An abstract cell model that describes the self-organization of cell function in living systems

The principal aim of systems biology is to search for general principles that govern living systems. We develop an abstract dynamic model of a cell, rooted in Mesarovi? and Takahara's general systems theory. In this conceptual framework the function of the cell is delineated by the dynamic processes it can realize. We abstract basic cellular processes, i.e., metabolism, signalling, gene expression, into a mapping and consider cell functions, i.e., cell differentiation, proliferation, etc. as processes that determine the basic cellular processes that realize a particular cell function. We then postulate the existence of a 'coordination principle' that determines cell function. These ideas are condensed into a theorem: If basic cellular processes for the control and regulation of cell functions are present, then the coordination of cell functions is realized autonomously from within the system. Inspired by Robert Rosen's notion of closure to efficient causation, introduced as a necessary condition for a natural system to be an organism, we show that for a mathematical model of a self-organizing cell the associated category must be cartesian closed. Although the semantics of our cell model differ from Rosen's (M,R)-systems, the proof of our theorem supports (in parts) Rosen's argument that living cells have non-simulable properties. Whereas models that form cartesian closed categories can capture self-organization (which is a, if not the, fundamental property of living systems), conventional computer simulations of these models (such as virtual cells) cannot. Simulations can mimic living systems, but they are not like living systems.     

The practical modelling of context-dependent causal processes--a recasting of Robert Rosen's thought

This paper is a critical recasting of some of Robert Rosen's thought. It is argued that a lot of the thrust of Rosen's work can be better understood when recast in terms of the context dependency of causal models. When recast in this way, I seek to highlight how his thought does not lead to the abandonment of formal modelling and a descent into relativism, but a more careful and rigours science of complex systems. This also sheds light on several aspects of modelling, including the need for multiple models, the nature of modelling noise, and why adaptive systems cause particular problems to modellers. In this way, I hope to decrease researchers fear that, by taking Rosen's criticisms seriously, they would have to abandon the realm of acceptable science.     

Re-mapping Robert Rosen's (M,R)-systems

The central concern of this paper is to re-evaluate Rosen's replicating (M,R)-systems, presented in his book 'Life Itself ', where M and R signify metabolism and repair, respectively. We look anew at Rosen's model of an organism in the light of extensive research into natural hierarchical systems, and the paper presents conclusions drawn from a comparison between Rosen's relational model and that of a birational complementary natural hierarchy. We accept that Rosen's relational model provides a useful stepping stone to understanding the nature of life, but also suggest that it induces potentially digressive conclusions. We conclude that a binary segregation of relational assemblies into mechanisms and organisms is insufficient, and indicate how a threefold segregation throws new light on Rosen's model. An organism is not 'the complement of a mechanism': the complement of a mechanism is its ecosystem. An organism is the 'complex interface' between mechanism and ecosystem.     

Organizational invariance and metabolic closure: analysis in terms of (M,R) systems

This article analyses the work of Robert Rosen on an interpretation of metabolic networks that he called (M,R) systems. His main contribution was an attempt to prove that metabolic closure (or metabolic circularity) could be explained in purely formal terms, but his work remains very obscure and we try to clarify his line of thought. In particular, we clarify the algebraic formulation of (M,R) systems in terms of mappings and sets of mappings, which is grounded in the metaphor of metabolism as a mathematical mapping. We define Rosen's central result as the mathematical expression in which metabolism appears as a mapping f that is the solution to a fixed-point functional equation. Crucially, our analysis reveals the nature of the mapping, and shows that to have a solution the set of admissible functions representing a metabolism must be drastically smaller than Rosen's own analysis suggested that it needed to be. For the first time, we provide a mathematical example of an (M,R) system with organizational invariance, and we analyse a minimal (three-step) autocatalytic set in the context of (M,R) systems. In addition, by extending Rosen's construction, we show how one might generate self-referential objects f with the remarkable property f(f)=f, where f acts in turn as function, argument and result. We conclude that Rosen's insight, although not yet in an easily workable form, represents a valuable tool for understanding metabolic networks.     

