The emergence of complexity: science coming of age or science growing old?

The emergence of a new field of science called complexity theory has made an impact on the community of scientists as well as the general public. This brief tutorial takes a very special view of this. The thesis is that complexity science has grown out of a general lack of satisfaction with traditional scientific practices and their failure to find a way of capturing anything but a shadow of complex reality. In spite of the many impressive advances from science and technology, it is clear that the picture delivered of the world is that of a surrogate world populated by machines and mechanisms. The nature of the real world demands more than traditional science can deliver. Yet traditional science has constraints and bounds on its universe of discourse. Complexity science, as presented here, demands that the barriers and constraints be removed in order to gain a more complete view of nature. This tutorial presents a summary of what is entailed by this new methodology.

Network thermodynamics and complexity: a transition to relational systems theory.

Most systems of interest in today's world are highly structured and highly interactive. They cannot be reduced to simple components without losing a great deal of their system identity. Network thermodynamics is a marriage of classical and non-equilibrium thermodynamics along with network theory and kinetics to provide a practical framework for handling these systems. The ultimate result of any network thermodynamic model is still a set of state vector equations. But these equations are built in a new informative way so that information about the organization of the system is identifiable in the structure of the equations. The domain of network thermodynamics is all of physical systems theory. By using the powerful circuit simulator, the Simulation Program with Integrated Circuit Emphasis (SPICE), as a general systems simulator, any highly non-linear stiff system can be simulated. Furthermore, the theoretical findings of network thermodynamics are important new contributions. The contribution of a metric structure to thermodynamics compliments and goes beyond other recent work in this area. The application of topological reasoning through Tellegen's theorem shows that a mathematical structure exists into which all physical systems can be represented canonically. The old results in non-equilibrium thermodynamics due to Onsager can be reinterpreted and extended using these new, more holistic concepts about systems. Some examples are given. These are but a few of the many applications of network thermodynamics that have been proven to extend our capacity for handling the highly interactive, non-linear systems that populate both biology and chemistry. The presentation is carried out in the context of the recent growth of the field of complexity science. In particular, the context used for this discussion derives from the work of the mathematical biologist, Robert Rosen.

Complexity, communication between cells, and identifying the functional components of living systems: some observations.

The concept of 'complexity' has become very important in theoretical biology. It is a many faceted concept and too new and ill defined to have a universally accepted meaning. This review examines the development of this concept from the point of view of its usefulness as a criteria for the study of living systems to see what it has to offer as a new approach. In particular, one definition of complexity has been put forth which has the necessary precision and rigor to be considered as a useful categorization of systems, especially as it pertains to those we call 'living'. This definition, due to Robert Rosen, has been developed in a number of works and involves some deep new concepts about the way we view systems. In particular, it focuses on the way we view the world and actually practice science through the use of the modelling relation. This mathematical object models the process by which we assign meaning to the world we perceive. By using the modelling relation, it is possible to identify the subjective nature of our practices and deal with this issue explicitly. By so doing, it becomes clear that our notion of complexity and especially its most popular manifestations, is in large part a product of the historical processes which lead to the present state of scientific epistemology. In particular, it is a reaction to the reductionist/mechanistic view of nature which can be termed the 'Newtonian Paradigm'. This approach to epistemology has dominated for so that its use as a model has become implicit in most of what we do in and out of science. The alternative to this approach is examined and related to the special definition of complexity given by Rosen. Some historical examples are used to emphasize the dependence of our view of what is complex in a popular sense on the ever changing state of our knowledge. The role of some popular concepts such as chaotic dynamics are examined in this context. The fields of artificial life and related areas are also viewed from the perspective of this rigorous view of complexity and found lacking. The notion that in some way life exists 'at the edge of chaos' is examined from the perspective of the second law of thermodynamics given by Schneider and Kay. Finally, the casual elements in complex systems are explored in relation to complexity. Rosen has shown that a clear difference in causal relations exists between complex and simple systems and that this difference leads to a uniquely useful definition of what we mean by 'living'. Rosen makes it very clear that the class of systems which are complex is a much larger class than those which we call living. For that reason, the focus of this review will be on complexity as a stepping stone towards the deeper question of what makes a system alive.

Determining the transient kinetic behavior of complex multi-enzyme systems by use of network thermodynamics.

