results showed that
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II constantly applied reduces the transitions to the virus-producing state.
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Removing II restores Tat expression, see Fig. 4C. Finally, we studied the
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effect of dCA in the system by using reaction (13). We observed that dCA
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applied at a constant concentration dramatically impairs the virus expression
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which is observed in the total inhibition of transitions to the virus-producing
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state. Removing dCA from the system affects the observed permanent in-
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hibitory effect. A permanent inhibition was observed for most of the cells,
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but a small fraction (6 cells) were able to restart a productive infection, see
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Fig. 4D.
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As a further measure of inhibitor efficiency, we calculated the switching time
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between the latent state and the virus-producing state. We observed that
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in a simulation with no inhibitor this transition time is characterized by a
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distribution with a peak close to the first three days of infection. NCI and
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dCA deform this original distribution to a long-tail shaped distribution with
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much smaller peaks during the first days of infection. For CI and II it was
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obtained an almost uniform distribution with low probability of transition.
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This result shows that Tat inhibitors act by reducing the total number of
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the transitions to the producing state during initial days of the infection and
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keep a small probability of transition for long periods, see Fig. 5.
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It is important to remark that the results obtained maybe be parameter de13
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pendent. For this reason, we performed a parameter scan using ranges of
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parameters one order of magnitude above and one order of magnitude be-
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low the nominal values given in Table 2. In this simulation, we varied the
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parameters and inhibitor concentrations and reported the average Tat con-
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centration in the virus-producing state. Three independent simulations were
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performed with 1000 trajectories representing individual cells. With this, we
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proved the robustness of our model predictions and corroborated that the re-
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sults obtained are consistent even using wide ranges of parameters. In Fig. 6
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A-C, it can be observed the effect of Tat inhibitors applied in temporal (left
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panel) and constant (right panel) schemes on the average expression of the
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Tat protein. The results prove that CI, NCI, and II applied in a temporal
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scheme result in a recovery of Tat expression after the inhibitor is removed,
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and only a permanent inhibition in Tat protein expression is observed by
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constantly applying those inhibitors. On the contrary, dCA showed a more
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permanent Tat inhibition during the constant application scheme, and only
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HIV expression was observed under the lowest concentration of dCA (see
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Fig. 6 D).
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4. Discussion
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The greatest barrier to eradicate HIV infection is the persistence of HIV la-
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tent infected cells. Two main strategies have been discussed for achieving a
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functional cure: The shock and kill strategy [26] and the less explored perma-
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nent HIV suppression [25]. So far, the shock and kill strategy is being actively
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studied and even clinical trails have been considered [33]. In contrast, per-
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manent HIV suppression still faces multiple challenges, the most important
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being the finding of stronger and permanent virus-suppressing agents [11]. In
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this project, we presented a mathematical study to understand the potential
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role of Tat inhibitors as virus-suppressing agents. In the presented model,
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we combined the well-known feedback circuits in HIV gene expression with
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the effect of different classes of Tat inhibitors. Our modeling strategy is sim-
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plistic enough to allow us to thoroughly understand the general dynamics of
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HIV gene expression and those of cells in latent and productive states. Our
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results suggest that diverse compounds with different mechanisms of inhibi-
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tion can achieve a substantial reduction in the virus-producing state.
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Summarizing our simulation results, it is possible to detect the main differ-
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ences between the studied Tat inhibitors. Removing Tat protein from the
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cell via CI, NCI or II results in a decrease in the overall HIV gene expression.
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Nevertheless, those compounds do not affect the viral genome integrated into
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the host genome. Thus the virus maintains its potential to “re-awake” after
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those inhibitors are removed. This re-awakening capacity can be understood
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at a system level by the low viral transcription that can be given even in
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total absence of Tat [27]. This basal transcription rate eventually restores
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the positive feedback loop in the system, by a slow but constant increase in
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Tat concentration. In contrast, dCA by promoting epigenetic modifications
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disrupts the integrated viral genome resulting in the loss of this re-awakening
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capacity [25]. The disruption of the integrated viral genome does not affect
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Tat protein instantaneously, but the virus-producing state is removed, re-
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sulting in the permanent extinction of the viral gene products. Our results
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suggest that a putative therapy with CI, NCI, and II would result in re-
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versible dynamics that could cause an ineffective scenario as that obtained
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with current HAART in latency [28]. On the contrary, we predict that a con-
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stant application of dCA can achieve a permanent inhibition. Nevertheless,
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it is important to remark the difference between a permanent Tat inhibi-
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tion and total viral eradication. Our results show that dCA can achieve a
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permanent Tat inhibition, but not an HIV-eradication. Analyzing Fig. 4D
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it can be observed that some trajectories transition to the productive state
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even after dCA application. Those cells escaped the effect of dCA because
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this inhibitor needs to interact with an active Tat-LTR complex. This means
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that dCA can only achieve total eradication of the virus if it is applied for
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a period longer than the last latent-productive transition event. dCA is a
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prominent candidate to achieve long-term Tat inhibition [25, 24].
