Durston: Functional Information

[swamidass (S. Joshua Swamidass)]

@Kirk

Before I explain/defend how I estimate the functional information required to code for a protein family, I want to ensure we are all on the same page regarding the basic principles of functional information.

Good plan. Looking these, over I do not think I will be able to sign off.

@Kirk

1. In general, Shannon information is the difference in Shannon entropy between two states. Shannon entropy is defined in Claude Shannon’s 1948 paper.

This needs to be more precise. Do you mean the conditional entropy? Or mutual information? Or conditional mutual information? Perhaps write the equations, and refer to the specific equations in shannon’s paper. http://math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf

@Kirk

The equation for functional information presented by Hazen et al. is merely a special case of Shannon information when the co-variable of function is included. It represents the difference in Shannon entropy between a non-functional ground state and a functional state.

That might true if you have defined shannon information correct. You seem to be using an idiosyncratic/non-technical definition of shannon information, so we can’t be sure.

@Kirk

You will note that Hazen’s equation looks quite a bit simpler than the normal equation for Shannon information (i.e., no summation signs, and no variable probabilities). This is because Hazen’s equation assumes that all sequences are equally probable. When that is done, then the normal equation for Shannon information simplifies to the form Hazen presents.

I agree. Also his equation assumes we have perfect knowledge of all functional and non-functional sequences.

@Kirk

In reality, not all sequences are equally probable. For example, when we estimate the functional information required to code for protein families, the genetic code ensures that not all amino acids are equally probable, hence, not all sequences are equally probable. Even ignoring that, not all sequences are equally probable across all taxa due to environmental and phenotypic constraints on functionality, etc. Nevertheless, it simplifies things to grant Hazen’s assumption and I’m happy to work with it so far as we can.

I am not happy to work with it as this one major way your method fails. You even recognize this in following points. So no, I do not accept that this is an acceptable simplification.

@Kirk

There is a difference between the functional information required to perform a function, and creating that information.

Not clear. There is no way to assess this as true or false.

@Kirk

Duplicating an existing sequence that carries functional information does not increase the amount of functional information created unless the two identical sequences in combination can perform a new function that a single sequence could not. Even then, the amount of information required to produce the duplicate sequence will not be 2X the amount to produce a single sequence, since the new ground state for producing the duplicate sequence already includes the original sequence. If the ground state includes the original sequence as well as a mechanism for duplicating a sequence, then the amount of functional information required to produce the duplicate sequence may be trivial or even zero.

I dispute this on several levels.

1. Duplicating a sequence can add the function of redundancy and error control, that is a new function.
2. This directly contradicts point #4, demonstrating that sequences are not equiprobable.
3. The method you use cannot correct for this effect.
4. FI here is not well defined, to the point of creating errors in analysis.

This last point is important. We can understand FI in several ways:

A. The bits of information required to modify a system without a function to produce a new function.
B. The number of bits in a system that preforms a system in total.
C. The amount of “function” we see (measured some how).
mA: The measured version of A by some specific method.
mB: The measured version of B by some specific method.

Several unjustified claims are often made by lumping these five concepts together. All are false.

1. High B does not mean A is high.
2. Low A does not mean C is high, because a small amount of A can produce a large amount of C.
3. mA and mB are not necessarily good estimates of A and B, and can be wildly off if the process that generates sequences is not modeled.

I could go on, but the key point is that FI has to be carefully qualified everytime the term is used. That is not done here. So I cannot agree with most of what you have written until it is clarified.

@Kirk

The problem with using Hazen’s equation to estimate the functional information required to code for a particular protein family is that it is a single equation with two unknowns. We haven’t the faintest idea what M(Ex) is, therefore, we cannot solve for I(Ex).

I disagree with this. We have very good estimates of M(Ex) for many functions. Regardless, this is all beside the point, because this tells nothing about how difficult it is to evolve a new function. The type of FI we need to compute is the conditional information from the sequences we already have to get to any sequence that works for any function, even if we have never seen that sequence before or never expected that function. @Kirk’s method does not compute this quantity.

I, however, did compute FI in cancer, as the mutual conditional information: Computing the Functional Information in Cancer. This is an important negative control going forward. Any method proposed needs to be able to show that cancer is possible without design. That does not appear possible without demonstrating Durston’s argument wrong.