As an example of the application of network thermodynamics to the treatment of complicated enzymatic systems, we have studied the transient kinetic behavior of a sequence of five enzymatic reactions, four with Michaelis-Menten kinetics and the final one with sigmoid kinetics. The object was to determine how the time-courses of the concentrations of all the intermediate substrates involved, depend on the effect of forward activation by the first substrate on the final enzymatic step. The case with forward activation exhibited an unexpected behavior with a reversal of the direction of the reaction before reaching equilibrium. The solution of the set of five non-linear differential equations was achieved using the student version of the simulation package PSPICE. The same approach can be utilized to study the behavior of any type of complex multienzymatic system (steady-states, transients, oscillations, chaos), or of combinations of enzymatic reactions with transmembrane transport in compartmental systems.

A modified neural network model of tumor cell interactions and subpopulation dynamics.

Tumors consist of phenotypically heterogeneous subpopulations of cells which are frequently affected by both autocrine and paracrine factors. Applying concepts from neural network theory, we have developed a computer model of chemical communication among hypothetical tumor cells, which simulates some of the complex epigenetic behavior of real tumors. Deletion of subpopulations often destabilized the whole population. The impact of deletion of specific subpopulations was affected by (a) which subpopulation was deleted, and (b) the timing of the deletion during tumor progression.

Effect of direct suppression of thymidylate synthase at the 5,10-methylenetetrahydrofolate binding site on the interconversion of tetrahydrofolate cofactors to dihydrofolate by antifolates. Influence of degree of dihydrofolate reductase inhibition.

An important unresolved issue in antifolate pharmacology is the basis for the observation that the major portion of cellular tetrahydrofolate cofactors is preserved after dihydrofolate reductase activity is abolished by antifolates despite the fact that tetrahydrofolate cofactor-dependent purine and pyrimidine biosynthesis ceases. This has been attributed to feedback inhibition of thymidylate synthase by dihydrofolate polyglutamates that accumulate in the presence of antifolates. This report combines network thermodynamic modeling and experimental observations to evaluate the effects of direct inhibition of thymidylate synthase at the 5,10-methylenetetrahydrofolate binding site with a potent lipophilic quinazoline antifolate PD130883 on folate oxidation in cells. Computer simulations predict and the data indicate that marked PD130883 suppression of thymidylate synthase only slows the rate but not the extent of tetrahydrofolate cofactor interconversion to dihydrofolate upon complete suppression of dihydrofolate reductase with trimetrexate. These observations are consistent with earlier studies from this laboratory with fluorodeoxyuridine inhibition at the deoxyuridylate binding site. Hence, the much weaker inhibition by dihydrofolate polyglutamates at the level of thymidylate synthase cannot account for the apparent preservation of tetrahydrofolate cofactor pools in cells and has virtually no pharmacologic significance under conditions in which antifolates completely suppress dihydrofolate reductase. The extent of interconversion of tetrahydrofolate cofactors to dihydrofolate is strongly influenced by residual dihydrofolate reductase catalytic activity. Exposure of cells to 0.1 microM trimetrexate results in only approximately 60% of maximum dihydrofolate levels achieved when dihydrofolate reductase activity is abolished. Network thermodynamic simulations predict, and experiments verify, that inhibition of thymidylate synthase at the 5,10-methylenetetrahydrofolate site by PD130883, when dihydrofolate reductase is only partially suppressed (approximately 85%) with 0.1 microM trimetrexate, substantially decreases (31-47%) the net level of interconversion of tetrahydrofolate cofactors to dihydrofolate. Further computer simulations predict that under conditions in which residual dihydrofolate reductase activity persists within the cells (more than about 5%), feedback inhibitory effects of dihydrofolate polyglutamates as well as other weak inhibitors of thymidylate synthase can significantly limit the extent of net interconversion of tetrahydrofolate cofactors to dihydrofolate and produce an apparent "compartmentation phenomenon" in which tetrahydrofolate cofactor pools are preserved within the cell in the presence of antifolates. Residual dihydrofolate reductase activity cannot, however, account for the partial interconversion of tetrahydrofolate cofactors to dihydrofolate after exposure to high trimetrexate or methotrexate levels.(ABSTRACT TRUNCATED AT 400 WORDS)

Modeling intestinal absorption and other nutrition-related processes using PSPICE and STELLA.

