( Hi Pedro, ----sorry for not contributing to the discussion. There was a
slot in
December when I did try to respond to a bunch of remarks that were made in
phrasing the question which I never got around to completing. For your
interest I am sending this fragment to you. Hope you are well. ---Sri )
Many thanks, Sri, it is a splendid text and I am reintroducing it into the
list. greetings. ---Pedro
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Introductory Remarks: 12 Questions about relations between molecular
bionetworks and information theory
(by Jerry L.R. Chandler)
1. From an informational perspective what would constitute a definitive
theory of the information content of molecular bionetworks?
"Historically, in the 1840s, Kirchoff's theory of flow in electrical
networks grounds the metaphor of the conceptual framework for
molecular bionetworks. However, the relatively simplicity of the flow
of electrons in comparison to the flow of life restricts the analogy
severely. Nevertheless, biomolecules are composed from electrical
particles and certain electron flow patterns are intrinsic to
metabolic networks in living systems."
The "relative simplicity" of electron flow is at some level a
primitive whose kernel needs to be split open. In some ways, this
already taps into one of the qualifying statements one needs to put in
place when talking about information in biological, specially
biomolecular systems. That crucial ingredient is one of coupling of
systems and the internal vs external descriptions of processes. I'll
come back to this later -- hold that thought.
The mere transport of matter is not always the key to determining
"flows" and thus, one could say that there is a non-trivial sense in
which the relationship between current (as flow of electrons) is
related to information flow (as flow of something else). Individual
electrons are not physically transported across macroscopic distances
in order to give rise to macroscopic currents. In biomolecular
networks, and in particular, signalling networks, the transfer of a
signal is not accompanied by the flow of matter. Heat flow is another
more mundane example. Jerry articulates the rhetorical bridge between
questions 2 and 3 as follows:
"2. From the perspective of information, how is it possible that
bionetworks construct the informed flows of electrical current flow and
how is it related metabolic flows?
Historically, the investigation of empirical basis of molecular
bionetworks (metabolism) started shortly after Pasteur's pioneering
experiments on the causes of fermentation (1870s). At that time, the
fermentation of grape juice was difficult to control but of great
economic importance. (Bad wine sells cheaply!) Quantitative analysis
of yeast fermentations showed that each molecule of glucose generated
two molecules of the 2-carbon alcohol and two molecules of carbon
dioxide. The yeast cell informed the specific destruction of the
sugar. (If the 6-carbon sugar was merely burned, then it produced
exactly six molecules of carbon dioxide.) Thus, the thermodynamic
question of why the yeast cell did not completely burn up the 6-
carbon sugar entirely into carbon dioxide arose.
3. From an informational perspective, what does this incomplete
fermentation process of glucose suggest about the role of
thermodynamics in living processes?"
Jerry' s third question focuses in on the issue of controlled
burning of sugar (glycolysis), which throws up the connection with
efficiency of heat engines studied in 19th century thermodynamics.
The flows of caloric had to be understood in order to harness the
energies of the Industrial Revolution. Contemporary interpretation of
caloric underscores the fact that heat is not a quantity; it reflects
a transfer that summarises the changes in internal degrees of freedom
of bodies in contact. In the context of this discussion group, these
degrees of freedom are quantitatively summarised by the notion of
entropy. Once again, the conceptual machinery that is brought into
play to advance our understanding is in the establishment of new
theoretical summaries of phenomenologically useful constructs which
then go on to have a life of their own, some legitimate, others
perhaps more profligate and less discerning.
Particularly in the confines of micron-length cells, the diffusional
processes that constitute the microscopic determinants of caloric
flows can and do play roles that, despite the uniformity of the underlying
physical laws, gives rise to properties take on biological
significance. In the low Reynolds number environs of the cell, where
dissipative forces swamp intertial motion, motion by diffusion can be
surprisingly quick. Even when there is a close coupling between the
burning of chemical energy supplies (such as ATP) to fuel movement (as
in the case of kinesin trucking along microtubular highways of the
cell's transportation system, diffusive contributions are part of the
chemical cycle that drives this locomotion. I'll come back to this
later, but let me float this subliminal link between motion, chemical
cycles, diffusion (as random motion) as we return to Jerry's
articulation of the program that determines controlled conversion of
substrate to product:
"The code of the cell for fermentation was that each chemical reaction
was catalysed by an informed agents, termed zwishenferments. These
agents are now known as enzymes. Thus, the question of how a cell
knows how to ferment sugar was regressed to a deeper informational
question: How does an enzyme know how to inform a chemical change?"
