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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

Contour plots of σ / μ  in three hyperplanes: (a) for ( v =vR, u , ϵ ), (b) for ( v , u =uR, ϵ ), and (c) for ( v , u , ϵ =ϵR). The position of the resistor model operating point is marked by the white circle. Contour lines are labelled by their respective σ/μ values (square boxes). Lighter (darker) regions indicate where noise does (does not) dominate the dynamics.
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Figure 3: Contour plots of σ / μ in three hyperplanes: (a) for ( v =vR, u , ϵ ), (b) for ( v , u =uR, ϵ ), and (c) for ( v , u , ϵ =ϵR). The position of the resistor model operating point is marked by the white circle. Contour lines are labelled by their respective σ/μ values (square boxes). Lighter (darker) regions indicate where noise does (does not) dominate the dynamics.

Mentions: Perhaps the biggest advantage with the hyperbolic coordinate system suggested is that the v dependence is very easy to visualize. Figures 3a, 3b, and 3c depict how the coefficient of variation η=σ/μ depends on the reaction rate parameters. Figures 3a and 3b demonstrate that when ϵ approaches the border of stability (ϵ→0) the coefficient of variation approaches infinity. Figures 3b and 3c show that if v is increased, the coefficient of variation always increases, no matter which values for u and ϵ are chosen. Figures 3a and 3c indicate that if noise is to be exploited for a treatment, one should design drugs that could move the operating point of the virus away from the regions around u≈0. These plots show in which regions of the parameter space the effects of noise are expected to dominate. Superficial analysis of these figures would suggest that one should choose rates β and δ as different as possible from each other, since this should increase the amount of noise relative to the mean. However, in doing so one might move the operating point such that despite the increase in fluctuations the threshold cannot be reached. A more quantitative analysis is needed in order to identify useful noise-based strategies. This is illustrated by a case study, where we suggest how the mathematical manual developed above can be used to guide experimental design.


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)

Contour plots of σ / μ  in three hyperplanes: (a) for ( v =vR, u , ϵ ), (b) for ( v , u =uR, ϵ ), and (c) for ( v , u , ϵ =ϵR). The position of the resistor model operating point is marked by the white circle. Contour lines are labelled by their respective σ/μ values (square boxes). Lighter (darker) regions indicate where noise does (does not) dominate the dynamics.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 3: Contour plots of σ / μ in three hyperplanes: (a) for ( v =vR, u , ϵ ), (b) for ( v , u =uR, ϵ ), and (c) for ( v , u , ϵ =ϵR). The position of the resistor model operating point is marked by the white circle. Contour lines are labelled by their respective σ/μ values (square boxes). Lighter (darker) regions indicate where noise does (does not) dominate the dynamics.
Mentions: Perhaps the biggest advantage with the hyperbolic coordinate system suggested is that the v dependence is very easy to visualize. Figures 3a, 3b, and 3c depict how the coefficient of variation η=σ/μ depends on the reaction rate parameters. Figures 3a and 3b demonstrate that when ϵ approaches the border of stability (ϵ→0) the coefficient of variation approaches infinity. Figures 3b and 3c show that if v is increased, the coefficient of variation always increases, no matter which values for u and ϵ are chosen. Figures 3a and 3c indicate that if noise is to be exploited for a treatment, one should design drugs that could move the operating point of the virus away from the regions around u≈0. These plots show in which regions of the parameter space the effects of noise are expected to dominate. Superficial analysis of these figures would suggest that one should choose rates β and δ as different as possible from each other, since this should increase the amount of noise relative to the mean. However, in doing so one might move the operating point such that despite the increase in fluctuations the threshold cannot be reached. A more quantitative analysis is needed in order to identify useful noise-based strategies. This is illustrated by a case study, where we suggest how the mathematical manual developed above can be used to guide experimental design.

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