Closure to efficient causation, computability and artificial life

The major insight in Robert Rosen's view of a living organism as an (M,R)-system was the realization that an organism must be “closed to efficient causation”, which means that the catalysts needed for its operation must be generated internally. This aspect is not controversial, but there has been confusion and misunderstanding about the logic Rosen used to achieve this closure. In addition, his corollary that an organism is not a mechanism and cannot have simulable models has led to much argument, most of it mathematical in nature and difficult to appreciate. Here we examine some of the mathematical arguments and clarify the conditions for closure.     

A Rosen etymology

This essay contains a few of my interpretations of Robert Rosen's conception of Nature. I shall study the four notions that form the core of his whole-lifetime's scientific work: simple system, mechanism, complex system, and organism. Their set-theoretic interconnections culminate in Rosen's new taxonomy of natural systems.     

Robert Rosen in the age of systems biology

The widespread use of the term Systems Biology (SB) signals a welcome recognition that organisms must be understood as integrated systems. Although just what this is taken to mean varies from one group to another, it generally implies a focus on biological functions and processes rather than on biological parts and a reliance on mathematical modeling to arrive at an understanding of these biological processes based on biological observations or measurements. SB, thus, falls directly in the line of reflection carried out by Robert Rosen throughout his work. In the present article, we briefly introduce the various currents of SB and then point out several ways Rosen's work can be used to avoid certain pitfalls associated with the use of dynamical systems models for the study of complex systems, as well as to inspire a productive path forward based on loosely organized cooperation among dispersed laboratories.     

Organizational invariance in (M,R)-systems

Robert Rosen's concept of (M,R)-systems was a fundamental advance in our understanding of the essential nature of a living organism as a self-organizing system, one that is closed to efficient causation, synthesizing, and maintaining all of the catalysts necessary for sustained operation during the whole period of its lifetime. Although it is not difficult to construct a model metabolic system to represent an (M,R)-system, such a model system will typically appear to lack organizational invariance, an essential property of a living (M,R)-system. To have this property, an (M,R)-system must not only be closed to external causation, it must also have its organization coded within itself, i.e., the knowledge of which components are needed for which functions must not be defined externally. In this paper, we discuss how organizational invariance may be achieved, and we argue that the apparent failure of previous models to be organizationally invariant is an artifact of the usual practice of treating catalytic cycles as 'black boxes'. If all of the steps in such a cycle are written as uncatalyzed chemical reactions, then it becomes clear that the organization of the system is fully defined by the chemical properties of the molecules that compose it.     

Laws, constraints, and the modeling relation--history and interpretations

The modeling relation and models of complex systems expressed by non-integrable constraints were developed during ca. 1970-1987, when I worked most closely with Robert Rosen. I contrast the modeling relation within the organism itself as a necessary condition for life and evolution, as Rosen developed it in his fundamental work 'Anticipatory Systems', with the modeling relation within our brain as a necessary condition for understanding life, as Rosen developed it in 'Life Itself'. Our approaches to the modeling relation were complementary. Rosen focused on the formal relational conditions necessary for life, and on the limitations that formal mathematical-symbol systems impose on our models. I focused on the physical conditions necessary for these abstract relations to be realized, and on the symbolic control in organisms that allows open-ended evolution. I contrast Rosen's views on physics and evolution in 'Anticipatory Systems' and later papers with his views in 'Life Itself', and I speculate on why they differ so greatly.     

A model of the gating of ion channels

The gating of ion channels in biological membranes has usually been described in terms of Markov transitions between a few discrete open or closed states. Such models predict that the distributions of open and closed durations decay as a sum of exponential terms. Recent experimental data have indicated that certain channels are not easily described by these models. We show that distributions of open and closed times similar to those seen experimentally are predicted by a model that involves only one open and closed state but that assumes the activation energy of the gating process to be stochastic. This model involves only a few parameters and these have direct physical interpretations. Measurements of the correlation between the durations of successive open or closed events is shown to provide an experimental method for distinguishing between this and other models.     

