Minimum Forms of Control in Prokaryotes and their Computational Meaning

Transcription

1 Minimum Forms of Control in Prokaryotes and their Computational Meaning Franco di Primio Institute for Autonomous intelligent Systems (AiS), GMD D Sankt Augustin and Andreas E. Kilian Institute for Autonomous intelligent Systems (AiS), GMD D Sankt Augustin Abstract The main goal of our work is to point out some aspects of basic control in biological and technical systems discussing similarities and differences. To keep things manageable and somewhat simpler we restrict our view to unicellular organisms and in particular to prokaryotes. There we find, as a matter of fact, minimum forms of molecular control structures that can be related to computational constructs, and that, in a formal sense, build an algorithmically sufficient set. Thus, the main result of this paper is that even prokaryotic cells have Turing machine power. The way biological control structures are combined within the cell to build more complex forms of control flow seems, however, to be different from that desirable or normally envisaged for the realization of technical systems. Biological computation is highly parallel and at the same time data and event driven, and therefore not simply amenable to a description in form of physically and functionally coherent modules. This and other obvious scale-specific aspects of the prokaryotic world suggest that the importance of cellbased approaches, in particular for flexible manufacturing systems (FMS), is questionable, at least in the sense that the level of abstraction and the point of view must be carefully chosen in order to get some profit from the biological model. Keywords: Control, prokaryotes, Turing machine, flexible manufacturing systems 1. Information processing approaches to cellular models Our starting point is the recent attempt of Lengeler [8] to describe the biological elements of a natural and holistic modeling procedure for metabolic networks. There a living cell is regarded as a signal processing system that is organized in a modular and hierarchical way, each level of complexity being characterized and governed by a regulatory (control) system. The lowest form of control relies on specific and locally acting regulator genes. At higher levels, regulator genes act more and more globally, control more and more structural genes and respond to physiological states of the cell rather than to specific stimuli. A hierarchical organization is given in the sense that higher level regulators become epistatic, i.e., they dominate those from lower levels. This view makes clear that the identification of control structures in the cell (regulator genes and their interaction with signal molecules) is intimately related to the identification of structural genes. Because a regulator gene can also be regulated, the role of genes is contextual and depends on the point of view. Lengeler [8] gives criteria how to identify functional units as the modules for modeling biological systems. These are, for instance, the identification of a common physiological task, a common genetic unit (location of the genes and their structuring within the genome), and a common signal transduction system. While the author does not exclude that his rules may also apply to the intercellular level of complexity, i.e., to multicelled aggregates and organisms, and beyond to populations and cenoses, we confine our attention as already mentioned to the sub- or intracellular level. An

2 important aspect is that the number of hierarchical levels between operons/regulons which control simple metabolic pathways and the highest control level, comprising, for instance, modulons which group up to 50 operons and regulons, and so-called sigma subunits, is unknown even for Escherichia coli, the best known organism. Furthermore, there are just a few general principles governing metabolic pathways and signal transduction, like protein-protein interactions, in particular the formation or figuration of protein complexes and reversible biochemical modification of such complexes, and the generation, modification or use of intracellular messengers. 2. Basic computational and biological control constructs In computer science, various minimal sets of control structures have been identified, meaning that other control structures can be replaced by appropriate combinations of those in the minimal set. Such a well-known set of constructs, which is sufficient for describing the control flow of every conceivable algorithm, is sequencing, selection among alternative actions (conditional branching), and iteration. Every Turing machine program can be written in this manner [2]. Sequencing means that different statements are executed in a specific order: 1 2 n. Selection has the form: 1 2, where is a condition, i.e., a predicative structure, while the statements i are of functional or procedural type, requiring an input which is