In summary, SPICE models are constructed by translating a highly organized biological system into a network diagram by using a disciplined, systematic method for converting flows through barriers and chemical reactions into branches in a network connecting the compartments in the tissue according to the identity of the flowing entities. The first step in building a simulation model is essentially the same as the first step in learning about the method. Simple mechanisms are mastered first; and then as proficiency and understanding of the system grow, these can be connected and elaborated to produce simulations more closely approximating the real complexity of the living system. Other methods exist that may be easier to deal with initially, but often they cannot be utilized as generally as SPICE owing to their inherent limitations. One program available on Apple machines that has a high degree of user friendliness is STELLA. We will make some brief comparisons here, since STELLA is often an easier way to get started in simulation and often perfectly adequate for smaller problems.

Folate-pool interconversions and inhibition of biosynthetic processes after exposure of L1210 leukemia cells to antifolates. Experimental and network thermodynamic analyses of the role of dihydrofolate polyglutamylates in antifolate action in cells.

Folate analogs that inhibit dihydrofolate reductase result in only partial interconversion of tetrahydrofolate cofactors to dihydrofolate with preservation of the major portion of reduced cellular folate cofactors in L1210 leukemia cells. One possible explanation for this phenomenon is that low levels of dihydrofolate polyglutamates that accumulate in the presence of antifolates block thymidylate synthase to prevent depletion of reduced folate pools. This paper correlates biochemical analyses of rapid interconversions of radiolabeled folates and changes in purine and pyrimidine biosynthesis in L1210 murine leukemia cells exposed to antifolates with network thermodynamic computer modeling to assess this hypothesis. When cells are exposed to 1 microM trimetrexate there is an almost instantaneous inhibition of [3H] deoxyuridine or [14C]formate incorporation into nucleotides which is maximal within 5 min. This is associated with a rapid rise in cellular dihydrofolate (t1/2 approximately 1.5 min), which reaches a steady state that represents only 27.9% of the total folate pool. Pretreatment of cells with fluorodeoxyuridine, to inhibit thymidylate synthase by about 95% followed by trimetrexate only slows the rate of folate interconversion (t1/2 approximately 25 min) but not the final dihydrofolate level achieved. This is consistent with computer simulations which predict that direct inhibition of thymidylate synthase by 97, 98, and 99% should increase the half-time of dihydrofolate rise after trimetrexate to 40, 60, and 124 min, respectively, but the final level achieved is always the same as in cells with normal thymidylate synthase activity. The data reflect the high degree of catalytic activity of thymidylate synthase relative to tetrahydrofolate cofactor pools in the cells and the enormous extent of inhibition of this enzyme that is necessary to slow the rate of folate interconversions after addition of antifolates. The model predicts, and the data demonstrate, that virtually any residual thymidylate synthase activity will permit the interconversion of all tetrahydrofolate cofactors available for oxidation to dihydrofolate when dihydrofolate reductase activity is abolished, but the rate of interconversion will be slowed. Additional simulations indicate that the time course of cessation of tetrahydrofolate-dependent purine and pyrimidine biosynthesis after antifolates in these cells can be accounted for solely on the basis of tetrahydrofolate cofactor depletion alone. These data exclude the possibility that direct inhibition of thymidylate synthase by dihydrofolate polyglutamates, or any other intracellular folates that accumulate in cells after antifolates, can account for the rapid but partial interconversion of reduced folate cofactors to dihydrofolate.(ABSTRACT TRUNCATED AT 400 WORDS)

Network thermodynamic analysis and stimulation of isotonic solute-coupled volume flow in leaky epithelia: an example of the use of network theory to provide the qualitative aspects of a complex system and its verification by stimulation.