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During the peer-review process of this paper, a similar work from Cao’s group was published, they studied the probability landscape of the Tat-circuit un-
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der different perturbations [5]. Comparing their results with our findings, we
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observed consistent outcomes for a ’shock and kill’ strategy and permanent
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inhibition.
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5. Conclusions
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Overall, our results showed that removing Tat protein from the system via
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inhibitors resulted in a temporary and reversible viral suppression. In con-
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trast, compounds that interact with Tat protein and disrupt the integrated
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viral genome produced a more permanent viral suppression. Future experi-
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ments are still needed to substantiate dCA significance in latency, i.e., how
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strong and for how long those epigenetic modifications would affect the HIV
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expression. Improving dCA understanding in Tat inhibition could give light
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in the design of novel therapeutic interventions to achieve the long searched
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functional cure.
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6. Funding
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LUA has been supported by postdoctoral grant 263795 from Consejo Na-
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cional de Ciencia y Tecnolog´ıa (CONACYT).
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7. Acknowledgments
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We gratefully thank Prof. Dr. Ursula Kummer and Christoph Zimmer
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for her helpful comments to develop the biological model and revising the
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manuscript. Finally, we thank Jocelyn Faberman for proofreading this manuscript.
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Figure captions
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Figure 1: Graphical representation of the processes involved in HIV gene expression. HIV gene expression is given by viral and cellular machinery. HIV gene transcription without Tat protein results in abortive pauses that occur by the formation of a secondary structure (TAR) in the nascent viral transcripts. Tat protein acts as a transcriptional factor binding to the newly synthesized transcripts. This relaxes the abortive secondary structure in the nascent RNA allowing the expression of complete viral transcripts. Complete viral transcripts will produce all the viral elements starting a productive infection. One of those viral products is the same Tat protein. Tat protein forms a positive feedback circuit in the expression of HIV. This last process is termed transactivation.
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Table 1: Initial conditions
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Initial Value 0 1 0 0 0
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Variable LT ROF F LT RON mRN A T at LT RON −T at
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Table 2: Parameter values Description Nominal Range Promoter activation constant 1 × 10−4 fixed Promoter inactivation constant 1 × 10−2 fixed Transcription rate 1 × 10−1 fixed Translation rate 10 fixed Tat binding to promoter rate 1 × 10−2 fixed Tat unbinding to promoter rate 1 × 10−2 fixed Degradation rate of mRNA 1 fixed Degradation rate of Tat 0.125 fixed Transactivation rate 5 fixed
kbCI kubCI kbN CI kubN CI k2bN CI k2ubN CI kbII δII/T at kdCA
Binding constant for CI Unbinding constant for CI Binding constant for NCI Unbinding constant for NCI 2nd binding constant for NCI 2nd unbinding constant for NCI Irreversible binding by II Degradation of II/Tat Irreversible binding by dCA
CI N CI II dCA
Competitive Inhibitor Noncompetitive Inhibitor Irreversible Inhibitor Didehydro-Cortistatin-A
[1 × 10−4 fixed [1 × 10−4 fixed fixed fixed [1 × 10−4 fixed [1 × 10−4
, 1 × 10−2 ] Cell/(Molecules*h) 1/h , 1 × 10−2 ] Cell/(Molecules*h) 1/h Cell/(Molecules*h) 1/h , 1 × 10−2 ] Cell/(Molecules*h) Cell/(Molecules*h) , 1 × 10−2 ] Cell/(Molecules*h)
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TS = This study.
1 × 10−3 1 × 10−5 1 × 10−3 1 × 10−1 1 × 10−4 1 × 10−1 1 × 10−3 1 × 10−3 1 × 10−3
Units 1/h 1/h 1/h 1/h 1/h 1/h 1/h 1/h 1/h
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Parameter kON kOf f km kT at kbind kunbind δm δT at ktrans
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1 × 103 1 × 103 1 × 103 1 × 103
[10 [10 [10 [10
, , , ,
2 × 103 ] 2 × 103 ] 2 × 103 ] 2 × 103 ]
Molecules/Cell Molecules/Cell Molecules/Cell Molecules/Cell
Ref. [31] [31] [31] [31] [31] [31] [31] [31] [31] TS TS TS TS TS TS TS TS TS TS TS TS TS
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Figure 2: Representation of the effect of different classes of Tat inhibitors. Multiple compounds have been described to inhibit Tat-dependent HIV transcription. Here we categorize them according to their mechanism of action: A) Competitive Inhibitors (CI) that reversibly bind to the LTR for the active site of Tat. B) Non-competitive Inhibitors (NCI) that reversibly bind to elements that are indispensable for Tat-dependent transcription. C) Irreversible Inhibitors (II) that promote proteasomal degradation of the Tat protein. D) Didehydro-Cortistatin-A (dCA) binds to the Tat protein and promotes the establishment of epigenetic modifications in the viral promoter.