transformed to whatever output. Iteration takes different equivalent forms. is one of them. The statement (or sequence of statements) is executed as long as the condition holds true. The combination of these constructs, even with arbitrarily deep nesting, retains the linearity of control flow, which is an important aspect for good software engineering [6, pp. 194ff]. Are there control structures in the prokaryotic cell that correspond to these computational constructs? The answer is clearly positive. In biological science, one of the bestunderstood models of gene regulation is the lac-operon suggested by Francois Jacob and Jacques Monod [10]. They were the first scientists to work on and elucidate the lactose metabolism in E. coli. To put it roughly, when such a bacterium is in an environment that contains lactose (and no glucose), it turns on the enzymes that are required for its degradation. E. coli 's prime source of food is glucose, since it does not have to be modified to enter the so-called respiratory pathway. So if both glucose and lactose are in the medium, the bacterium turns off the lactose metabolism in favour of glucose metabolism. In more detail, when the level of glucose is high, the transcription of a regulator gene leads to a repressor protein which inhibits the transcription of the structural genes necessary for the enzymes β-galactosidase, permease and transacetylase. The repressor protein binds to the operator and inhibits the RNA-polymerase to start translation from the promotor. In conditions of low glucose and in presence of the effector and substrate lactose the repressor can dissociate (the protein is allosteric, a term we are going to explain below) and transcription of the genes leads to translation of the three enzymes. The β-galactosidase catalyzes lactose into glucose and galactose. To activate the lac-operon also a catabolite activator protein (CAP) and cyclic adenosinemonophasphate (camp) are necessary. The end-product glucose inhibits the synthesis of camp and inhibits also indirectly the transcription of the lac-operon. Depending on the quantity of metabolites, expression of genes is regulated in a fine tuned iteration of the process. The lac-operon model shows that transcription of genes is regulated by two ways involved in one feedback loop: The presence of the effector by a simultaneous absence of one end-product leads to expression of genes whereas the presence of one end-product or the absence of the effector inhibit transcription. We will now explain some aspects of the above description in technical and schematic terms. A first general point to retain is that the organization of regulator and structural genes in modules or functional units corresponds, computationally speaking, to the problem of composing control (and data) structures from basic structures. To view this, it is better first to address the biological meaning of the most elementary computational statement. Statements are the units from which programs are constructed. A program is a sequence (control structure!) of statements (or instructions, as they are called at the machine-code level). The assignment of a value to a variable is the most basic form of statement. Biologically, this corresponds to the binding of molecules, for instance, the interaction of proteins with other proteins or proteins with pieces of DNA, i.e., nucleotides, or amino acids. Most relevant for control purposes are allosteric proteins. These are proteins that change their conformation when bounded to specific (regulatory) molecules, and, as a consequence, loose or acquire the ability to recognize and bind to some other molecules 1. Such a protein may play the role of an on/off switch (i.e., a Boolean, or dual control variable) and block or activate, for instance, the transcription of parts of DNA. Thus, it serves as the basic constituent (the test or predicative part) of a selection structure. Conditional branching in cell biology can indeed be seen as the result of an abstraction about temporary differences of the interaction properties of molecules. For instance, enzymes that are permanently trying to transcribe parts of DNA into mrna can accomplish their work some specific molecule (the corepressor) is not bound to another specific molecule (the apo-repressor) which is the product of the expression of a regulator gene. Apo- and co-repressor together form the holo-repressor that is able to connect to the operator gene 1 Besides the binding of a small molecule, a second method, that is commonly used to regulate a protein s function, is the addition of a phosphate group covalently to one of its amino acid side chains (phosphorilation). This and the reverse reaction of phosphate removal (dephosphorilation) cause the shift from one conformation to another. Many if not most proteins are allosteric. This is true not only for enzymes but also for receptors, structural proteins, and motor proteins [1, pp. 174ff].