A network thermodynamic model was developed to provide insights into the nature of isotonic solute-coupled volume flow in "leaky" epithelia, where the transepithelial volume flow is assumed to be primarily through the cellular pathway. The coupled flows of solute and volume at each membrane in this four membrane model are described by the practical phenomenological equations as developed by Kedem & Katchalsky (1958). The model contains one permeable non-electrolyte solute (s) and a fixed amount of an impermeable non-electrolyte (i) inside the cell. The cell is assumed to be capable of volume regulation under the steady-state experimental conditions simulated. A solute-pump, located in the basolateral membrane, uses feedback regulation to adjust Cs in the cell in order to maintain cell volume at or near control levels in all simulations. Model behavior is, in general, very consistent with experimental observations with respect to tonicity and magnitude of volume flow over a wide range of experimental conditions. Examination of the parameter space suggests the following important features when isotonic solute-coupled volume flow moves primarily through the cellular pathway: (1) the apical membrane reflection coefficient must be less than that of the basolateral membrane; (2) the basement membrane reflection coefficient must be small; (3) the apical membrane solute permeability and reflection coefficient are the two most "sensitive" parameters and need to vary in an inverse manner in order to maintain isotonicity when both solute and volume flows increase; and (4) relationships (1) and (3) above imply the need for at least two separate solute pathways in the apical membrane, one that is shared with volume flow and one that is not.

Exploration of apical sodium transport mechanisms in an epithelial model by network thermodynamic simulation of the effect of mucosal sodium depletion: I. Comparison of three different apical sodium permeability expressions.

A model based on that of Koefoed-Johnsen & Ussing (1958) and elaborated by Hviid Larsen (1978) and Lew et al. (1979), is designed using network thermodynamic theory and used to simulate experiments performed on epithelia. Three different expressions for the apical sodium permeability are tested for their ability to reproduce the saturation of the short-circuit current with increasing mucosal sodium concentration. Using the parameters from the previous models, the sodium entry step is shown to be the rate limiting step. If the apical sodium permeability is constant, there is no saturation of the short-circuit current with increasing mucosal sodium. The saturation of the short-circuit current is simulated with versions of the model which include a variable apical sodium permeability. The phenomenological expressions used for the variable permeabilities are those proposed by Fuchs et al. (1977) and Civan & Bookman (1982). They describe the so-called feedback effect of the mucosal and intracellular sodium concentrations.

Exploration of apical sodium transport mechanisms in an epithelial model by network thermodynamic simulation of the effect of mucosal sodium depletion: II. An apical sodium channel and amiloride blocking.

This paper is the second part of a modeling study on apical sodium transport mechanisms in tight epithelia. In the first part (this issue) we explored three expressions for the apical membrane sodium permeability (PapNa) and showed that only a PapNa which varies as a function of sodium concentration allows simulation of the well known saturation of the short-circuit current with increasing mucosal sodium concentration. However, the ad hoc expressions used have no mechanistic interpretation. We show here that if, instead of an ad hoc expression, one includes a one-site, two-barrier sodium channel in the apical membrane, the model also simulates this saturation. In addition, the equivalent apical sodium permeability computed from the simulations appears to be very similar to the phenomenological equation used by Fuchs et al. (1977) to fit the decrease of the apical sodium permeability with increasing mucosal sodium. The apical sodium channel simulated here is thus a possible mechanism for the feedback effect of the mucosal and intracellular sodium concentrations on the apical sodium permeability. This channel also allows the simulation of the competitive inhibition of the sodium current by amiloride, and the concomitant inhibition of the apical sodium permeability.

Role of topology in bioenergetics of sodium transport in complex epithelia.

There has been some controversy as to whether in sodium-transporting epithelia (e.g., frog skin, toad urinary bladder) the Na-O2 ratio is independent of the net rate of transepithelial sodium transport or remains constant over a wide range of transport rates. This computer simulation study shows that both views are defensible, depending on whether one wishes to exclude or include "static head" energy in the calculations. This energy arises from intramembrane sodium recirculation, as shown here when applying a multicompartment epithelial membrane model. Assuming reasonable kinetic parameters of a transport model whose sodium transport rate is varied over a wide range by a step-by-step simulated amiloride action, the computations have shown the following. When static head energy (O2 consumption) is excluded from the calculations, the Na-O2 ratio is constant over a wide range of transepithelial sodium flux, up to the tested value of 20 neq X cm-2 X min-1, a "normal" value found in frog skin. The Na-O2 ratios were 19.4 and 28.7 in low- and high-sodium models, respectively. If the static head energy is included in the calculations, the Na-O2 ratios increase with increasing transport rate from zero values to values up to 15.7. These data are in good agreement with laboratory results, as are derived data on phenomenological coefficients and thermodynamic coupling coefficients (LNa = 80, 128; LNa,r = 4.4; Lr = 0.27, 0.58; q = 0.50, 0.90, depending on the chosen model parameters).