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Figure 3: Simulations for the intracellular model. A) Stochastic simulations were computed using reactions 1 to 7, initial conditions given in Table 1 and parameter values given in Table 2. 1,000 individual trajectories that represent single cell dynamics are shown for a simulated time-span of 24 days. A representative trajectory that presents a single cell dynamics is given by the blue line. At the right-hand side, a histogram of the final trajectories is given. Red line represents the threshold used to consider cells in the virus-producing state, the number of cells in each state is given next to the histogram.
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Figure 4: Effect of Tat inhibitors in Tat intracellular dynamics. The effect of different inhibitors in Tat expression was computed using 1,000 individual stochastic simulations. In the left panel, the inhibitors were applied for 8 days of simulation time and then removed from the simulation (the time of inhibitor application is inside the vertical black lines). In the right panel, the inhibitors were continuously applied during the 24 days of simulation time. A) Stochastic simulations with CI. B) Stochastic simulations with NCI. C) Stochastic simulations with 23 II. D) Stochastic simulations with dCA. The parameters used for the simulations are given in Table 2.
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Figure 5: Distribution of the switching time between latent and virus-producing states. Simulations were performed for 1,000 individual cells. The time when each cell transitioned between latent state to virus-producing state was recorded and used to build a probability distribution. The different distributions represent simulations for the system with no inhibitor and the corresponding inhibitor as given in the legend.
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Figure 6: Effect of varying parameters in Tat expression. In the left panel, the inhibitors were applied for 8 days of simulation time and then removed from the simulation. In the right panel, the inhibitors were continuously applied during the 24 days of simulation time. Simulations were computed using the initial conditions given in Table 1 and parameter ranges given in Table 2. Constants and inhibitor concentrations were varied according to the figure axis. Colormap represents the total concentration of Tat protein (Molecules/Cell) at the end of 24 days of simulation time. A) HIV intracellular dynamics 25NCI. C) HIV intracellular dynamics with II. with CI. B) HIV intracellular dynamics with D) HIV intracellular dynamics with dCA. Three independent simulations were performed with 1000 trajectories representing individual cells.
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Modeling the Effect of Tat Inhibitors on HIV Latency. Luis U. Aguilera, Jesus ´ Rodr´ıguez-Gonzalez ´ PII: DOI: Reference:
S0022-5193(19)30159-6 https://doi.org/10.1016/j.jtbi.2019.04.018 YJTBI 9893
To appear in:
Journal of Theoretical Biology
Received date: Revised date: Accepted date:
14 August 2018 7 February 2019 16 April 2019
Please cite this article as: Luis U. Aguilera, Jesus Modeling the Ef´ Rodr´ıguez-Gonzalez, ´ fect of Tat Inhibitors on HIV Latency., Journal of Theoretical Biology (2019), doi: https://doi.org/10.1016/j.jtbi.2019.04.018
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Highlights • Mathematical study to understand Tat-inhibitors as virus-suppressing
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• HIV-productive and latent cell phenotypes are described by stochastictransitions.
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• Competitive and non-competitive inhibitors produce reversible viral suppression.
• Didehydro-Cortistatin A (dCA) achieves a more permanent viral inhi-
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Modeling the Effect of Tat Inhibitors on HIV Latency. Luis U. Aguilera
, Jes´ us Rodr´ıguez-Gonz´alezb,
Department of Modeling of Biological Processes, COS Heidelberg / Bioquant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany. b Centro de Investigaci´ on y Estudios Avanzados del Instituto Polit´ecnico Nacional, Unidad Monterrey, Via del Conocimiento 201, Parque PIIT, CP 66600 Apodaca NL, M´exico.
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Abstract
Even in the presence of a successful combination therapy stalling the progress of AIDS, developing a cure for this disease is still an open question. One of the major steps towards a cure would be to be able to eradicate latent HIV
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reservoirs present in patients. During the last decade, multiple findings point to the dominant role of the viral protein Tat in the establishment of latency.
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Here we present a mathematical study to understand the potential role of Tat inhibitors as virus-suppressing agents. For this aim, we implemented
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a computational model that reproduces intracellular dynamics. Simulating an HIV-infected cell and its intracellular feedback we observed that remov-
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ing Tat protein from the system via inhibitors resulted in a temporary and reversible viral suppression. In contrast, we observed that compounds that
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interact with Tat protein and disrupt the integrated viral genome produced a more permanent viral suppression.
