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Fluctuations in Tat copy number when it counts the most: a possible mechanism to battle the HIV latency.

Konkoli Z, Jesorka A - Theor Biol Med Model (2013)

Bottom Line: For both noise-free and noise-based strategies we show how operating point off-sets induce changes in the number of Tat molecules.The major result of the analysis is that for every noise-free strategy there is a noise-based strategy that requires lower dosage, but achieves the same anti-latency effect.It appears that the noise-based activation is advantageous for every operating point.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, Gothenburg, Sweden. zorank@chalmers.se

ABSTRACT
The HIV-1 virus can enter a dormant state and become inactive, which reduces accessibility by antiviral drugs. We approach this latency problem from an unconventional point of view, with the focus on understanding how intrinsic chemical noise (copy number fluctuations of the Tat protein) can be used to assist the activation process of the latent virus. Several phase diagrams have been constructed in order to visualize in which regions of the parameter space noise can drive the activation process. Essential to the study is the use of a hyperbolic coordinate system, which greatly facilitates quantification of how the various reaction rate combinations shape the noise behavior of the Tat protein feedback system. We have designed a mathematical manual of how to approach the problem of activation quantitatively, and introduce the notion of an "operating point" of the virus. For both noise-free and noise-based strategies we show how operating point off-sets induce changes in the number of Tat molecules. The major result of the analysis is that for every noise-free strategy there is a noise-based strategy that requires lower dosage, but achieves the same anti-latency effect. It appears that the noise-based activation is advantageous for every operating point.

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Related in: MedlinePlus

The meaning of the noise-free and the noise-based activations. The figure illustrates the meaning behind the noise-free and noise-based activations. All graphs were drawn by hand. Γi(Φ) with i=0,1,2 are distribution functions for the observable Φ for three systems in three operating points: the latent cell i=0, the cell that has been activated using the noise-based therapy (i=1), and the cell that has been activated using noise-free therapy (i=2).  and Σi are the means and the standard deviations. The noise free therapy (NFT) shifts the operating point of the virus from the stable (latent) operating point OP0 to the operating point OP2. This almost certainly activates the virus since . The noise-based therapy (NBT) induces the shift from the OP0 to the operating point OP1 where the activation is less certain but still possible since the tail of the Γ1 enters into the activation region and . Variable κ is a numerical factor close to 1.
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Figure 1: The meaning of the noise-free and the noise-based activations. The figure illustrates the meaning behind the noise-free and noise-based activations. All graphs were drawn by hand. Γi(Φ) with i=0,1,2 are distribution functions for the observable Φ for three systems in three operating points: the latent cell i=0, the cell that has been activated using the noise-based therapy (i=1), and the cell that has been activated using noise-free therapy (i=2). and Σi are the means and the standard deviations. The noise free therapy (NFT) shifts the operating point of the virus from the stable (latent) operating point OP0 to the operating point OP2. This almost certainly activates the virus since . The noise-based therapy (NBT) induces the shift from the OP0 to the operating point OP1 where the activation is less certain but still possible since the tail of the Γ1 enters into the activation region and . Variable κ is a numerical factor close to 1.

Mentions: Since trajectories are stochastic, the variable Φ is also stochastic and can be described by some probability distribution function Γ(Φ). Assume that two types of treatments have been designed which adjust the operating point of the stable latent virus (OP0) so that the respective distributions for Φ are obtained as depicted in Figure 1 (OP1, OP2). The two distinct scenarios will be referred to as the “noise-free” (NFA) and the “noise-driven (based)” (NBA) activations. The distributions are characterized by their respective means (, ) and standard deviations (Σ1, Σ2). The NFA activates with absolute certainty since . The NBA is less successful, since there are many instances where but due to frequent fluctuations the threshold is reached often and . Thus in strict mathematical terms, a noise-free treatment ignores fluctuations and aims to establish an operating point such that . A noise-based treatment does not achieve the equality but there are frequent fluctuations that do, and


Fluctuations in Tat copy number when it counts the most: a possible mechanism to battle the HIV latency.