Network thermodynamic modeling of hormone regulation of active Na+ transport in cultured renal epithelium (A6).

A network thermodynamic model was developed to describe steady-state ion flows (Na+,K+, and Cl-) and related electrical events in a cultured renal epithelium (A6) derived from toad kidney. Three hypotheses for explaining the steady-state increases in short-circuit current (SCC) produced by aldosterone and/or insulin were examined using the model. Changing only the number of basolateral Na+-K+ pumps produced virtually no change in SCC and was ruled out. Changing only the number of apical Na+ channels could produce sufficient increases in SCC but presented problems in the pattern of changes produced in cell ion concentrations and therefore appeared unlikely. Changing both apical and basolateral parameters in a balanced, coordinated manner produced the maximal changes in SCC with the minimal changes in cell ion concentrations and appeared to be the "best" hypothesis. In addition, it was found necessary for tight junction permeability to increase as active Na+ transport increased under open-circuit conditions. Simulations, using these results, compared favorably with experimental data on the stimulatory effects of aldosterone and insulin, both separately and together, on active Na+ transport.

Compartmental analysis of the Na+ flux ratio with application to data on frog skin epidermis.

In this computer simulation study, the role of the topological factor on the Na+ influx/backflux (efflux) ratio in multicompartmental model membranes with active Na+ transport has been investigated. As in the classical "three compartment model", so also in multicompartment models with series order of compartments (series topology), the flux ratios are time-independent. By contrast, in models with series-parallel order of compartments (series-parallel topology), inclusive shunt pathways, the flux ratios are time-dependent. The values of the ratios can increase, or decrease with time, reaching steady state values, depending on the nature of the chosen topology. In a similar manner, the apparent value of the driving force, ENa, of the Na+-pumps, calculated from the Ussing-Teorell flux ratio equation and using global flux ratios, can vary in models with series-parallel topology. This is not the case in models with series topology. On the other hand, the true value of the driving forces of the Na+ pumps, calculated from local flux ratios, are higher, and time-independent. In the absence of Na+ pumps (simulated ouabain effect) the flux ratios have in all cases the values of 1.0. These theoretical results are in good agreement with the theoretical results recently published by Sten-Knudsen & Ussing (1981) whose analysis utilized principles differing from those used here. In the design of the multicompartment model and the choice of kinetic parameters, frog skin epidermis served as a guide, such that simulated outputs closely agreed with experimental data in the literature. This includes the realization of a "fast" paracellular, and a "slow" cellular pathway for transepidermal flow of Na+.

Regulatory aspects of Na+ transport in complex epithelia (frog skin).

In the multilayered epithelial membranes, topological factors, in addition to factors operating in cell units, must be considered in the regulation of ion transport. One such factor, i.e., the role of cell-to-cell junctions as regulators, is considered in the present computer simulation study. The primary aim was to correlate electron microprobe data on cellular Na+ pool sizes of frog skin with well-known rates of transepidermal Na+ influx and efflux under several laboratory conditions, including single or combined application of ouabain and amiloride. A complete kinetic analysis of data obtained on a simplified multicompartmental model of the epidermis suggests, on purely topological grounds, the occurrence in the epidermis of multiple physiological steady states in which Na+ is pumped transepidermally at equal rates but associated with very different states of intercellular Na+ flow dynamics. The possible significance of these multiple states for the understanding of the responses of the epidermis to perturbing influences is discussed.

Network thermodynamics: a candidate for a common language for theoretical and experimental biology.

Effective interaction between theory and experimentation in biology requires that there be a common language, which workers in both areas understand. Because the backgrounds of biomedical researchers are often more descriptive than quantitative, it would be useful to have a diagrammatic method for defining models of systems that would easily translate into a rigorous quantitative description susceptible to computer simulation. Network thermodynamics is the next logical step in the evolution of thermodynamic thinking and meets these criteria. Network thermodynamics has already begun to be used in a variety of areas in experimental biology and is accessible to direct use by the experimenter. Network thermodynamics is not restricted by the traditional constraints on classical and nonequilibrium thermodynamics, such as reversibility, linearity, nearness to equilibrium, etc. Since living systems are inherently hierarchical in their nature, the network approach incorporates this feature in a natural way and, in a sense, supplies the "missing link" between traditional physics and chemistry and the vitalists' concern for the complexity of living systems. In the future, the use of a common language for theoretical and experimental biology should result in an increased understanding of human biology by the scientific community.