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Email address: [email protected] (Jes´ us Rodr´ıguez-Gonz´ alez) Present Address: Colorado State University.
Preprint submitted to Journal of Theoretical Biology
April 17, 2019
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Keywords: Viral suppression, Stochastic model, Tat circuit 1. Introduction
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Treating patients infected with the Human Immunodeficiency Virus (HIV)
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has strongly progressed during the last years. Although until today HIV in-
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fection cannot be eradicated in patients, Highly Active Antiretroviral Ther-
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apy (HAART) decreases viral loads during the infection and prevents clin-
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ical progression to the Acquired Immunodeficiency Syndrome (AIDS) [38].
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A major barrier to achieving HIV eradication is the existence of a reservoir
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of resting memory CD4+ T-lymphocytes (T4-cells) carrying latent provirus
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[7, 10]. HIV latency is a reversible non-virus-producing phenotype in an in-
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fected cell [21].
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It is not entirely clear what molecular processes dictate a latent or productive
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cell infection. Multiple mechanisms have been suggested to contribute to HIV
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latency [18, 20]. However, important findings point to the dominant role of
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the viral protein Tat in latency [30]. Tat is a transactivating regulatory pro-
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tein. Its activation is a key mechanism that promotes viral gene expression
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[4]. Thus, once Tat protein is produced, it enhances HIV gene expression by
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binding to the trans-activating response element (TAR), a stem-loop that is
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present in the 5 end of newly synthesized viral transcripts. Tat changes the
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effective transcription rate of the respective genes up to 100-fold over basal
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expression levels by recruiting the positive transcription elongation complex
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(P-TEFb) made of Cyclin T1 and CDK9 [27]. Since this process also accel-
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erates Tat transcription itself, it constitutes a positive feedback loop in the
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system. The absence of the Tat protein results in premature termination of
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transcription. Over-expression of Tat protein is sufficient to induce the pro-
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duction and spread of HIV from resting memory T4-cells [9]. The complete
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scheme of HIV gene expression is given in Fig. 1.
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Altogether, the cellular fate of individual cells is determined mainly by the
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number of molecules, e.g. of Tat protein present in the cell. Therefore,
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like other cellular events which involve low molecule numbers, cellular fate
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should be strongly affected by the stochasticity of discrete molecular events
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[2]. The central role of stochasticity in the processes carried out by the
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Tat protein was confirmed by studies conducted in the group of Weinberger.
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They modeled the Tat-circuit and adjusting it to the experimental data they
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determined a monostable architecture, which after introducing stochasticity
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showed bimodal dynamics [37]. Subsequently, they proved that HIV expres-
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sion is dictated by the time that the Tat protein remains in the inactive
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(deacetylated) state, which is longer than the time that it remains in the
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active state (acetylated) [36]. Recently, the same group proved that the
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transition between a latent to a productive infection depends solely on the
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Tat circuit, independent of the cellular state [31].
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As previously stated, the biggest barrier to eradicating HIV infection is the 5
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persistence of HIV latent infected cells [33]. Two main strategies have been
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discussed for achieving a functional cure. The first one is known as the
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”shock and kill” strategy, and it involves the purge of latent reservoirs by up-
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regulating HIV expression in combination with antiviral therapy [26]. The
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second less explored approach involves the long-term control of the virus by
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achieving a permanent HIV suppression in the absence of HAART [8, 29]. So
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far, the shock and kill strategy is being actively studied and clinical studies
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have been discussed [22]. In contrast, the only example of permanent inhibi-
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tion is the use of the Tat inhibitor didehydro-cortistatin-A, a natural alkaloid
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that restricts viral reactivation probably by the establishment of epigenetic
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modifications at the viral promoter [24]. Permanent HIV suppression still
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faces multiple challenges; the most important is the finding of stronger and
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permanent virus-suppressing agents [11].
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Intense research has been done to develop specific compounds to affect the
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Tat-dependent transcription. Those compounds include specific Tat com-
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petitive inhibitors and indirect inhibitors to cell machinery used during the
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Tat-dependent transcription. However, the effect of those inhibitors in viral
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latency is not completely understood [25]. Little attention has been paid to
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understand the potential role of Tat inhibitors as virus-suppressing agents.
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To test our hypothesis, we developed a series of computational experiments
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that allowed us to simulate the temporal HIV infection in the presence of Tat
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inhibitors. Our simulation results showed that competitive, non-competitive
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and irreversible Tat inhibitors confer a dose-dependent viral inhibition and
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that removal of those inhibitors resulted in viral expression. Contrarily, by
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simulating the suggested mechanism of action of didehydro-cortistatin-A, we
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predicted a more permanent inhibition in the viral gene expression.
