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06/10 Starting Viramune (Nevirapine) + Kivexa (Epzicom = 3TC / abacavir)

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--- Quote from: eric48 on July 20, 2013, 06:22:56 PM ---

There is not a day where I do not think of you... Here, we are working hard here to find reservoir reducing molecules that help people move to full recovery... I will publish what I am allowed to, here, but this is not always easy (for legal reasons)

We hope to establish a new biotec company soon to finance a clinical trial. It is a lot of stress, trying to find a solution to this hurdle, but, the people I am working with are very enthusiastic. It is inspiring.

--- End quote ---

Thanks Eric,...

As always, will be looking forward to your updates when available !

Take care--Ray  8)

you can't understand dynamics in continuous media if you don't understand differential equations!

Blood is a continuous media (a liquid moved by a pump) and all experimental work that has been done and have thus far concluded that HAART is a lifetime treatment (Faucy in 99, Siliciano 2003, SMART study 2006) all share the same underlying hypothesis. That the infected CD4 pool decreases logarithmically, in the same way that VL decreases. In the same fashion that radioelements have a logarithmic decay (measured by the so called half life), we speak of CD4 half lives.

The concept of logarithmic decay (or half live) relies on the predicate that the probability for a radioactive element atom to lose its 'radioactivity' in the course of time is a constant, independent from time. In otherwords a radioelement decay event is a no-memory phenomena.

If the piece of radioactive material you are studying shows persistence, then, it is because some of its elements have a long, long half life (or low probability to die, if you prefer)

This would be very true if the only means of viral persistence was through virions entry alone. Yet there are many type of viral material persistence:

A- some CD4 are new borns (in the thymus or bonemarrow) and a few stems cells (mother cells) may be infected (pretty much like vertically infected babies)
B- some viral material will be transferred by virions entry
C- some viral material will be transferred by cell-to-cell bridge (A. Segal 2012)
D- under homeostatic stabilization, or infection attack, HIV infected CD4s (as well as uninfected CD4s) clone themselves thousands or millions of times, hence refuelling the tank.

A - is memory phenomena (as long as the stems cells maintain memory)
B - is a no-memory event, governed by the number of virions
C - is a no-memory, governed by the number of infected CD4 (and the physical proximity
D - is a memory effect: a past event (proliferation) drives the persistence dynamics: our SCQD model takes this into account

as promised our model results go graphic

Blue dots are uninfected CD4s (as per our SCQD model)
Red ones are short lived CD4s that compensate the shortage in uninfected cell
(they are not important at this point and very theoretical concept need for model, hence, I called them 'virtual')

Next post, we will validate the model...graphically

Enjoy ! Eric

Our model's purpose is to find when the Infected CD4 population goes extinct. Extinction of that species is not exactly eradication. Eradication is when we are sure there is none left and meds can be interrupted. Extinction is more to find when the virus is so low that there is no way it can, by its sole actions, be of any harm. Extinction comes before eradication. As per Pr Siliciano, non-eradication is due to latency of time-isolated, spore-like, quasi-immortal infected CD4 cell. This cannot be modeled by CD4 dynamics. But the almost-zero point of extinction can.

Our models yielded only 3 data points:
at month X there are Y uninfected cells and Z (uninfected+homeostatic compensation)
3,0   145   1127
7,5   383   876
28,2   669   734

Model validation
Be be satisfying the model should be self consistent (not show obvious errors), satisfactory confronted to actual lab test results, give the extinction point and we should then find a way to prove that the extinction point is achieved. Finally, it should be predictive.

Self consistent:
Using Excel, we plot our points and add a default logarithmic trend line.
For both sets, the R2 is very close to 1.0 (0.997 and 0.93, respectively).
on the drawing below I also show a singular point labelled A.

This shows that there is a lag time before uninfected cell starts to appear. They start to appear ca. 1 month after meds initiation, which is very satisfactory and quite convincing. If the trend had hit the Y axis, that would have meant that there was a population on uninfected cells and, with my initial VL of 50K, I do not think this could be possible. If the virus free cells had started to appear quite many months after meds initiation, this would have been inconsistent with my clinical history

Most population growth, such as bacteria in a Petri dish, do exhibit a tiny lag time. So the existence of the tiny lag time is a good point.

An other point of interest is point G (as in Graal, or Goal) this is when homeostatic replication and virion based infection has ceased. It is satisfactory that this point is not way too close to meds initiation. and good to know that it exists! The system is converging.

BTW, I am convinced that in rare patients, the system is not converging; the 2 lines never cross.

More over, the uninfected cell pool is not taking an exponentially explosing shape, so that we are not ending with a million CD4/mL ;-)

confronted to actual lab test results:

Here again the picture is quite satisfactory: all data points are included within the 2 envelopes of our model: CD4 reading are never less than the modelized uninfected cells and never more than uninfected + infected (red line). Blue line cells have a 'normal' half life, whereas red line is a mix or 'normal' half live and 'shortened' half life (due to the infection)

Interestingly enough, the green line is showing a typical damped oscillation pattern.
A good example of a damped oscillation pattern bordered with 2 envelopes is shown here:

So we are quite happy for today !

