Re: The Language of Cells

Dear Pedro and Jose:
Dear Everyone:

Pedro and Jose have put forward an interesting hypothesis. In
responding to it, I am reminded of Arturo Rosenbluth and Norbert
Weiner's comments in "The Role of Models in Science". They classified
two types of models: material models and formal (or symbolic) models.
While these ideas are slightly obsolete, they are worth quoting:

They defines these as:

"A material model is the represntation of a complex system which is
assumed simpler and which is also assumed to have some properties
similar to those selected for study in the original complex system.
"A formal model is a symbolic assertion in logical terms of an idealized
relatively simple situation sharing the structural properties of the
original factual models."

They then puts the limitations of scientific models in perspective:

"Consider first material models. They start by being rough
approximations, surrogates for the real facts studied. Let the model
appraoch asymptocically the complexity of the real situation. As a
limit, it will become identical to the real system."

They continues by generating a Platonic ideal:
" The ideal formal model would be one which would cover the entire
universe, which would agree with its complexity and which would have a
one to one correspondence with it. Anyone capable of elaborating and
comprehending such a model in its entiriety would find the model
unnecessary because he could grasp the universe as a whole. He would
possess the third category of knowledge described by Spinoza."

When I read your "Language of the Cell", I conjecture that it fits
between the simpler model of information theory and the relative
ordering relationships and chemical structural graphs. The language
appears to me as more complex than information theory but less complex
than chemistry.

Thus, I would next ask, what advantages does it offer the practioner?
Can you give examples which compare this cellular language to the
information variety - for example, T. Schneider's 'molecular machine
theory' which is developed from information theory?

The second issure is the question of the role of composition. Have you
considered the role of potential commutative relations in sequential
compositions? Would this give your partitioning relations deeper
meaning in terms of creating categorical algebras?

Why reject chemical structures as a language for cells?
One reason is that no one knows how to calculate the information content
of chemical structures! Nor, do we know how to calculate the total
number of possible isomers for nearly all molecules with more than a few
atoms. Thus, we do not have a method to calculate the distributions
required for Shannon's formula! The fact that experiments are conducted
in the material context of chemical structures certainly does not imply
that the symbolic analysis can be done only in terms of classical
physical-chemical variables!

Would you see your compostional partitions as a way to leap over these
intractable chemical problems?

I agree that this approach has some conceptual advantages - can these
conceptual advantages be clearly demonstrated with analysis of
biological observations?