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2. Materials and Methods
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2.1. Model for intracellular HIV gene expression.
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To reproduce the overall dynamics of the intracellular HIV infection, we used
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the simple and tractable mathematical model developed by Razooky et al.
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[31]. In the model the dynamics of viral biomolecules are lumped in the
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following reactions: First, reaction (1) gives the viral promoter switching
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between active (LT RON ) and inactive (LT ROF F ) states. Subsequently, in
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reaction (2) a constant term represents the basal transcription rate of HIV
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which is given by the TATA-binding protein, NF-κB, Sp1 and RNAPII [27].
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Reaction (3) describes a complex formed by the viral promoter and Tat
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protein, transactivation is represented in reaction (4). Translation of Tat
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protein is shown in reaction (5), and finally, first order terms that represent
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the degradation of the mRN A and Tat are specified in reactions (6) and (7),
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respectively.
k
ON −−− −− * LT ROF F ) − LT RON ,
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(1)
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k
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bind −− − −− * T at + LT RON − ) − − LT RON −T at ,
kunbind
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trans −→ LT RON −T at + mRN A, LT RON −T at −−
T at mRN A −− → mRN A + T at,
δ
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(4)
(5)
(6)
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mRN A −−m→ ∅,
(2)
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LT RON −−m→ mRN A + LT RON ,
δ
T at T at −− → ∅.
(7)
Model initial conditions are given in Table 1, and all the parameters in the
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reactions have ranges defined by experimental reports and are depicted in
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Table 2. The stochastic model dynamics were solved using the Gillespie’s
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algorithm [12] coded in COPASI [14].
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2.2. Tat dependent transcription inhibitors.
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To describe the mechanism of action from Tat inhibitors, we borrowed termi-
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nology from enzyme kinetics and defined three categories according to their 8
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mechanism of action [32]. Additionally, given the particular mechanism of
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action of didehydro-cortistatin-A, it was considered in an independent cate-
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gory. In the simulations, we considered inhibitor concentrations as constants.
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This can be justified by assuming a large inhibitor concentration so that the
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formation of complexes does not change the inhibitor dynamics [15]. The de-
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scription of additional reactions and mechanisms of action for Tat inhibitors
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are given as follows:
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Competitive Inhibitors (CI) compete with the LTR for the active site of the
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Tat. Examples of those inhibitors are oligonucleotides that mimic the TAR
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structure [19, 1, 39] (see Fig. 2A). The inhibition constant (IC), for those
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compounds, is reported to be of the order of 250nM. The effect of those
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compounds was incorporated in the model by adding a reversible reaction
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(8), that describes the binding of the CI to T at.
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k
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kubCI
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Non-Competitive Inhibitors (NCI) reversibly bind to elements that are indis-
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pensable for Tat-dependent transcription but not the active site. Examples
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of NCI include Flavopiridol and its derivatives that bind and inactivate the
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cellular factor P-TEFb that is indispensable on the Tat-dependent transcrip-
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tion, with IC value of 10nM [6, 3], 6BIOder with an IC value of 40nM [17, 13],
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and Tat peptide inhibitors with IC ranging from 0.1 to 3.5 µM [34]. A graph-
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ical representation for the mechanism of action of these compounds is given
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in Fig. 2B. The effect of those compounds was incorporated in the model
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by adding reversible reaction (9), describing the binding of the NCI to the
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complex LT RON −T at and reversible reaction (10) that represents the binding
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of the NCI to T at. k
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bN CI −− −− −− * N CI + LT RON −T at − ) − N CI/LT RON −T at ,
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k2ubN CI
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(10)
Irreversible Inhibitors (II) exert their action by forming an irreversible com-
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plex that promotes proteosomal degradation. Examples include Triptolide
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(a natural diterpenoid epoxide) with IC ranging from 0.32 - 1.6 nM [35], and
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dominant negative mutants of Cycling T1 that promote Tat protein degra-
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dation [16] (see Fig. 2C). The effect of these compounds was incorporated
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in the model by adding reaction (11) that describes the inactivation of T at
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by binding the II, and reaction (12) that describes the degradation of the
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complex.
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Didehydro-cortistatin-A (dCA) is a natural alkaloid that dramatically re10
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stricts viral reactivation promoting a state of permanent latency. dCA mech-
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anism of action is not fully understood, but it has been shown that it binds
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specifically to the Tat protein. Additionally, it has been suggested that it
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promotes the establishment of epigenetic modifications at the viral promoter
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[23]. This compound has a IC ranging from 0.7 pM to 2.6 nM [25, 24] (see
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Fig. 2D). The effect of dCA was incorporated into the model by adding a
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reaction (13), describing the irreversible binding of the dCA to the complex
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LT RON −T at .