3 and block the transcription of the structural genes. Sequential structures consisting of an operator gene and several structural genes are called operons. Thus, a regulator gene together with the corresponding operon is an instance of the basic biological conditional statement in a cell. the regulator does not interact with the operator the structural genes are expressed. Iteration is realized biologically in the following way. There are first sequences of active elements (like enzymes or ribozymes) that transform an initial substance (the substrate) into a final substance through intermediate steps (also substances). Sometimes, on the basis of such sequential structures (metabolic pathways), cycles are formed because the final substance circulates back (through diffusion) and interacts with the constituents of the sequence that produce the intermediate or initial substances. So the end-product of a transformation chain may regulate the activity of the elements involved in its production. A concrete (and relatively simple if compared with the lac-operon) example is the anabolic pathway used by some cells to synthesize the amino acid isoleucine from threonine, another amino acid. The pathway consists of five steps, the first enzyme being threonine deaminase. As isoleucine, the end-product of the pathway, accumulates, it slows down its own synthesis by allosterically inhibiting the threonine deaminase. This prevents the cell from wasting chemical resources to synthesize more isoleucine than is necessary [4, p. 96] 2. This form of feedback certainly is a major point in cell control. Formally, it can be expressed in the following way: If 1 n is a chain of processing elements (for instance enzymes), 0 is the initial substance (the input to 1 ), n the final substance (the output of n ), i the intermediate substance produced by i on the basis of i-1, then n can regulate (inhibit or stimulate) the activity of 1 or some i with i < n. Since the i are also produced substances, as a special case, n can regulate the production of some i (for instance, the expression of the genes needed to synthesize the enzyme 0). From this point of view, the interaction of a regulator gene with an operon can be viewed as an iterative control structure: the regulator does not interact with the operator express the structural genes. Summing up: a prokaryotic cell possesses a sufficient set of control structures (sequencing, selection, and iteration), and has therefore the power of a Turing machine 3. 2 Concerning the general speed or efficiency of iteration and regulation processes, it is worth noticing that in the case of chains of enzymes the entire cycle happens so fast that a single enzyme molecule typically acts on about a thousand substrate molecules per second [4, p. 93]. 3 Notice that the term of Turing machine is only used here as a theoretical concept for computational power. In reality, a machine with an "infinite" tape cannot exist. In previous work [3], the DNA transcription-translation process was viewed as a system of two pipelined Turing machines. In the same context, the claim was made that "two-way Turing machines exist in the cell" [3, p. 20]. Here we base our result that cells have Turing machine "power" on the evidence of algorithmic 3. Similarities and differences A fundamental difference between computer-based and cell-biological processing concerns the relationship between control and data structures. In computer science, control and data structures constitute an irreducible duality: data structures have to do with the memory, control structures with the processor of a computer. Clearly, they have to be both present in order to get a reasonable system, and there is also a logical relationship between the different forms of data and control structures. Thus, a vector (as a data structure) corresponds to sequencing as control structure; an array corresponds to nested loop structures (iterations) and a tree is related to recursion as control structure. In the cell there is no clear-cut difference between data and control structures. The basic units are molecules that interact with each other. The interaction is based on a sort of key-lock principle. A key molecule is at the same time data and medium for the transport of the information (data carrier). A lock molecule is at the same time memory structure, recognizer and translator of the information (receptor). More precisely, the three-dimensional structure of the key molecule is a data. The recognition of this data by a lock molecule turns data into information 4. The key-lock principle is also a duality, but a conceptual, i.e., observer-dependent one. Physically, the distinction between information (signal) and information carrier (medium or receptor) on the one hand, and the distinction between the resources memory, as the amount of storage required by an algorithm, and hardware, as the amount of physical mechanism required for the execution of the algorithm, on the other hand, is blurred. The hard- (or better the wet-) ware works according to the uniform principles of chemistry: bond breaking (with absorption of energy), and bond forming (with release of energy), and there is no need for an externally controlled balance, or trade-off, between resources. The input/output notion is also too rigid. The solution of a biological problem involves rather ongoing behavior, that need not lead to termination at all, and is best specified as a desired state, or global constraint, the most general one being selfpreservation. It is the ongoing flow of molecules that controls the cell s behavior. But the molecules are not (passive) data, they are also (active) processing elements, building by themselves events and conditions as the basis of their parallel and concurrent mode of operating. Another difference (related to the first one) concerns the way feedback processes are realized. In cell biology, what is called regulation of activities by the end-products or feedback inhibition (Campbell 99, p. 96) is a general principle. Computationally, this can be simulated by introducing programs that monitor the output of a sufficiency of the (metabolic) control structures, without committment to the existence of Turing machines in the cell. 4 This change from data to information is the starting point of the next step in metabolism or signal transduction. If several metabolic pathways are involved simultaneously, threedimensional information turns through synchronization, so-tospeak, into four-dimensional information flux which describes the state of a cell. This state is the knowledge of a cell what to do next in ontogenesis.