What does robotics offer animal behaviour?

There is a growing body of robot-based research that makes a serious claim to be a new methodology for biology. Robots can be used as models of specific animal systems to test hypotheses regarding the control of behaviour. At levels from learning algorithms to specific dendritic circuits, implementing a proposed controller in a robotic device tests it against real environments in a way that is difficult to simulate. This often provides insight into the true nature of the problem. It also enforces complete specifications and combines bodies of data. Current work can sometimes be criticized for drawing unjustified conclusions given the limited evaluation and inevitable inaccuracies of robot models. Nevertheless, this approach has led to novel hypotheses for animal behaviour and seems likely to provide fruitful results in the future. Copyright 2000 The Association for the Study of Animal Behaviour.     

A Cluster Operating System Supporting Parallel Computing

The single factor limiting the harnessing of the enormous computing power of clusters for parallel computing is the lack of appropriate software. Present cluster operating systems are not built to support parallel computing – they do not provide services to manage parallelism. The cluster operating environments that are used to assist the execution of parallel applications do not provide support for both Message Passing (MP) or Distributed Shared Memory (DSM) paradigms. They are only offered as separate components implemented at the user level as library and independent servers. Due to poor operating systems users must deal with computers of a cluster rather than to see this cluster as a single powerful computer. A Single System Image of the cluster is not offered to users. There is a need for an operating system for clusters. We claim and demonstrate that it is possible to develop a cluster operating system that is able to efficiently manage parallelism, support Message Passing and DSM and offer the Single System Image. In order to substantiate the claim the first version of a cluster operating system, called GENESIS, that manages parallelism and offers the Single System Image has been developed.     

Model building and model checking for biochemical processes

A central claim of computational systems biology is that, by drawing on mathematical approaches developed in the context of dynamic systems, kinetic analysis, computational theory and logic, it is possible to create powerful simulation, analysis, and reasoning tools for working biologists to decipher existing data, devise new experiments, and ultimately to understand functional properties of genomes, proteomes, cells, organs, and organisms. In this article, a novel computational tool is described that achieves many of the goals of this new discipline. The novelty of this system involves an automaton-based semantics of the temporal evolution of complex biochemical reactions starting from the representation given as a set of differential equations. The related tools also provide ability to qualitatively reason about the systems using a propositional temporal logic that can express an ordered sequence of events succinctly and unambiguously. The implementation of mathematical and computational models in the Simpathica and XSSYS systems is described briefly. Several example applications of these systems to cellular and biochemical processes are presented: the two most prominent are Leibler et al.'s repressilator (an artificial synthesized oscillatory network), and Curto-Voit-Sorribas-Cascante's purine metabolism reaction model.     

Quality and irreversibility: constraints on ecosystem development.

We discuss one of the most general mathematical tools for analysing dynamical systems: the master equation (ME). The ME is used to derive models for entropy production in closed and open systems. Due to dissipation in open systems, the direction of evolution of important characteristics can be opposite to those imposed on closed systems. When applying these models to soil organic matter it can be shown that the principle of minimum entropy production necessitates that more and more recalcitrant organic matter is produced the further the decomposition proceeds. The necessity to dissipate entropy can also impose a limit on the degree to which litters can decompose, but interaction between litters of differing ages can remove this constraint. This is an example of the 'priming' effect.     

A hybrid systems framework for cellular processes

With the availability of technologies that allow us to obtain stimulus-response time series data for modeling and system identification, there is going to be an increasing need for conceptual frameworks in which to formulate and test hypotheses about intra- and inter-cellular dynamics, in general and not just dependent on a particular cell line, cell type, organism, or technology. While the semantics can be quite different, biologists and systems scientists use in many cases a similar language (notion of feedback, regulation, etc.). A more abstract system-theoretic framework for signals, systems, and control could provide the biologist with an interface between the domains. Apart from recent examples to identify functional elements and describing them in engineering terms, there have been various more abstract developments to describe dynamics at the cell level in the past. This includes Rosen's (M,R)-systems. This paper presents an abstract and general compact mathematical framework of intracellular dynamics, regulation and regime switching inspired by (M,R)-theory and based on hybrid automata.     