Cheers to all.
Jerry

Pedro C. Marijuan wrote:
>
> THE LANGUAGE OF CELLS
>
> Pedro C. Marijuan & Josi Pastor
> Department of Electronics and Communications Engineering
> Universidad de Zaragoza, Zaragoza 50015, Spain
>
> 1. Introduction: Positional versus Compositional Information
>
> The notion of a "language" of cells does not look consistent in relation
> with the standard views of Information Theory applied to biology. Although
> Shannon and Wiener (1948) distinguished between discrete, continuous, and
> mixed information sources, the standard application of their ideas to the
> biology of the cell has been heavily influenced by the DNA and RNA
> sequential structure, and only the discrete-positional case has been
> traditionally considered (e.g., Gatlin, 1972). As a consequence, the lack
> of distinction between "positional" and "compositional" forms of
> information and the subsequent neglect of the latter--we are going to argue
> here--have implied an analytical dead-end concerning the possibilities of
> elucidating formal mechanisms of cellular languages.
>
> In biology and in human to human communication, the assumed preconditions
> for information transmission, and for any workable language, refer to
> sequences of messages containing combinations of symbols which will be
> accepted (or emitted, or read, or transmitted, or deciphered) always
> following a positional order. Therefore, Shannon's formula appears as the
> natural way of measuring the average combinatory content of these messages,
> and of establishing their relative index of surprise, in order to design
> appropriate channels, codes, etc. A workable language can be created,
> subsequently, as a series of grammatical (Markovian) rules to abide by when
> connecting successive positional messages comprised within the dictionary
> scope of the language.
>
> However, one can point at a number of instances in natural and social
> communication where symbols are used in a rather different way. Instead of
> a "positional" context, a "compositional" one is the case. In this
> alternative context, messages are exchanged as presences or absences of
> symbols which have been accumulated upon predetermined sets of objects. No
> meaningful positional relationships among the objects within the set or
> among the symbols accumulated upon the objects are assumed. For example,
> several glasses on a tray may contain a variable number of different
> symbolic items (ice cubes, soda, vermouth, olives, cherries). The set of
> glasses on the tray become the message, each glass being an individual
> object that accumulates several symbols which precisely configure it as a
> distinguishable object. Communication among two subjects could be
> established by the exchange of trays, with variable number of glasses and
> variable contents within them. Theoretically, that messages might be
> reliably distinguished and transmitted by this method "of concurrent
> processing of discrete states of media" has been postulated by Karl
> Javorszky (1996). A whole body of partitional calculus (or granularity
> algebra) has been envisioned by this author (Javorszky, 1995).
>
> More reasonable examples of the compositional way of information exchanges
> may be found in the communicational use of colors, odors and tastes by
> individual organisms; also in social insects' pheromones; and anecdotally
> in the etiquette "language of flowers"; and perhaps within musical
> compositions and within the formative frequencies of vowels and consonants
> of our own spoken languages as well. The "language of cells", we will
> discuss here, may be one of the most interesting instances of communication
> by means of such compositional tools; and it has been the forerunner of any
> further means of biological communication.
> Marshall Mc Luhan's famous dictum "the medium is the message" and the
> particular disdain this author showed about Shannon's information theory
> (Mc Luhan, 1968) are worth be remembered when considering this fundamental
> distinction between positional and compositional forms of information
> exchange.
>
> 2. Analyzing a Compositional Message
>
> When receiving a compositional message encrusted upon a set of N elements,
> there is very little a subject can do: just counting the presence of the
> different symbols on each element of the set. Hence the elements can be
> grouped in homogeneous classes of overlapping or non-overlapping nature
> (each class is defined by the presence of a specific symbol, and it
> actually demarcates a partition of the set N). After the classes defined by
> single symbols, the more complex coincidences of combinations of symbols
> (class overlaps) among the elements can be counted. It can be easily proved
> that all the possible countings of symbolic presences among the N elements
> of the set, in the first case of linear or one-dimensional partitions for
> single symbols, conduce to the whole set of partitions of N, known as E(N)
> (Javorszky, 1995). Whereas the coincidences or overlaps of successive
> combinations of two, three, four symbols, etc., can be considered as second
> order partitions, third order, fourth order ones, etc.--E2(N), E3(N),
> E4(N)...
>
> Mathematically, partitions are a very straight concept: the additive
> decompositions of natural numbers. For instance, the set { (5), (4,1),
> (3,2), (3,1,1), (2,2,1), (2,1,1,1), (1,1,1,1,1) } represents the whole
> onedimensional partitions of 5. By adhering to this mathematical treatment,
> one can use the well-known partitional properties of numbers to discuss the
> most probable logical states of a compositional message encrusted upon the
> elements of the set N.
>
> The set of partitions E(N) can be transformed right away into a
> probability body. The probability of any state of the set to exist as is
> described by a specific partition is given by the relative frequency of
> this partition among all partitions. For instance, on E(5) the probability
> is
>
> 1/7 - for states (5), (2,1,1,1) and (1,1,1,1,1) each,
> 2/7 - for states with either 2 or 3 summands each,
> 15/20 - for any summand to be an odd number.
>
> Kmax is that number (1..n < N) which generates the most numerous set of
> partitions of N into k summands. In this most probable partitional state,
> the set shows Kmax distinct summands with respect to a one-describing
> dimension. In the case of E (5), there is a Kmax shared both by 2 and 3.