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k
dCA −→ dCA/LT RON −T at . dCA + LT RON −T at −−
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3. Results
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To reproduce the latent-productive decision at single-cell resolution stochas-
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tic dynamics were taken into account. Here we performed multiple stochastic
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simulations using the Direct Method from Gillespie [12] and the intracellular
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model (reactions (1) to (7)) obtaining trajectories that represent the dynam-
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ics of T at in one infected cell. In our simulations, we used the dynamics of
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T at to define a threshold to differentiate latent and virus-producing states.
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This threshold was assumed to be similar to the one used by Razooky et
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al. [31]. Latency is characterized by low expression of viral gene products,
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and for that reason, a low concentration of T at (T at < 100 Molecules/Cell)
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was used to define the latent state. In contrast, the virus-producing state
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we assumed the virus-productiing state if T at reached values larger than
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100 Molecules/Cell. The simulation results showed cellular activation prob-
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abilistically reactivates latent virus starting in the initial condition (latent
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state) and then - with increasing time - stochastically changing to the virus-
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productive state, see Fig. 3.
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To understand the effect of Tat inhibitors in the HIV intracellular dynam-
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ics, we performed a set of simulations where the inhibitors were introduced
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in two approaches. The first one represents the effect of having a constant
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inhibitor in the system, and the second one represents the effect of applying
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the inhibitor for an intermediate time of 8 days and then removing it for
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the rest of the total simulation time. For those experiments, we used the
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intracellular model (reactions (1) to (7)), and we observed the effect of the
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different classes of inhibitors. Modeling the inhibitors in the system requires
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binding and unbinding constants that were initially adjusted to obtain the
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latent state. All simulations were performed using parameters values given
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in Table 2. To model the effect of CI in the system, we introduced reaction
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(8). We observed that CI applied at a constant concentration delays Tat
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expression, but when it is removed, the Tat expression recovers a dynamics
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similar to a system without inhibitor, see Fig. 4A. Subsequently, we studied
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the effect of NCI, and we found that a constant application of NCI reduced
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most transitions to the virus-producing state. Removing NCI restores Tat
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expression, see Fig. 4B. Then, we analyzed the effect of II in the system
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through the introduction of reactions (11) and (12). Our results showed that
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II constantly applied reduces the transitions to the virus-producing state.
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Removing II restores Tat expression, see Fig. 4C. Finally, we studied the
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effect of dCA in the system by using reaction (13). We observed that dCA
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applied at a constant concentration dramatically impairs the virus expression
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which is observed in the total inhibition of transitions to the virus-producing
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state. Removing dCA from the system affects the observed permanent in-
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hibitory effect. A permanent inhibition was observed for most of the cells,
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but a small fraction (6 cells) were able to restart a productive infection, see
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Fig. 4D.
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As a further measure of inhibitor efficiency, we calculated the switching time
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between the latent state and the virus-producing state. We observed that
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in a simulation with no inhibitor this transition time is characterized by a
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distribution with a peak close to the first three days of infection. NCI and
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dCA deform this original distribution to a long-tail shaped distribution with
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much smaller peaks during the first days of infection. For CI and II it was
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obtained an almost uniform distribution with low probability of transition.
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This result shows that Tat inhibitors act by reducing the total number of
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the transitions to the producing state during initial days of the infection and
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keep a small probability of transition for long periods, see Fig. 5.
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It is important to remark that the results obtained maybe be parameter de13
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pendent. For this reason, we performed a parameter scan using ranges of
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parameters one order of magnitude above and one order of magnitude be-
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low the nominal values given in Table 2. In this simulation, we varied the
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parameters and inhibitor concentrations and reported the average Tat con-
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centration in the virus-producing state. Three independent simulations were
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performed with 1000 trajectories representing individual cells. With this, we
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proved the robustness of our model predictions and corroborated that the re-
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sults obtained are consistent even using wide ranges of parameters. In Fig. 6
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A-C, it can be observed the effect of Tat inhibitors applied in temporal (left
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panel) and constant (right panel) schemes on the average expression of the
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Tat protein. The results prove that CI, NCI, and II applied in a temporal
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scheme result in a recovery of Tat expression after the inhibitor is removed,
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and only a permanent inhibition in Tat protein expression is observed by
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constantly applying those inhibitors. On the contrary, dCA showed a more
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permanent Tat inhibition during the constant application scheme, and only
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HIV expression was observed under the lowest concentration of dCA (see
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Fig. 6 D).