4 function (for instance, measure the quantity of some produced substance) and send the result to the program (or processing element) at the beginning of the (transformation) chain which then decides whether to intensify or stop the production. For a technical system (like a production line), it would not be very sensible to expect that parts of the final product diffuse back in order to control the quantity to be produced. Clearly, this has to do with the scale of the system. Over microscopic distances, diffusion of chemicals from high concentrations to low usually provides a rate of transport sufficient to meet metabolic need. But for the transport over large distances, energy and some form of circulation (for instance blood circulation) is necessary [5, pp. 6ff]. For a (macroscopic) technical system, the transport of information (in form of energy waves) might be sufficient to obtain the desired results. A further major point is that within a prokaryote the only structural order generating principle is the specificity of molecular binding that produces various types of molecules. For instance, enzymes are substrate-specific, and may arrange in groups with other enzymes, associating in pathways. There are over 2000 known enzymes, each of which is involved with one specific chemical reaction. But with respect to control, different cyclically operating chains of such processing elements, that in a simple cell like E. coli amount to millions, form networks, where the (intermediate) products of a chain may regulate the activity of the processing elements of other chains. This interdependence is rather bad news for technical analogies and cell-oriented biomimetics, because linearity of control is not retained 5. Maybe, the principle of compartmentation, which is so to speak a data structuring principle, and which is realized at the level of eukaryotic (but not prokaryotic) cells, is one way to partly reduce the complexity of this problem. Eukaryotes are in this respect very different from prokaryotes whose interior is relatively formless. They are typically 10,000 times as large, measured by volume, and are not only divided into many different compartments by membranes, but also contain up to several thousand specialized units or organelles that carry out specific tasks (like the mitochondria, which act as energy sources) [1, pp. 447ff]. In any case, this is surely the part where biology becomes more difficult to understand. More biological research is needed to uncover the relationships between intra- and intercellular structures and functions. Considering that, according to a widely accepted theory, eukaryotes evolved from prokaryotes by way of a kind of 5 Computer scientists know that the de facto situation for complex software systems can indeed be analogue to the cellbiological one. What we mean here with respect to control is the de jure or prescriptive position of the state of art in software engineering. The fundamental problem in the analogy is the opposition between programmability (in the strict meaning of the term) and evolvability. Technical systems should be programmable (possibly in a "structured" mode). Biological systems are the result of evolution ("programming" based on mutations and selections), and that not only takes too much time but also is "messy". At least, we do not yet fully understand the mechanisms governing them. symbiosis [9], what happens within an eukaryote cell belongs to the intercellular domain. Computational analogies are also difficult, because they concern parallelism, distributed and ongoing concurrency, which are concepts strictly related to aspects of decentralization and self-organization [11]. It is unclear (to us) whether typical abstractions and constructs invented for coping with difficulties arising in this context (like schedulers, global clocks for achieving coordination or semaphores for the solution to the producer/consumer problem [7, pp. 257ff]) have any correspondence at all at the biological cellular level. 4. Consequences for FMS Flexible manufacturing systems consist of groups of machines with automated loading and unloading of parts, automated guided vehicles for moving parts from one machine to another, and other automated elements. Flexibility means primarily the ability to cope with unattended production of parts. In response to customers needs, an increasingly larger variety of products must be produced quickly (and just in time) in ever smaller quantities. The key to flexibility is seen in a comprehensive computer system that is used to control the entire manufacturing system, and possibly also parts of its environment. The idea of considering the biological manufacturing system of the cell in order to gain some knowledge to build still more flexible or even autonomous factories is tempting [3]. The aspects mentioned in the previous section suggest, however, that it is questionable whether cell biology can be a comprehensive model for the construction of such systems. First of all because the flexibility of a cell relies on the fact that not only products but also machines are produced just in time (and disassembled catabolized when no longer needed). Secondly, the control system of a cell is only partly hierarchic, and in no way centralized. Also from a design point of view the principles governing the control in prokaryotic cell cannot be used extensively for the realization of FMS, at least not if the goal is to get possibly similar physical, functional, and state-based behavioral decompositions of the technical system. But maybe such a specification constraint is only good for extrinsic maintenance and not for intrinsic, i.e., selfmaintenance, and is not appropriate at all for a technical realization of flexibility and adaptivity in the biological sense. 