Recasting this back in terms of the engines of the 19th and the
chemical engineering works of the early 20th century, this might be
the time to relate this question to Pedro' s segue into the basics of
the problem of molecular information:
"If I could bring order into these studies, the starting point, or say
one of the basic pillars of the "information bridge" upon the
biomolecular turbulent waters, in my opinion, should be built around
the characterization of molecular recognition events, downwards and
upwards."
Enzymatic modulation of reaction rates of biomolecular reactions have
often been characterised as requiring molecular recognition events
metaphors such as lock and key, induced fit, etc. have been used
as short cuts to think through the effective behaviour of quantum
mechanical events averaged in some sense at the length and time
scales relevant to macromolecular biochemistry. If substrate and
product can be interpreted as input and output of a program, surely
the enzyme appears as the quintessential elementary biomolecular
program, executing its embodied logic. However, again I hover with
my earlier hint of the need to consider biomolecular systems from an
internal or external viewpoint.
Once a particular subsystem has been isolated for inspection,
experimentation and analysis, the rest of the system, indeed the
*organism*, is viewed as external to it. This list needs no reminder
that holism demands surgical sequestration for discursive convenience
should not eliminate the need for creative reconstruction of the
whole. Thus, mere biochemical currents, be they transfers of ionic
components, relative concentrations of (say, covalently) modified and
unmodified proteins, and so on, derive "meaning" only in the context
of downstream processes the subsystems are coupled to. And in a
broad-brush sweep, this meaning is typically subservient (at the
biomolecular level) to the necessity of the organism to stay alive and
well. While this does seem rather crude and reductionist, I have
inserted the qualifying locator -- at the biomolecular level. I do
not intend to characterise the downstream effects of calcium influx
into a neuron of someone reading this message on the FIS list as one
of a mere battle for survival, although some would associate that in
the evolutionary scheme of things to such possibilities. Yes, and
are these the downwards and upwards functional units that Pedro refers
to? I believe they are exactly in the spirit of Jerry's remark that
"Biomolecular networks consist of all the molecules in a cell. One
crucial feature of such networks is the capacity to generate biological
functions."
So I will be rather bold here to suggest a broad answer to Jerry's
fourth question:
"4. From an informational perspective, what is the nature of the code
that an enzyme contains such that it conducts an informed catalytic
process? "
Since information is a short-cut we propose from the externalist
perspective to the causal links between subsystems, we need to
identify the physical features of an enzyme in its biological context,
as part of the network. Thus we need to characterise the network
properties -- numbers of each species, the conformational states,
their free energy or chemical potential representations, etc., note
their dynamics in the presence of noise. Each of these is a potential
"signal," each of these could be imbibed with "meaning" by the
organism. Since fluctuations are the norm within a cell, each of
these physical quantities, each with potentially "meaning"-laden
attributes can be characterised by probability distributions, from
which the more familiar entropic definitions can be proffered. Some
of these will only be useful once the temporal windows over which key
biological events are meaningful have been identified. One can begin
to articulate a general outline, but there needs to be an accumulated
body of systems where such a program has had some empirical clout,
else this would "not even be false" to paraphrase Wolfgang Pauli.
I will ignore the rest of Jerry's questions which have to do with DNA
as there has been lots written about the genetic code and its
information content, etc. I don't think there is a lot to be learnt
from general considerations of that sort, despite their popularity and
books such as The Selfish Gene. However, there is one aspect that he
mentions -- that of the temporal dimension to biological processes
that I will come back to in order to revisit Pedro's question about
the centrality of molecular recognition events. Time plays an
important role in that.
