eric48:
Like all good Darwinians, we look toward theory to guide us through the plethora of facts

recommended readings Chomont's group produce real good stuff. Had to read several times to realize how groundbreaking this might be... Programmed Death-1 Is a Marker for Abnormal Distribution ... http://www.ncbi.nlm.nih.gov/pubmed/23918986

The following is very obscure, BUT, in someway, it resembles the mathematical model underlying those graphs I am showing here. Just scroll down past the equations (*) and go right to the graphs p. 23-26.Don't they look pretty much like those on my posts above ?

TWO-DIMENSIONAL STABILITY ANALYSIS IN A HIV MODEL... http://arxiv.org/pdf/1211.0136v1.pdf (*): I prefer graphing: it is more fun

Let's include CD8 to our standard (linear) time scale plot

changes - Added CD8s (plain purple) - Added CD8 trending, simply the default MS Exp trending, - the trend (fit) is in dashed purple

And then we go SemiLog, so the CD8 exponential trend will dress as a \__ and we will remove the data plots, keeping just the LOG/Linear/EXP fits

changes: - beware this is SemiLog time axis - Data : dashed, fits : plain

Aren't this immuno-dynamics (straight) lines amazing ? (remember in this dress code a straight line can hide either of LOG/Linear/EXP)

about Quiz and Twitter: the quiz hints will appear on the twitter line feed. So regular followers get a bonus primer TinyUrLs are to be created with direct pointer to key 'chapter' headers in this thread (for easier navigation and reference), then to individual 'main' post later on

Quiz: Which real world object combines 3 movements : 2 wavelike sigmoids and one Exponential ?

I can assure you this is a real real COOL artifact. Easy and Fun to display at a gang bang party (oups!) Kid's Museum

Stay tuned : @HIVPharmaCure Cheers ! Eric As of 2013-09-13 : CD4: 1130 CD4%: 39 CD8: 811 CD8%: 28 pointer : http://tinyurl.com/HIVPharmaCure-12

eric48:
all well-mixed populations resemble one another, but every structured population is structured in its own way

recommended readings

Incredibly concise, incredibility rich, by very productive A.S. Perelson: MODELLING VIRAL AND IMMUNE SYSTEM DYNAMICS http://tinyurl.com/kw2wgqo

Answers lots of questions: why 3 molecules? Why CD8 are so important in controlling the dynamics? Why is modelling so important, etc.

We will use data found in this one, not free, but the supplemental table is Effect of CMV-induced immune response, ... ANRS CO3 cohort http://tinyurl.com/oowe8rn

Why we need a good understanding of Pharmacodynamics? Well... If we want a PharmaCure, or understand the Viramune Paradox, or what to expect once achieved extinction/eradication, or how we prove it, how we reduce time-to-market, etc.

Yet, we need a pause in graphing as I am short of post-G data (takes 1 year to get 6 points... and I missed 2 labs, so ...) So why don't we play with this funny CD4/CD8 ratio in the interim?

CD4/CD8 ratio is of interest because it is the only surrogate marker for reservoir depletion that you and I can easily have access to. I had 2 labs with Proviral DNA (back in 2012) and still working on these research guys to give them to me... It is also a component to multiple T-cell marker recovery (MTMR), defined as CD4+ T cells >500/mm(3) plus %CD4 T cells >29% plus CD4+/CD8+ T-cell ratio >1.

Because it is a composite parameter, it is hard to master. But let's start with this: in the uninfected population its range is 1 to 4. Not a 'normal' Gaussian distribution, but a skewed, Log-normal distribution, like: http://tinyurl.com/k7re5wf

It is 'centered' on 1.7 (and not 2.5, as you might expect) This one below provides a slightly lower range, but, here again, the mean is not at the center, the distribution is slightly skewed http://tinyurl.com/qy54ngd

Do people who have normalized their ratio, have a normal ratio ?

???

Say, one Hiver under meds has a ratio of 1.2: ratio is back to 'normal'. But, if ALL Hivers, with 'normal' ratio, have a ratio of 1.2, then this population, as a group, is not 'normal'.