Competing Models of Stability in Complex, Evolving Systems: Kauffman vs. Simon

I criticize Herbert Simon's argument for the claim that complex natural systems must constitute decomposable, mereological or functional hierarchies. The argument depends on certain assumptions about the requirements for the successful evolution of complex systems, most importantly, the existence of stable, intermediate stages in evolution. Simon offers an abstract model of any process that succeeds in meeting these requirements. This model necessarily involves construction through a decomposable hierarchy, and thus suggests that any complex, natural, i.e., evolved, system is constituted by a decomposable hierarchy. I argue that Stuart Kauffman's recent models of genetic regulatory networks succeed in specifying processes that could meet Simon's requirements for evolvability without requiring construction through a decomposable hierarchy. Since Kauffman's models are at least as plausible as Simon's model, Simon's argument that complex natural systems must constitute decomposable, mereological or functional hierarchies does not succeed.     

Mathematical modelling in the post-genome era: understanding genome expression and regulation--a system theoretic approach

This paper introduces a mathematical framework for modelling genome expression and regulation. Starting with a philosophical foundation, causation is identified as the principle of explanation of change in the realm of matter. Causation is, therefore, a relationship, not between components, but between changes of states of a system. We subsequently view genome expression (formerly known as 'gene expression') as a dynamic process and model aspects of it as dynamic systems using methodologies developed within the areas of systems and control theory. We begin with the possibly most abstract but general formulation in the setting of category theory. The class of models realised are state-space models, input--output models, autoregressive models or automata. We find that a number of proposed 'gene network' models are, therefore, included in the framework presented here. The conceptual framework that integrates all of these models defines a dynamic system as a family of expression profiles. It becomes apparent that the concept of a 'gene' is less appropriate when considering mathematical models of genome expression and regulation. The main claim of this paper is that we should treat (model) the organisation and regulation of genetic pathways as what they are: dynamic systems. Microarray technology allows us to generate large sets of time series data and is, therefore, discussed with regard to its use in mathematical modelling of gene expression and regulation.     

A need for niches?

The idea that different species must have distinct ecologies if they are to coexist has been challenged recently by the claim that some models involving stochastic factors or clumped spatial distributions permit stable coexistence of species that are identical or differ only in competitive ability. However, these models have been misinterpreted; except in rather limited circumstances, they provide further support for the notion that species must be sufficiently ecologically distinct to coexist stably. The possible, limited, exceptions to this rule involve social factors by which individuals of a species discriminate between heterospecifics and conspecifics without there being any true ecological differences between species.     

Causes and consequences of living in closed societies: lessons from a long-term socio-genetic study on Bechstein's bats

Understanding the ecological, behavioural and genetic factors influencing animal social systems is crucial to investigating the evolution of sociality. Despite the recent advances in population genetic methods and the analysis of social interactions, long-term studies exploring the causes and consequences of social systems in wild mammals are rare. Here, we provide a synthesis of 15?years of data on the Bechstein's bat (Myotis bechsteinii), a species that raises its young in closed societies of 10-45 females living together for their entire lives and where immigration is virtually absent. We discuss the potential causes and consequences of living in closed societies, based on the available data on Bechstein's bat and other species with similar social systems. Using a combination of observational and genetic data on the bats together with genetic data on an ecto-parasite, we suggest that closed societies in Bechstein's bats are likely caused by a combination of benefits from cooperation with familiar colony members and parasite pressure. Consequences of this peculiar social system include increased sensitivity to demographic fluctuations and limits to dispersal during colony foundation, which have broad implications for conservation. We also hope to illustrate by synthesizing the results of this long-term study the diversity of tools that can be applied to hypothesize about the factors influencing a species' social system. We are convinced that with the expansion of the number of social mammals for which comparably detailed socio-genetic long-term data are available, future comparative studies will provide deeper insights into the evolution of closed societies.