Mathematical model of the Tat-Rev regulation of HIV-1 replication in an activated cell predicts the existence of oscillatory dynamics in the synthesis of viral components

Frequency response in splicing regulation under mRNA auto-depletion control

Nowadays, there exists a huge literature about stochastic model of transcriptional and translational control in gene networks. However, results related to post-transcriptional regulation via splicing and its connection with transcriptional and translational regulation are almost missing in the current literature and only related to the steady state moments investigation. Nowadays, it is becoming of paramount importance the need for modeling post-transcriptional regulation via splicing especially for DNA viruses or retroviruses. However, there exists only few studies in the literature about splicing regulation and none of them investigate its behavior in the frequency domain that can unveil important features of dynamical stochastic systems that cannot be revealed by the sole steady state moment investigation. The aim of this work is to theoretically investigate a simple gene network subject to splicing regulation with negative feedback control, implemented through mRNA auto-depletion under a frequency domain perspective. This study showed the pivotal role of the burst size, enhancing the noise power spectrum, as well as the splicing conversion rates capable to increase and decrease the noise power spectrum in the pre-mRNA and mRNA, respectively, for high values of conversion rates. Importantly, it shows the capability of the mRNA autodepletion control to modulate the noise as a frequency-dependent amplifying control as a function of the negative feedback strengths.

Frequency analysis of splicing regulation

In the past decades, mathematical modelers developed a huge literature to model and analyze gene networks under both deterministic and stochastic formalisms. Such literature is predominantly focused on modeling transcriptional and translational regulation, while the development of proper mathematical frameworks to model and study post-transcriptional regulation via splicing and its connection with transcriptional and translational regulation are almost missing. Nowadays, it is becoming of paramount importance the need for modeling post-transcriptional regulation via splicing especially for bacteria or viruses. However, current literature is focused on investigating splicing regulation at steady state and none of them have the purpose to investigate gene networks behavior in the frequency domain, thus providing only a partial investigation about the system dynamical response. The aim of this work is to theoretically investigate a simple gene network subjects to splicing regulation with/without negative feedback control under a frequency domain perspective. This study showed the pivotal role of the burst size, as well as splicing conversion rates to modulate the noise and the power spectrum response. It also shows an interesting behavior under the frequency domain induced by the merging effect of burst size, splicing conversion rates and negative feedback strength.

Markov Chain-Based Stochastic Modelling of HIV-1 Life Cycle in a CD4 T Cell

Replication of Human Immunodeficiency Virus type 1 (HIV) in infected CD4+ T cells represents a key driver of HIV infection. The HIV life cycle is characterised by the heterogeneity of infected cells with respect to multiplicity of infection and the variability in viral progeny. This heterogeneity can result from the phenotypic diversity of infected cells as well as from random effects and fluctuations in the kinetics of biochemical reactions underlying the virus replication cycle. To quantify the contribution of stochastic effects to the variability of HIV life cycle kinetics, we propose a high-resolution mathematical model formulated as a Markov chain jump process. The model is applied to generate the statistical characteristics of the (i) cell infection multiplicity, (ii) cooperative nature of viral replication, and (iii) variability in virus secretion by phenotypically identical cells. We show that the infection with a fixed number of viruses per CD4+ T cell leads to some heterogeneity of infected cells with respect to the number of integrated proviral genomes. The bottleneck factors in the virus production are identified, including the Gag-Pol proteins. Sensitivity analysis enables ranking of the model parameters with respect to the strength of their impact on the size of viral progeny. The first three globally influential parameters are the transport of genomic mRNA to membrane, the tolerance of transcription activation to Tat-mediated regulation, and the degradation of free and mature virions. These can be considered as potential therapeutical targets.