>
> Heuristically, it appears that a compositional message can be univocally
> described by its corresponding "trace" of unidimensional partitions
> (Javorszky, 1996), if a few additional statistical measures that act as a
> sort of context or shared background in the communicational process have
> been previously established: most probable message length, ratio of
> symbols/elements, structural depth, shallowness, etc. Then the use of
> partitions of further order (second, third, etc.) becomes redundant--and
> its inclusion would notably complicate the mathematical description of the
> message.
>
> Additionally, the Kmax. dimension of every property or symbolic presence
> may be used as an origin or natural cannon to which the respective
> deviations of successive messages can refer. This further simplifies the
> partitional "trace" describing a specific message in the context of an
> ongoing communication process.
>
> Karl Javorszky (1996) has argued that an efficient communication procedure,
> massively parallel, can be built around such minimized partitional traces
> or message simplifications. It seems to work particularly well with data
> sets of a moderate size, which are preferably prestructured and come in a
> quasi continuous stream, so that the number of possible symbols is always
> kept rather finite--although symbols might come from an infinite multitude,
> there should be a relatively small collection of distinguishing items
> employed at the communicational session, and their group relations should
> not generate a cardinality overstatement symbols/elements above a certain
> limit.
> In the extent that Javorszky4s estimates are correct, the overall capacity
> of a compositional channel making use of discrete states of media can be
> generically expressed as
>
> T(N) = E(N) exp ln E(N),
>
> understanding T(N) as the number of different logical states which can be
> distinguished by means of collections of symbols put on the elements of the
> set N -only non-redundant states are counted, for redundant symbol groups
> can always substitute by single symbols, coalescing into a unique logical
> state. E (N) is the already mentioned number of partitions of the set N.
>
> Calculating the respective probabilities and taking logarithms, one could
> obtain an expression in bits for the compositional-channel capacity (or the
> entropy of a compositional information-source) somehow paralleling the
> famous Shannonian entropy.
>
> It is also interesting the comparison between T(N) and the strictly
> positional use of the same elements of the set N in a combinatory way
> (which, in principle, should provide a total of N! different messages or
> logical states). In this comparison, T(N) yields a larger number of logical
> states than N! for values of N in between 31 and 95, with a maximum around
> 63-64. However, for N = 12, the number of combinations N! reaches a maximum
> with respect to T(N).
>
> Seemingly, several parameters of the genetic code would correspond with
> such max./min. extremes that characterize the compositional-positional
> interrelationship (see Javorszky, 1995, for detailed expression of all
> these formulae and calculations).
>
> 3. A Partitional Approach to Cellular Communication
>
> How can the above compositional considerations be applied to the analysis
> of inter- and intra-cellular processes? Instead of DNA sequences, it seems
> that the natural target of this new approach should be the "mysterious"
> processing operations performed by the cellular signaling system.
>
> The basic idea to play with is that any array (sample) of chemical
> compositions detected by the set of cellular receptors may be recast as a
> partitional state, for we may consider that it has been obtained by
> distinguishing the presence of a series of specific chemical signs within
> an hypothetical set of N elements or receptor complexes--it is a transient
> message coming from the environment through an ongoing compositional
> communication process.
>
> Then, an immediate question arises. Could the system of receptors,
> membrane-bound enzyme and protein complexes, second messengers, and the
> dedicated kinase and phosphatase chains, be understood as an abstract
> partitional processing-system capable of extracting the minimized "trace"
> or relative information differences within the stream of incoming
> compositional messages and physically transport these differences down to
> final effectors at the nucleus, cytoplasm, or membrane? That's the basic
> hypothesis these two authors are presently trying to explore.
>
> If (and what a big "if") cells would make use of formal tools of
> partitional nature in their management by means of the cellular signaling
> system of the compositional messages they receive, then the notion of a
> genuine cellular language, with specific dialects for every organismic
> tissue, could be seriously argumented. And perhaps more interesting than
> that, quite a few other bizarre aspects of the signaling system could
> receive some more formal (and simpler) treatment: the cross-talk between
> signaling pathways, the checkpoints relating signaling operations with
> cell-cycle stages, and even the widespread formation of aggregates and
> complexes among signaling components...
>
> Partitions are very direct formal tools, but at the same time sophisticated
> ones. For instance, if natural numbers are left to "oscillate" and
> simultaneously their corresponding partitions are allowed to grow and
> shrink (Javorszky, 1998), then there emerges a variety of self-organization
> patterns and internally-driven numerical processes which seemingly parallel
> the constructive/degradative aspects so prevalent in biological and social
> occurrences (and even physical ones).
>
> The studies by Caianiello (1987) on the partitional dynamics inherent of
> monetary systems and the suggestion by one of us (Marijuan, 1998) about the
> "currency" role actually played by the set of second messengers in the
> internal measurement of cellular function might finally be stepping stones
> pointing out in the same direction.
>
> ----------------
>
> -----------------------------------------------------------
> Pedro C. Marijuan --FAX 34 976 761 861 --TEL 34 976 761 927
> Dto. Ingenieria Electronica y Comunicaciones
> CPS, Universidad de Zaragoza
> Zaragoza 50015, SPAIN
Received on Wed Mar 11 05:47:00 1998