Paul Offit's 10,000 Vaccine Comment

Discussion in 'Vaccines' started by Travis, Sep 13, 2017 at 5:43 AM.

  1. Travis

    Travis Member

    Jul 14, 2016
    In 2002, the journal Pediatrics published this article by Paul Offit:

    Offit, Paul A., et al. "Addressing parents’ concerns: do multiple vaccines overwhelm or weaken the infant’s immune system?." Pediatrics 109.1 (2002): 124-129.

    (He has vaccine patents
    Rotavirus reassortant vaccine
    Aqueous solvent encapsulation method, apparatus and microcapsules
    And more

    In which he originally wrote his famous, and often paraphrased, quote"...each infant would have the theoretical capacity to respond to about 10 000 vaccines at any one time."
    There is something funny about this. A cursory glance leads you to realize that "dividing 10⁷ B cells per mL by 10³ epitopes per vaccine" leaves you with the quite unusual units of B-cells·vaccine/epitopes·mL. Further examination reveals his error:

    Below is his six claims, which I turn into mathematical symbols. I use the standard footnote symbols just for reference (†‡§¶):

    Offit's Claims
    1) approximately 10 ng/mL of antibody is likely to be an effective concentration of antibody per epitope
    ¹¶ effective concentration = (10ngA/mL)​
    2) generation of 10 ng/mL requires approximately 10³ B-cells per mL
    ²¶ (10ngA/mL) = (10³·ᵦCₑ/mL)
    You need to make this distinction between general B-cells (ᵦC) and progeny B-cells (Cₑ), which are daughter cells of the B-cell clone. Offit doesn't do this, but it is necessary. The reason for this will be proved shortly. He is obviously talking about progeny cells here because to get an effective concentration of antigens, you need cells derived from a vaccine-stimulated cell (progeny cells).​
    3) a single B-cell clone takes about 1 week to reach the 10³ progeny B-cells required to secrete 10 ng/mL
    of antibody (therefore, vaccine-epitope-specific immune responses found about 1 week after immunization can be generated initially from a single B-cell clone per mL
    ³¶ (ᵦC₀/mL) = (10³·ᵦCₑ/mL) || (ᵦC₀/10³·ᵦCₑ) = 1
    You must make the distinction between to B-cell clone and the B-cell progeny because, if you don't, this happens (following first sentence is Offit's claim #3): B-cell = 10³ B-cell || This is a massive fail. Rearranged, this becomes B-cell/B-cell = 10³, or 1 = 1,000. By definition, one does not equal one thousand. Therefore, these cannot be made equivalent. A progeny B-cell is abbreviated as ᵦCₑ and the initial vaccine-infected clone cell is abbreviated as ᵦC₀. Subscript zero is commonly used to denote an initial condition, and the letter "e" was chosen because there weren't many better unicode subscripts to choose from. (And I was kinda thinking about the natural logarithm base "e" (Euler's number) since cellular reproduction often follows exponential growth.)​
    4) each vaccine contains approximately 100 antigens and 10 epitopes per antigen (ie, 10³ epitopes)
    ⁴¶ vaccine = 10³·epitope || (vaccine/10³·epitope) = 1​
    5) approximately 10⁷ B cells are present per mL of circulating blood
    ⁵¶ mL·blood = 10⁷·ᵦC || (10⁷·ᵦC/mL) = 1
    This B-cell type, abbreviated as ᵦC, has no subscript yet. Later it will be made equivalent with sum of unique B-cell progeny cells after one week.​
    [6] ...then each infant would have the theoretical capacity to respond to about 10,000 vaccines at any one time (obtained by dividing 10⁷ B cells per mL by 10³ epitopes per vaccine).

    ⁶¶ epitope = ᵦC₀ || (epitope/ᵦC₀) = 1
    There is an implicit assumption that is never stated, but needs to be defined. The entire assumption is that one epitope interacts with one initial B-cell. This is how immunity is created. The B-cell creates specific antibodies to one epitope, one specific part of the antigen. This makes the production of monoclonal antibodies possible. One B-cell: One epitope: One specific antibody.
    The figure 10⁷·ᵦC/mL is mentioned in Offit claim #6 and he uses it in his final calculation to derive the "10⁴ vaccine figure." This is the concentration of B-cells in the bloodstream. The implications is that it cannot be exceeded and must be held constant. This makes sense, as if you could increase the B-cell cell level to infinity, you could theoretically-respond to an infinite amount of vaccines. This would be ridiculous. This is the ceiling, and the concentration of 10⁷·ᵦC/mL cannot be exceeded. This is what me and Paul Offit could agree on.

    § limit = (10⁷·ᵦC/mL)
    § limit = (10⁷·Σ(ᵦCₑ)/mL) || [⁸¶, by substitution; see below]
    § limit = (10⁷·Σ(ᵦCₑ)/mL) × (ᵦC₀/10³·ᵦCₑ)* × (epitope/ᵦC₀)† × (vaccine/10³·epitope)‡ = 10·vaccine(s) || [³¶*, ⁶¶†, ⁴¶‡]

    All units cancel but "vaccine." After one week, the sum of the progeny B-cells (Σ(ᵦCₑ)) become confluent and co-mingle with the steady-state circulating B-cells. And since this calculation is determining the theoretical maximum, the sum of the progeny B-cell's concentration must equal the B-cell concentration of 10⁷·ᵦC/mL. This is the maximum.