Konkoli Z, Jesorka A - Theor Biol Med Model (2013)

The meaning of the noise-free and the noise-based activations. The figure illustrates the meaning behind the noise-free and noise-based activations. All graphs were drawn by hand. Γi(Φ) with i=0,1,2 are distribution functions for the observable Φ for three systems in three operating points: the latent cell i=0, the cell that has been activated using the noise-based therapy (i=1), and the cell that has been activated using noise-free therapy (i=2).  and Σi are the means and the standard deviations. The noise free therapy (NFT) shifts the operating point of the virus from the stable (latent) operating point OP0 to the operating point OP2. This almost certainly activates the virus since . The noise-based therapy (NBT) induces the shift from the OP0 to the operating point OP1 where the activation is less certain but still possible since the tail of the Γ1 enters into the activation region and . Variable κ is a numerical factor close to 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3686706&req=5

Figure 1: The meaning of the noise-free and the noise-based activations. The figure illustrates the meaning behind the noise-free and noise-based activations. All graphs were drawn by hand. Γi(Φ) with i=0,1,2 are distribution functions for the observable Φ for three systems in three operating points: the latent cell i=0, the cell that has been activated using the noise-based therapy (i=1), and the cell that has been activated using noise-free therapy (i=2). and Σi are the means and the standard deviations. The noise free therapy (NFT) shifts the operating point of the virus from the stable (latent) operating point OP0 to the operating point OP2. This almost certainly activates the virus since . The noise-based therapy (NBT) induces the shift from the OP0 to the operating point OP1 where the activation is less certain but still possible since the tail of the Γ1 enters into the activation region and . Variable κ is a numerical factor close to 1.
Mentions: Since trajectories are stochastic, the variable Φ is also stochastic and can be described by some probability distribution function Γ(Φ). Assume that two types of treatments have been designed which adjust the operating point of the stable latent virus (OP0) so that the respective distributions for Φ are obtained as depicted in Figure 1 (OP1, OP2). The two distinct scenarios will be referred to as the “noise-free” (NFA) and the “noise-driven (based)” (NBA) activations. The distributions are characterized by their respective means (, ) and standard deviations (Σ1, Σ2). The NFA activates with absolute certainty since . The NBA is less successful, since there are many instances where but due to frequent fluctuations the threshold is reached often and . Thus in strict mathematical terms, a noise-free treatment ignores fluctuations and aims to establish an operating point such that . A noise-based treatment does not achieve the equality but there are frequent fluctuations that do, and

Bottom Line: For both noise-free and noise-based strategies we show how operating point off-sets induce changes in the number of Tat molecules.The major result of the analysis is that for every noise-free strategy there is a noise-based strategy that requires lower dosage, but achieves the same anti-latency effect.It appears that the noise-based activation is advantageous for every operating point.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Microtechnology and Nanoscience-MC2, Chalmers University of Technology, Gothenburg, Sweden. zorank@chalmers.se

ABSTRACT
The HIV-1 virus can enter a dormant state and become inactive, which reduces accessibility by antiviral drugs. We approach this latency problem from an unconventional point of view, with the focus on understanding how intrinsic chemical noise (copy number fluctuations of the Tat protein) can be used to assist the activation process of the latent virus. Several phase diagrams have been constructed in order to visualize in which regions of the parameter space noise can drive the activation process. Essential to the study is the use of a hyperbolic coordinate system, which greatly facilitates quantification of how the various reaction rate combinations shape the noise behavior of the Tat protein feedback system. We have designed a mathematical manual of how to approach the problem of activation quantitatively, and introduce the notion of an "operating point" of the virus. For both noise-free and noise-based strategies we show how operating point off-sets induce changes in the number of Tat molecules. The major result of the analysis is that for every noise-free strategy there is a noise-based strategy that requires lower dosage, but achieves the same anti-latency effect. It appears that the noise-based activation is advantageous for every operating point.

Show MeSH
Related in: MedlinePlus