5. Outlook In this paper we have investigated the meaning of the very basic control principles in prokaryotic cells, concentrating on the first level of the modular control architecture proposed by Lengeler [8]. We have found out that the control elements for Turing machine power are present, but this is only a first step toward the elucidation of the cell programming system. Computationally speaking, we understand the basic elements of a language but not yet the mechanisms producing abstractions for data and control structures. To make progress in this direction,

5 more research work is needed both in biology and computer science. The overall (abstract) problem is to understand how data is transformed into information, and information into knowledge, and how information and knowledge produce actions and (intelligent) behavior. In concrete terms, the interaction and communication between cells and their functional change in time has to be focused on and explained in computational terms. In our opinion, the key is to understand how differentiation works. The underlying principle seems here to be clear: differentiation means that in spatially distributed cells a regulation system provides on the basis of the same genetic program at certain times in certain cells that certain genes are expressed (and certain others not). The basic mechanisms of such a regulation system (which is itself also a product of the genetic program and variable in time) are signals and maybe internal and external clocks. Suppose you have a group of cells of the same type, say A, at time t 1. Same type means that the cells are in the same geneexpression-state. For the cells to change to another state B at some other time t n, an internal clock could be assumed. Since the cells are of the same type, this would mean, however, that all cells would change their state to B, and so the initial symmetry would be maintained, i.e., no differentiation could happen. A differentiation, or symmetry breaking, is only possible if the cells that change first their state (maybe on the basis of an internal clock) emit signals that are interpreted by the cells that have not yet changed their state as information to do something different. This can work, of course, because absolute simultaneousness is impossible. The necessity of signals (communication), or more generally, the importance of environment factors for (coordinated) differentiation processes is evident. How such regulation networks and the bootstrapping from an initial cell to a population or a complete organism work, is, however, still almost a mystery even for a nematode consisting of a few thousand cells. [4] Campbell, N. A:, Reece, J. B. & Mitchell, L. G. (1999). Biology, Addison-Wesley, Menlo Park, 1999 [5] Dusenbery, D.B. (1996). Life at Small Scale The Behavior of Microbes, New York: Scientific American Library [6] Farley, R. (1986). Software Engineering Concepts, McGraw-Hill, New York, 1986 [7] Harel, D. (1987). Algorithmics The Spirit of Computing, Addison-Wesley, Wokingham, 1987 [8] Lengeler, J. W. (2000). Metabolic networks: a signal-oriented approach to cellular models Biol. Chem. 381(9-10): (i-iv*) [9] Margulis, L. (1981). Symbiosis in Cell Evolution, Freeman, New York, 1981 [10] Monod, J., Pardee, A. B. & Jacob, F. (1959). The genetic control and cytoplasmic expression of `inducibility' in the synthesis of b-galactosidase by Escherichia coli, in: J. Mol. Biol., 1, pp [11] Resnick, M. (1994). Turtles, Termites, and Traffic Jams, MIT Press, Cambridge (MA), 1994 Acknowledgements Many thanks to Stevo Bozinovski, Rainer Worst as well as to Thomas Christaller, head of the GMD Institute for Autonomous intelligent Systems (AiS) for encouragement and helpful comments. Last but not least, we thank Ursula Bernhard for reading the English text. References [1] Alberts, B., Bray, D., Johnson, A., Lewis, J., Raff, M., Roberts, K. & Walter, P. (1998). Essential Cell Biology, Garland Publishing, New York, 1998 [2] Böhm, C. & Jacopini, G. (1966). Flow Diagrams, Turing Machnines, and Languages with only Two Formation Rules, in: Comm. ACM, vol. 9, no. 5, May 1966, [3] Bozinowski, S. in cooperation with Müller, B.S. & di Primio, F. (2000). Biomimetic Autonomous Factories Autonomous Manufacturing Systems and Systems Software, GMD Report 115, Sankt Augustin, 2000