Evolution and extinction can occur rapidly: a modeling approach

Fossil record of Earth describing the last 500 million years is characterized by evolution discontinuity as well as recurring global extinctions of some species and their replacement by new types, the causes of which are still debate. We developed a model of evolutionary self-development of a large ecosystem. This model of biota evolution based on the universal laws of living systems functioning: reproduction, dependence of reproduction efficiency and mortality on biota density, mutational variability in the process of reproduction and selection of the most adapted individuals. We have shown that global extinctions and phases of rapid growth and biodiversity stasis can be a reflection of the emergence of bistability in a self-organizing system, which is the Earth’s biota. Bistability was found to be characteristic only for ecosystems with predominant sexual reproduction. The reason for the transition from one state to another is the selection of the most adapted individuals. That is, we explain the characteristics of the Earth’s fossil record during the last 500 million years by the internal laws of Earth’s ecosystem functioning, which appeared at a certain stage of evolution as a result of the emergence of life forms with an increased adaptive diversification associated with sexual dimorphism.

Viral Infection Dynamics Model Based on a Markov Process with Time Delay between Cell Infection and Progeny Production

Many human virus infections including those with the human immunodeficiency virus type 1 (HIV) are initiated by low numbers of founder viruses. Therefore, random effects have a strong influence on the initial infection dynamics, e.g., extinction versus spread. In this study, we considered the simplest (so-called, ‘consensus’) virus dynamics model and incorporated a delay between infection of a cell and virus progeny release from the infected cell. We then developed an equivalent stochastic virus dynamics model that accounts for this delay in the description of the random interactions between the model components. The new model is used to study the statistical characteristics of virus and target cell populations. It predicts the probability of infection spread as a function of the number of transmitted viruses. A hybrid algorithm is suggested to compute efficiently the system dynamics in state space domain characterized by the mix of small and large species densities.

A Minimal Stochastic Model of Transcriptional and Splicing Regulation

In the past decades an extensive mathematical literature was developed to model and analyze gene networks under both deterministic and stochastic formalisms. However, such literature is predominantly focused to deal with the modeling of transcriptional and translational regulation, but results related to post-transcriptional regulation and its connection with transcriptional regulation are poorly investigated. However, it is becoming of paramount importance the need for modeling post-transcriptional regulation via splicing especially for minor organisms or viruses.The aim of this study is to propose a first general basic modeling scheme for modeling gene expression via alternative splicing and investigating the basic deterministic and stochastic features of the pre-mRNA, mRNAs and proteins under different biological conditions.This first study showed the dynamical properties of alternative splicing, the faster kinetics of the pre-mRNA compared to the mRNA and the importance to stochastically model gene networks when considering the post-transcriptional regulation.

Modeling of the HIV-1 Life Cycle in Productively Infected Cells to Predict Novel Therapeutic Targets

There are many studies that model the within-host population dynamics of Human Immunodeficiency Virus Type 1 (HIV-1) infection. However, the within-infected-cell replication of HIV-1 remains to be not comprehensively addressed. There exist rather few quantitative models describing the regulation of the HIV-1 life cycle at the intracellular level. In treatment of HIV-1 infection, there remain issues related to side-effects and drug-resistance that require further search "...for new and better drugs, ideally targeting multiple independent steps in the HIV-1 replication cycle" (as highlighted recently by Teldury et al., The Future of HIV-1 Therapeutics, 2015). High-resolution mathematical models of HIV-1 growth in infected cells provide an additional analytical tool in identifying novel drug targets. We formulate a high-dimensional model describing the biochemical reactions underlying the replication of HIV-1 in target cells. The model considers a nonlinear regulation of the transcription of HIV-1 mediated by Tat and the Rev-dependent transport of fully spliced and singly spliced transcripts from the nucleus to the cytoplasm. The model is calibrated using available information on the kinetics of various stages of HIV-1 replication. The sensitivity analysis of the model is performed to rank the biochemical processes of HIV-1 replication with respect to their impact on the net production of virions by one actively infected cell. The ranking of the sensitivity factors provides a quantitative basis for identifying novel targets for antiviral therapy. Our analysis suggests that HIV-1 assembly depending on Gag and Tat-Rev regulation of transcription and mRNA distribution present two most critical stages in HIV-1 replication that can be targeted to effectively control virus production. These processes are not covered by current antiretroviral treatments.