Next post, we will refine the trend line, using a better fit pattern that the basic log pattern that Bill Gates offers and plot the 'true' infected cell population: the one that we want to go extinct

Stay tuned, Eric

I am preparing a series of 3 more graphic posts:

1-a- revisit log and sine trending
1-b- estimation of infected cell pool (finally...)

2-a- changing scale to log base scale (stunning graphic effect)
2-b- enter into and through point G with 3D hyperspace motion (very geeky)

3-a- validating our  model with predicting and proving what happens past point G
3-b- the aesthetic beauty of the big SCQD picture

A recommended (easy) reading can be found here (note: go all the way through the presentation until last page - 52)
which tiny is:

revisit log and sine trending
For easier understanding, I have used Excel default Log trending.
In fact, Log trending is satisfactory at first glance, but Log is an ever increasing function and after a few year you'd find yourself with thousands of 'healthy' CD4s per mL
Therefore we have to change trending to one that is asymptotic.
The following work great for both the blue and red envelopes

Uninfected (blue) = alpha x (1-exp(gamma x time)) + beta
with time expressed in months we have:
alpha = 803.91 ; beta = -113.39 ; gamma = -0.12855
same with the red upper envelope:
alpha = -781.98 ; beta = 1514.68 ; gamma = -0.22700

This additional accuracy seem ludicrous, but, will turn very useful

I kind of implied that CD4 fluctuations are a sine function. Look at the curvature: it is not! Of course, it may help understand this key point: CD4 count go up and down, but NOT erratically: there are driving forces to make it go up and driving forces to make is go down
For the sake of accuracy, let's just forget the sine model, since this is a succession of exponential and quadratic curves
(Quiz for the chemical mind, just a hint: this is a mirror pattern to a Maxwell-Boltzman equation. Have fun!)

1-b- estimation of infected cell pool
Easy: infected cell pool = CD4 count minus the Uninfected (blue envelope)
and there you go, with some minor changes(*)

(*) changes:
- replaced the SCQD data points by their all new exponential fit for clarity
- changed color of upper envelope to orange so that red is free for infected
- introduced months where VL became <50 and <20
- Unchanged : point A and G

to better understand infection maintenance through proliferation (cell cloning):

200 Infected CD4 while VL < 20 !? Possible? Yes or No ?, and explain why...

Follow this thread on twitter (New !!) :

Stay Tuned! Eric

Latest from Siliciano's (free & revolutionnary) sheds new light on PIs:
Multi-step inhibition explains PI pharmacodynamics & resistance

Then, a good reminder of anatomic compartments and their consequences:
Tissue-specific HIV-1 infection: why it matters

The Viramune Paradox unveiled earlier (higher initiation risk, very good long term results), certainly lies on meds ability to diffuse in all anatomic compartments.
Makes life easier: no need to modelize anatomic compartments.

Why these models and why share here?
- SCQD was originally designed to support a proof of concept for a new class of meds (thus, grants, funding and patenting...)
- Share because my numbers & graphs have little interference from 'noise' such as CMV, HVC, thus easier to visualize
- Graphic perspective may help those uncomfortable w/ V&K or meds
- Finally... This is FUN !

Need a refresher on nonlinear modeling?

compartments ?? see page 78. More on Compartments? see:

All models are wrong but some are useful...

And why not.. predictive... while we are at it.
Forecast dated 2013-08-15 for upcoming labs:
2013-09-15 : CD4/CD8 = 2.44 +/- 0.15
2013-11-15 : CD4/CD8 = 2.60 +/- 0.15
Most likely estimate for longer term:
CD4%: 55 CD8%: 16. Wait & see... & remain modest.

Differing from empirical models, SCQD is a mechanistic model: we suggest a mechanism, write (differential) equations, solve, then find unknowns by best fit methods to get our initial data grid. (blue and red squares)

2-a- changing X-axis (Months) to log base scale
It is cool to graph in semi-log. Easier to read... as the human eye evolved to detect edges, lines, not rectangular hyperbolas or exponentials !
Dress code in Semi-log:
- horizontal line (CD4=700) stays horizontal: ---
- a log function gives a straight line with an angle: \
- exponentials give broken lines: \_

- individual data points removed for clarity
- dashed lines are either data, model or result lines
- solid lines are their Log / Exp / Linear fits (see dress code)
- introduced point E for Extinction
Soon we will include CD8s and past point G data !

Of interest
A- CD4 lab test (green dashed) results average (green solid) is like an arrow entering the funnel-like envelopes. This is why we needed this upper envelope, as it demonstrates the funnel nature of convergence (hence extinction)
B- We easily see: CD4 lab test show an remarkably stable limit cycles, dampened in amplitude with the time to complete a cycle going longer and longer (remember, time axis is a log scale!)

Quiz: what set of differential equations give this type of limit cycle ?

Stay tuned : @HIVPharmaCure       Eric


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