Quite fortunately, it appears to be normal. In the absence of table data (infected/normalized and uninfected), we can only compare distribution mode and skewness. If they are similar, then the distribution very likely are

Data for Hivers from Chomont (source: nm.1972-S1.pdf) among 33 UD Hivers, had CD4/CD8 >1 : 38 %, among these 38%, : median ratio : 1.66, average 1.7 had a ratio > 1.5 : 61% and a ratio > 2 : 15 % (distribution is skewed)

Data for Hivers from ANRS CO3 cohort among 200 UD Hivers , had CD4/CD8 >1 : 30 %, among these 30 % , had a ratio of >1.5 : 43% (thus median slightly less than 1.5) and a ratio > 2 : 20% (distribution is skewed) (note: in this cohort % of Hivers on statins = 20% ...)

Uninfected population: Skewed distribution, range 1-4, median: 1.5 to 1.7 (depending from source, see http://tinyurl.com/qgyxd5r)

So indeed, Hivers who have normalized their ratio, have a normal ratio

Viramune paradox: 33% of viramune users achieve CD4/CD8 >1, so not superior to either cohort, so CD4/CD8 tells us nothing here.

Beware: CD4/CD8 can flicker, especially around 1. If yours does, then use cautiously. Rule of thumb: Ratio << 1 : usually stable, ratio >> 1 : varies a lot with time, but remains > 1 ; around 1 : flickers between <1 and >1

Quiz: No obvious relationship ration vs reservoir (in the >1 group, nor in the <1 group): Why ?

Next post will be FUN: non-inferiority of a random generator vs Lab test !

Stay tuned : @HIVPharmaCure Cheers ! Eric pointer : http://tinyurl.com/HIVPharmaCure-13

J.R.E.:
Hey Eric,...

Per my last PM, ... It's been since June 2012, that a CD 3, CD8 percentage has been shown in my results: ( From 6/2012)

eric48:
Thanks Ray, this will turn very usefull and gives us 2 complete readings (reconstructed data: in DEC 2011: CD8% =56%)

Cartographers of yore would have inscribed the warning “there be monsters here”. In the uncharted realms of a HIV Pharmaceutical Cure adventure : monsters be here indeed!

So let's have FUN

recommended readings WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION (Munz et al. 2009) available on one of the authors' own page at: http://tinyurl.com/2vrajmf

This original paper got a lot of attention; but, this one may be easier to read:

Mathematical Modeling of a Zombie Outbreak, by Jean Marie Linhart http://tinyurl.com/mlh34mv

Pr Siliciano's original set of equation (2003) is all about Target cells and Infected cells (within-patient infection). In population and adaptive dynamics, the targets are named Susceptibles, Infected: Infected (aka Zombies), and... Cured: Removed, Recovered or Imunized-Recovered.(aka SIR, Predator-Prey model and here SZR)

These are autonomous differential equations... Seemingly simple, they have no analytic solution, and can only be approximated numerically

When making some assumptions, it is possible to solve limit equations by calculus. This is a cornerstone to Siliciano's work and to the Latency Theory. Yet, some of the assumptions, dating 2003, may have to be revisited

In Zombies papers, you may easily go past the equations. Stories, descriptions and boxed interaction blocs (see p. 19, 26, 32) are more interesting! Enjoy!

Playing with this funny CD4/CD8 ratio with a random generator

somehow, I felt an urge to play with my ... random generator, testing robustness. The one that amused me most is to generate CD3% (CD3% be herefrom considered as CD3% = CD4% +CD8%), between its observed boundaries 65% to 75%

Then use the measured CD4% to calculate the CD4/CD8 ratio as CD4%/(CD3%-CD4%) and plot over the measured CD4/CD8 ratio.

And same the other way around using measured CD8% and random CD3%.

There you go

and

Quiz: randomized values are close to measured values. Why ?

Next post: all roads lead to Rome and CD4/CD8 to 1 !

Stay tuned : @HIVPharmaCure Cheers ! Eric pointer : http://tinyurl.com/HIVPharmaCure-14