Differences in Transcriptional Dynamics Between T-cells and Macrophages as Determined by a Three-State Mathematical Model

HIV-1 viral transcription persists in patients despite antiretroviral treatment, potentially due to intermittent HIV-1 LTR activation. While several mathematical models have been explored in the context of LTR-protein interactions, in this work for the first time HIV-1 LTR model featuring repressed, intermediate, and activated LTR states is integrated with generation of long (env) and short (TAR) RNAs and proteins (Tat, Pr55, and p24) in T-cells and macrophages using both cell lines and infected primary cells. This type of extended modeling framework allows us to compare and contrast behavior of these two cell types. We demonstrate that they exhibit unique LTR dynamics, which ultimately results in differences in the magnitude of viral products generated. One of the distinctive features of this work is that it relies on experimental data in reaction rate computations. Two RNA transcription rates from the activated promoter states are fit by comparison of experimental data to model predictions. Fitting to the data also provides estimates for the degradation/exit rates for long and short viral RNA. Our experimentally generated data is in reasonable agreement for the T-cell as well macrophage population and gives strong evidence in support of using the proposed integrated modeling paradigm. Sensitivity analysis performed using Latin hypercube sampling method confirms robustness of the model with respect to small parameter perturbations. Finally, incorporation of a transcription inhibitor (F07#13) into the governing equations demonstrates how the model can be used to assess drug efficacy. Collectively, our model indicates transcriptional differences between latently HIV-1 infected T-cells and macrophages and provides a novel platform to study various transcriptional dynamics leading to latency or activation in numerous cell types and physiological conditions.

Highly Mutable Linker Regions Regulate HIV-1 Rev Function and Stability

HIV-1 Rev is an essential viral regulatory protein that facilitates the nuclear export of intron-containing viral mRNAs. It is organized into structured, functionally well-characterized motifs joined by less understood linker regions. Our recent competitive deep mutational scanning study confirmed many known constraints in Rev’s established motifs, but also identified positions of mutational plasticity, most notably in surrounding linker regions. Here, we probe the mutational limits of these linkers by testing the activities of multiple truncation and mass substitution mutations. We find that these regions possess previously unknown structural, functional or regulatory roles, not apparent from systematic point mutational approaches. Specifically, the N- and C-termini of Rev contribute to protein stability; mutations in a turn that connects the two main helices of Rev have different effects in different contexts; and a linker region which connects the second helix of Rev to its nuclear export sequence has structural requirements for function. Thus, Rev function extends beyond its characterized motifs, and is tuned by determinants within seemingly plastic portions of its sequence. Additionally, Rev’s ability to tolerate many of these massive truncations and substitutions illustrates the overall mutational and functional robustness inherent in this viral protein.

Interplay between reaction and diffusion processes in governing the dynamics of virus infections

Spreading of viral infection in the tissues such as lymph nodes or spleen depends on virus multiplication in the host cells, their transport and on the immune response. Reaction-diffusion systems of equations with delays in cell proliferation and death by apoptosis represent an appropriate model to study this process. The properties of the cells of the immune system and the initial viral load determine the spatiotemporal regimes of infection spreading. Infection can be completely eliminated or it can persist at some level together with a certain chronic immune response in a spatially uniform or oscillatory mode. Finally, the immune cells can be completely exhausted leading to a high viral load persistence in the tissue. It has been found experimentally, that virus proteins can affect the immune cell migration. Our study shows that both the motility of immune cells and the virus infection spreading represented by the diffusion rate coefficients are relevant control parameters determining the fate of virus-host interaction.

Spatiotemporal Dynamics of Virus Infection Spreading in Tissues

Virus spreading in tissues is determined by virus transport, virus multiplication in host cells and the virus-induced immune response. Cytotoxic T cells remove infected cells with a rate determined by the infection level. The intensity of the immune response has a bell-shaped dependence on the concentration of virus, i.e., it increases at low and decays at high infection levels. A combination of these effects and a time delay in the immune response determine the development of virus infection in tissues like spleen or lymph nodes. The mathematical model described in this work consists of reaction-diffusion equations with a delay. It shows that the different regimes of infection spreading like the establishment of a low level infection, a high level infection or a transition between both are determined by the initial virus load and by the intensity of the immune response. The dynamics of the model solutions include simple and composed waves, and periodic and aperiodic oscillations. The results of analytical and numerical studies of the model provide a systematic basis for a quantitative understanding and interpretation of the determinants of the infection process in target organs and tissues from the image-derived data as well as of the spatiotemporal mechanisms of viral disease pathogenesis, and have direct implications for a biopsy-based medical testing of the chronic infection processes caused by viruses, e.g. HIV, HCV and HBV.