Glucose utilization in rat adipocytes. The interaction of transport and metabolism as affected by insulin.

The relative contributions of transport and intracellular metabolism of glucose to the control of overall glucose utilization were evaluated in rat adipocytes. Transport of 3-O-methylglucose and hexokinase activity in crude homogenates were measured and the derived kinetic parameters incorporated into network thermodynamic computer simulations. Hexokinase was found to be inhibited in a fully noncompetitive pattern by glucose 6-phosphate (Ki = 0.46 mM). When this feature was incorporated into the computer simulations, they reflected measured rates of overall glucose utilization as well as intracellular glucose 6-phosphate concentrations, both in the presence and absence of insulin. The effect of the hormone was represented in the simulations solely by an increase in the number of hexose carriers. A predominant stimulation of transport rather than metabolism was also suggested by the finding that intracellular glucose concentrations assessed by glucose-induced 3-O-methylglucose counter-transport were higher in the presence than in the absence of insulin over a wide range of extracellular glucose concentrations. Nevertheless, it was also found that insulin induced a significant countertransport gradient while the oxidant H2O2 did not, which suggests that insulin-stimulated metabolism does increase overall glucose utilization independently of effects on transport. These studies show that the kinetic patterns of basal and insulin-stimulated glucose utilization in adipocytes may be generated simply by coupling transport and phosphorylation steps and providing for inhibition of the latter by accumulated glucose 6-phosphate.

A network thermodynamic approach to the Hill-King and Altman approach to kinetics: computer simulation.

The network simulation of kinetic systems is a rather painless way to produce dynamic analogs of these models without becoming involved in needless mathematical difficulty. The methods of King and Altman, Hill, Mason, and others fall into a universal paradigm applicable in both the kinetic and thermodynamic coordinate systems. (It is a small extra step to turn the state concentrations into chemical potentials and affinities using diode subcircuits during any simulation. This will be spelled out in detail in future work. Thus the simulation can be carried out using the exact kinetic rate laws, but the results are readily put into a form which allows the energetics to be analyzed as well). Another virtue of network modeling and simulation is the hierarchical nature of the networks and its correspondence to that of the living system. It is now possible to simulate complicated multicellular epithelial membranes with channels and/or carriers in certain selected cell membranes. The only limitation to progress in this area is the lack of experimental information to feed into the models. On the other hand, the network models are rapidly becoming an indispensable aid in experimental design for precisely this reason. Living systems have always been characterized by their morphology to a great extent. There is no reason why that morphology can be ignored as their function is analyzed. In the past, it often had to be simplified due to the weakness of the analytical tools available. Now, by utilizing the same methods that have caused an explosion of progress in electronics, it is possible to hope to understand the structure-function relationship of living systems with equal facility. The challenge remaining is to develop experimental techniques which will keep up with the demand for information generated by the models.

The simple model of adipocyte hexose transport. Kinetic features, effect of insulin, and network thermodynamic computer simulations.

Kinetic studies of the rat adipocyte hexose transport system were performed using the integrated rate approach and these compared to the simple carrier model of transport. Equilibrium exchange 3-O-methylglucose entry and exit studies showed directional symmetry with Km = overall dissociation constants = 8-10 mM. Comparison of zero-trans and equilibrium exchange entry also revealed similar Km and Vmax values. Insulin pretreatment increased the maximal rate of transport at 20 mM 3-O-methylglucose about 5- to 6-fold with each procedure. Studies of glucose-induced steady state 3-O-methylglucose countertransport provided evidence that carrier permeability and not carrier-substrate dissociation was rate limiting for overall transport. These data, therefore, indicate equal mobility of the loaded and unloaded carriers. Network thermodynamic computer simulations of the simple carrier model using kinetic parameters derived from zero-trans experiments provided good fits of actual data. The effect of insulin was best represented by an increase in total number of carrier units. It is concluded that the adipocyte hexose carrier displays bidirectional symmetry, limitation of transport by carrier movement rather than substrate-carrier interaction, equal rates of movement of loaded and unloaded carriers, and adherence to a simple carrier model in which insulin increases the total number of carrier units.