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4. Discussion
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The greatest barrier to eradicate HIV infection is the persistence of HIV la-
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tent infected cells. Two main strategies have been discussed for achieving a
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functional cure: The shock and kill strategy [26] and the less explored perma-
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nent HIV suppression [25]. So far, the shock and kill strategy is being actively
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studied and even clinical trails have been considered [33]. In contrast, per-
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manent HIV suppression still faces multiple challenges, the most important
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being the finding of stronger and permanent virus-suppressing agents [11]. In
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this project, we presented a mathematical study to understand the potential
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role of Tat inhibitors as virus-suppressing agents. In the presented model,
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we combined the well-known feedback circuits in HIV gene expression with
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the effect of different classes of Tat inhibitors. Our modeling strategy is sim-
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plistic enough to allow us to thoroughly understand the general dynamics of
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HIV gene expression and those of cells in latent and productive states. Our
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results suggest that diverse compounds with different mechanisms of inhibi-
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tion can achieve a substantial reduction in the virus-producing state.
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Summarizing our simulation results, it is possible to detect the main differ-
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ences between the studied Tat inhibitors. Removing Tat protein from the
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cell via CI, NCI or II results in a decrease in the overall HIV gene expression.
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Nevertheless, those compounds do not affect the viral genome integrated into
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the host genome. Thus the virus maintains its potential to “re-awake” after
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those inhibitors are removed. This re-awakening capacity can be understood
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at a system level by the low viral transcription that can be given even in
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total absence of Tat [27]. This basal transcription rate eventually restores
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the positive feedback loop in the system, by a slow but constant increase in
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Tat concentration. In contrast, dCA by promoting epigenetic modifications
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disrupts the integrated viral genome resulting in the loss of this re-awakening
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capacity [25]. The disruption of the integrated viral genome does not affect
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Tat protein instantaneously, but the virus-producing state is removed, re-
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sulting in the permanent extinction of the viral gene products. Our results
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suggest that a putative therapy with CI, NCI, and II would result in re-
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versible dynamics that could cause an ineffective scenario as that obtained
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with current HAART in latency [28]. On the contrary, we predict that a con-
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stant application of dCA can achieve a permanent inhibition. Nevertheless,
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it is important to remark the difference between a permanent Tat inhibi-
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tion and total viral eradication. Our results show that dCA can achieve a
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permanent Tat inhibition, but not an HIV-eradication. Analyzing Fig. 4D
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it can be observed that some trajectories transition to the productive state
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even after dCA application. Those cells escaped the effect of dCA because
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this inhibitor needs to interact with an active Tat-LTR complex. This means
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that dCA can only achieve total eradication of the virus if it is applied for
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a period longer than the last latent-productive transition event. dCA is a
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prominent candidate to achieve long-term Tat inhibition [25, 24].
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During the peer-review process of this paper, a similar work from Cao’s group was published, they studied the probability landscape of the Tat-circuit un-
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der different perturbations [5]. Comparing their results with our findings, we
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observed consistent outcomes for a ’shock and kill’ strategy and permanent
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inhibition.
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5. Conclusions
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Overall, our results showed that removing Tat protein from the system via
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inhibitors resulted in a temporary and reversible viral suppression. In con-
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trast, compounds that interact with Tat protein and disrupt the integrated
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viral genome produced a more permanent viral suppression. Future experi-
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ments are still needed to substantiate dCA significance in latency, i.e., how
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strong and for how long those epigenetic modifications would affect the HIV
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expression. Improving dCA understanding in Tat inhibition could give light
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in the design of novel therapeutic interventions to achieve the long searched
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functional cure.
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6. Funding
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LUA has been supported by postdoctoral grant 263795 from Consejo Na-
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cional de Ciencia y Tecnolog´ıa (CONACYT).
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7. Acknowledgments
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We gratefully thank Prof. Dr. Ursula Kummer and Christoph Zimmer
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for her helpful comments to develop the biological model and revising the
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manuscript. Finally, we thank Jocelyn Faberman for proofreading this manuscript.
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Figure captions
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Figure 1: Graphical representation of the processes involved in HIV gene expression. HIV gene expression is given by viral and cellular machinery. HIV gene transcription without Tat protein results in abortive pauses that occur by the formation of a secondary structure (TAR) in the nascent viral transcripts. Tat protein acts as a transcriptional factor binding to the newly synthesized transcripts. This relaxes the abortive secondary structure in the nascent RNA allowing the expression of complete viral transcripts. Complete viral transcripts will produce all the viral elements starting a productive infection. One of those viral products is the same Tat protein. Tat protein forms a positive feedback circuit in the expression of HIV. This last process is termed transactivation.