Rev-RRE Functional Activity Differs Substantially Among Primary HIV-1 Isolates

The HIV-1 replication cycle requires the nucleocytoplasmic export of intron-containing viral RNAs, a process that is ordinarily restricted. HIV overcomes this by means of the viral Rev protein, which binds to an RNA secondary structure called the Rev response element (RRE) present in all unspliced or incompletely spliced viral RNA transcripts. The resulting mRNP complex is exported through interaction with cellular factors. The Rev-RRE binding interaction is increasingly understood to display remarkable structural plasticity, but little is known about how Rev-RRE sequence differences affect functional activity. To study this issue, we utilized a lentiviral vector assay in which vector titer is dependent on the activity of selected Rev-RRE pairs. We found that Rev-RRE functional activity varies significantly (up to 24-fold) between naturally occurring viral isolates. The activity differences of the Rev-RRE cognate pairs track closely with Rev, but not with RRE activity. This variation in Rev activity is not correlated with differences in Rev steady state protein levels. These data suggest that Rev sequence differences drive substantial variation in Rev-RRE functional activity between patients. Such variation may play a role in viral adaptation to different immune milieus within and between patients and may be significant in the establishment of latency. The identification of differences in Rev-RRE functional activity in naturally occurring isolates may also permit more efficient production of lentiviral vectors.

A structurally plastic ribonucleoprotein complex mediates post-transcriptional gene regulation in HIV-1

HIV replication requires the nuclear export of essential, intron-containing viral RNAs. To facilitate export, HIV encodes the viral accessory protein Rev which binds unspliced and partially spliced viral RNAs and creates a ribonucleoprotein complex that recruits the cellular Chromosome maintenance factor 1 export machinery. Exporting RNAs in this manner bypasses the necessity for complete splicing as a prerequisite for mRNA export, and allows intron-containing RNAs to reach the cytoplasm intact for translation and virus packaging. Recent structural studies have revealed that this entire complex exhibits remarkable plasticity at many levels of organization, including RNA folding, protein-RNA recognition, multimer formation, and host factor recruitment. In this review, we explore each aspect of plasticity from structural, functional, and possible therapeutic viewpoints. WIREs RNA 2016, 7:470-486. doi: 10.1002/wrna.1342 For further resources related to this article, please visit the WIREs website.

Distinct promoter activation mechanisms modulate noise-driven HIV gene expression

Latent human immunodeficiency virus (HIV) infections occur when the virus occupies a transcriptionally silent but reversible state, presenting a major obstacle to cure. There is experimental evidence that random fluctuations in gene expression, when coupled to the strong positive feedback encoded by the HIV genetic circuit, act as a ‘molecular switch’ controlling cell fate, i.e., viral replication versus latency. Here, we implemented a stochastic computational modeling approach to explore how different promoter activation mechanisms in the presence of positive feedback would affect noise-driven activation from latency. We modeled the HIV promoter as existing in one, two, or three states that are representative of increasingly complex mechanisms of promoter repression underlying latency. We demonstrate that two-state and three-state models are associated with greater variability in noisy activation behaviors, and we find that Fano factor (defined as variance over mean) proves to be a useful noise metric to compare variability across model structures and parameter values. Finally, we show how three-state promoter models can be used to qualitatively describe complex reactivation phenotypes in response to therapeutic perturbations that we observe experimentally. Ultimately, our analysis suggests that multi-state models more accurately reflect observed heterogeneous reactivation and may be better suited to evaluate how noise affects viral clearance.