    The steady-state B-cell concentration cannot be exceeded or else you would be able to theoretically "respond to" an infinite amount of vaccines.
    So where does Paul Offit get 10,000 vaccines? Let's re-examine Offit claims #5 and #6:
    "5) approximately 10⁷ B cells are present per mL of circulating blood"
    "[6] then each infant would have the theoretical capacity to respond to about 10,000 vaccines at any one time (obtained by dividing 10⁷ B cells per mL by 10³ epitopes per vaccine)."
    What do we get when we actually do this?
    "10⁷ B cells per mL" ÷ "10³ epitopes per vaccine"
    10⁷·Bcell/mL ÷ 10³·epitope/vaccine
    10⁷·Bcell/mL × 10³·vaccine/epitope
    Division is equivalent to multiplying the dividend's inverse.​
    10⁴·(Bcell/mL) × (vaccine/epitope)
    10⁴·vaccine × (Bcell/mL·epitope)

    Redistributing the units, we immediately find that Bcell/mL·epitope must equal one for Offit's statement to be true. Rearranged, it becomes:
    (Bcell/mL·epitope) || epitope = (Bcell/mL)​
    Does this make sense? Well, Offit claim #3 states: "therefore, vaccine-epitope-specific immune responses found about 1 week after immunization can be generated initially from a single B-cell clone per mL." Almost. One epitope equals one incipient B-cell clone per milliliter. So we have:
    ⁷¶ epitope = (ᵦC₀/mL) || ((ᵦC₀/mL·epitope) = 1
    So it only makes sense if you assume that Paul Offit is talking about incipient B-cells clones. But remember, after one week a clone becomes 10³ progeny B-cells (³¶). The entire premise of Offit's argument is that immunity created from having a critical concentration of progeny B-cells after one week (#13). And after one week, the progeny cells greatly outnumber the initial vaccine-infected clone cells 10³ to 1. This is why he is off by a factor of 1,000. The true answer is ten (§, see above).

    Here is the Offit division again, corrected:
    10⁴·vaccine × (Bcell/mL·epitope)
    10⁴·vaccine × (ᵦC/mL·epitope)
    The "Bcell" in this equation refers to steady-state B-cells (ᵦC). This only equals one with initial vaccine-infected B-cells (ᵦC₀). The relation progeny B-cells (ᵦCₑ) and vaccine-infected B-cells (ᵦC₀) is given by ³¶.​
    10⁴·vaccine × (ᵦC/mL·epitope·) × (ᵦC₀/10³·ᵦCₑ)* || [³¶*]
    10⁴·vaccine × (Σ(ᵦCₑ)/mL·epitope) × (ᵦC₀/10³·ᵦCₑ)* || [⁸¶*]
    And after one week the steady-state generic B-cells equal the sum of progeny cells.​
    10⁴·vaccine × (1/mL·epitope) × (ᵦC₀/10³)
    10⁴·vaccine × (ᵦC₀/mL·epitope) × (1/10³)
    (10⁴·vaccine/10³) × (ᵦC₀/mL·epitope)
    10·vaccine × (ᵦC₀/mL·epitope)
    10·vaccine × 1 || [⁷¶]

    Is the true answer. He conflates the three types of B-cells he introduces and makes them all equivalent. As I've shown, this leads to ridiculous conclusions. You cannot do this. These three types of cells are only equivalent only at certain times:

    At time of injection:
    ⁷¶ ᵦC ⇒ ᵦC₀
    At the time of vaccination, all circulating B-cells have the potential to become initial vaccine-stimulated clone cells. Not all B-cells becomes antibody-producing cells.​
    One week later:
    ⁸¶ ᵦC = Σ(ᵦCₑ)
    This holds for these Offit-type calculations on this page. The maximum theoretical amount of vaccines "responded to" is achieved when all circulating B-cells are antibody-producing progeny cells—or the sum of all monoclonal lines expressing unique antibodies to one individual epitope. This creates the most antigens and delivers the maximum amount of immunity. The concentrations of the progeny cells rise to their maximum after a certain amount of time and then decay as immunity wanes. Offit chose the time period of one week.​

    You cannot ignore the temporal aspect of the B-cells or you can make 1 = 10³ (see above), or 10 = 10⁴ (see above).

    By following Offit's theoretical line-of-thought and not making ridiculous assumptions with the units, or time-traveling B-cells, leads to a much more realistic value of only ten vaccines.
  2. ecstatichamster

    ecstatichamster Member

    Nov 21, 2015
    Hat tip to you Travis.
  3. lisaferraro

    lisaferraro Member

    May 31, 2015
    Dallas, TX
    Totally hat tip to Travis. Great read. Educational.
  4. OP

    Travis Member

    Jul 14, 2016

    Obviously, ten-thousand vaccines exceed the volumetric capacity of the infant—so it's wrong right there. But these pro-vaccine people online always then say something like, "Well, that's not the point. You could increase the concentration of the vaccine."

    But even his calculation turns-out to be wrong! You could almost say that the "math" seems right, but it's wrong. And the logic is wrong. All units must cancel, and his don't! When units cancel, they become one:

    (cell/mL) × (mL/cell) = (mL/mL) × (cell/cell) = 1 × 1

    ..................[↑example↑]......................................... [↑redistribution↑]..........................[↑all units cancel]

    I think he could have been intentionally deceptive. Paul Offit is vaccine millionaire. The logic behind his passage seemed painfully-constructed in a way to make it confusing and seem true after a slight investigation. Further investigation reveals that he's trying to pull a fast one, or just unintentionally wrong.
  5. Regina

    Regina Member

    Aug 17, 2016
    sounds like a psychopath
  6. michael94

    michael94 Member

    Oct 11, 2015