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Table 1: Initial conditions
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Variable LT ROF F LT RON mRN A T at LT RON −T at
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Table 2: Parameter values Description Nominal Range Promoter activation constant 1 × 10−4 fixed Promoter inactivation constant 1 × 10−2 fixed Transcription rate 1 × 10−1 fixed Translation rate 10 fixed Tat binding to promoter rate 1 × 10−2 fixed Tat unbinding to promoter rate 1 × 10−2 fixed Degradation rate of mRNA 1 fixed Degradation rate of Tat 0.125 fixed Transactivation rate 5 fixed
kbCI kubCI kbN CI kubN CI k2bN CI k2ubN CI kbII δII/T at kdCA
Binding constant for CI Unbinding constant for CI Binding constant for NCI Unbinding constant for NCI 2nd binding constant for NCI 2nd unbinding constant for NCI Irreversible binding by II Degradation of II/Tat Irreversible binding by dCA
CI N CI II dCA
Competitive Inhibitor Noncompetitive Inhibitor Irreversible Inhibitor Didehydro-Cortistatin-A
[1 × 10−4 fixed [1 × 10−4 fixed fixed fixed [1 × 10−4 fixed [1 × 10−4
, 1 × 10−2 ] Cell/(Molecules*h) 1/h , 1 × 10−2 ] Cell/(Molecules*h) 1/h Cell/(Molecules*h) 1/h , 1 × 10−2 ] Cell/(Molecules*h) Cell/(Molecules*h) , 1 × 10−2 ] Cell/(Molecules*h)
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1 × 10−3 1 × 10−5 1 × 10−3 1 × 10−1 1 × 10−4 1 × 10−1 1 × 10−3 1 × 10−3 1 × 10−3
Units 1/h 1/h 1/h 1/h 1/h 1/h 1/h 1/h 1/h
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Parameter kON kOf f km kT at kbind kunbind δm δT at ktrans
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1 × 103 1 × 103 1 × 103 1 × 103
[10 [10 [10 [10
, , , ,
2 × 103 ] 2 × 103 ] 2 × 103 ] 2 × 103 ]
Molecules/Cell Molecules/Cell Molecules/Cell Molecules/Cell
Ref. [31] [31] [31] [31] [31] [31] [31] [31] [31] TS TS TS TS TS TS TS TS TS TS TS TS TS
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Figure 2: Representation of the effect of different classes of Tat inhibitors. Multiple compounds have been described to inhibit Tat-dependent HIV transcription. Here we categorize them according to their mechanism of action: A) Competitive Inhibitors (CI) that reversibly bind to the LTR for the active site of Tat. B) Non-competitive Inhibitors (NCI) that reversibly bind to elements that are indispensable for Tat-dependent transcription. C) Irreversible Inhibitors (II) that promote proteasomal degradation of the Tat protein. D) Didehydro-Cortistatin-A (dCA) binds to the Tat protein and promotes the establishment of epigenetic modifications in the viral promoter.
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Figure 3: Simulations for the intracellular model. A) Stochastic simulations were computed using reactions 1 to 7, initial conditions given in Table 1 and parameter values given in Table 2. 1,000 individual trajectories that represent single cell dynamics are shown for a simulated time-span of 24 days. A representative trajectory that presents a single cell dynamics is given by the blue line. At the right-hand side, a histogram of the final trajectories is given. Red line represents the threshold used to consider cells in the virus-producing state, the number of cells in each state is given next to the histogram.
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Figure 4: Effect of Tat inhibitors in Tat intracellular dynamics. The effect of different inhibitors in Tat expression was computed using 1,000 individual stochastic simulations. In the left panel, the inhibitors were applied for 8 days of simulation time and then removed from the simulation (the time of inhibitor application is inside the vertical black lines). In the right panel, the inhibitors were continuously applied during the 24 days of simulation time. A) Stochastic simulations with CI. B) Stochastic simulations with NCI. C) Stochastic simulations with 23 II. D) Stochastic simulations with dCA. The parameters used for the simulations are given in Table 2.
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Figure 5: Distribution of the switching time between latent and virus-producing states. Simulations were performed for 1,000 individual cells. The time when each cell transitioned between latent state to virus-producing state was recorded and used to build a probability distribution. The different distributions represent simulations for the system with no inhibitor and the corresponding inhibitor as given in the legend.
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Figure 6: Effect of varying parameters in Tat expression. In the left panel, the inhibitors were applied for 8 days of simulation time and then removed from the simulation. In the right panel, the inhibitors were continuously applied during the 24 days of simulation time. Simulations were computed using the initial conditions given in Table 1 and parameter ranges given in Table 2. Constants and inhibitor concentrations were varied according to the figure axis. Colormap represents the total concentration of Tat protein (Molecules/Cell) at the end of 24 days of simulation time. A) HIV intracellular dynamics 25NCI. C) HIV intracellular dynamics with II. with CI. B) HIV intracellular dynamics with D) HIV intracellular dynamics with dCA. Three independent simulations were performed with 1000 trajectories representing individual cells.
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