Let me point out a formal computational framework within which this
could be brought together as a programme of thought, perhaps in the
sense of Lakatos. For inspiration I need to acknowledge Gordana's
post, but more importantly the simple framing that Kevin Kirby
provided in his forst posting:
"One way to further this approach is to turn to biological systems, and
take a look at the simulation relation. How do we say a biological system
computes X? Well, we see if there is a dynamics-preserving mapping
between inputs and states of the biological system and a given formal
system for X. This relation is usually written as a commutative diagram.
The simulation relation is central in automata theory and was recast into
a category-theoretic framework by Arbib and Goguen (taking different
approaches). But the notion of a mapping between a biological system
and a formal system, seems to be, at first glance, a category mistake!
As soon as one identifies a fragment of nature as a system, one has
locked in some set of states, and it is hard to separate the true
computational power of a living system from what accrues merely to our
conventional state assignment. This is taken up nicely by the philosopher
David Chalmers in a response to a very strong statement at the
conventionality end by Hilary Putnam. (One could see this as a recasting
of the debate in Plato's Cratylus in computational terms!)
This tension between the formal and the material seems to lie at the
heart of the field of natural computing. The work of Michael Conrad
emphasized the special role of biological material to explain the
fantastic outcomes of evolution, as opposed to any power inhering in the
class of relatively simple Darwinian algorithms. In the
mutation-absorption model of the enzyme, we can begin to see how
computational power emerges from the breakdown in the simulation
relation, by the failure of commutativity (and, in the mathematical
sense, the creation of torsion). This seems to be the vexing locus of
this new field: clarifying precisely what happens when formal systems
fail to track changes in fragments of nature."
Even before I can articulate what I wanted to say, I have this nagging
feeling that I am about to get mired in questions on the Axiom of
Choice here, but since my grasp of such matters is minimal, let me
carry on anyway. If indeed one can lay out the physical foundations
of meaning making -- the its of the biological network and their
attendant physical (mathematical) properties as I have pointed to, and
one lays out the functional attributes of biological systems, we might
have just the sort of setting that Kevin talks about. However, given
the different time scales for describing the relevant events, the
different steady states and transients defined with respect to some
biologically determined processes, it would be necessary to have at
hand mutiple mappings and formalisations of this sort. And here we
might need to extend the sorts of mappings Barwise (and Seligman)
define and exemplify in their monograph. The infomorphisms between
different type systems would have to be generalised to these
formal-physical mappings carved up from our externalist perspective,
but which would provide the appropriate glue to not preclude the
internalist view as well.
(For those not familiar with Barwise and Seligman, here's how I
remember what they do. They construct analogs of a continuous
function in basic calculus. In fact, their construction has a
category-theoretic construction via Chu spaces, for which the
high-school definition of a continuous function emerges as its
realisation in the category of topological metric spaces. The
inclusion relationship between points in the range of a function and
its preimage to the the sets in the domain and range has to be
specified to define a continuous function. Roughly, the direction of
arrows in a mapping (X to Y) and the relations of inclusions of open
sets in the domain and range which contain the paired points of
interest are in opposite directions. Similarly, instances or events
are all given a type in a classification scheme (rather like elements
and the sets they are contained in) so that events of a certain type
are meant to carry information about events of a different type is a
statement about the relationship between two classification
systems. This map also has the same bi-directional nature as one would
expect of sets in the domain and range of functions that have the
property of being continuous. Such a map is called an infomorphism.)
These different classification schemes could be used to characterise
the physical features and their biological, interpretive counterparts,
at different scales, with different, possible overlapping subsystems,
each with different functional roles in the whole. That is no more
than an outline. It will take a lot of effort to put this programme
into practice and realise it in empirically worthwhile ways. Any takers?
--------------------------------------------------------------------------
Srinandan Dasmahapatra
Science and Engineering of Natural Systems Group
School of Electronics and Computer Science
University of Southampton
Highfield, Southampton SO17 1BJ, UK
phone: 00 44 (0)2380594503
fax: 00 44 (0)2380593313
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Received on Thu Feb 23 12:58:45 2006
