Catalysis in Reaction Networks

We define catalytic networks as chemical reaction networks with an essentially catalytic reaction pathway: one which is “on” in the presence of certain catalysts and “off” in their absence. We show that examples of catalytic networks include synthetic DNA molecular circuits that have been shown to perform signal amplification and molecular logic. Recall that a critical siphon is a subset of the species in a chemical reaction network whose absence is forward invariant and stoichiometrically compatible with a positive point. Our main theorem is that all weakly-reversible networks with critical siphons are catalytic. Consequently, we obtain new proofs for the persistence of atomic event-systems of Adleman et al., and normal networks of Gnacadja. We define autocatalytic networks, and conjecture that a weakly-reversible reaction network has critical siphons if and only if it is autocatalytic.     

Siphons and siphonal grooves in the digestive systems of the Echinoidea (Echinodermata)

Here we use histological sections and, to a limited extent, scanning electron microscopy to ascertain whether siphons or siphonal grooves parallel the stomach of five sea urchin species representing five higher taxa in the Echinoidea. We find a siphonal groove in Centrostephanus coronatus of the Diadematidae and in Caenopedina diomedeae of the Pedinidae; we find a siphon in Tromikosoma panamense of the Echinothurioida and in Strongylocentrotus purpuratus of the Camarodonta; and we find a hemisiphon in Aspidodiadema hawaiiense of the Aspidodiadematidae (it is currently unsettled whether this last group belongs in the Pedinoida or the Diadematoida). Several recent accounts of echinoid gut anatomy have claimed that species in the Echinothurioida have a siphonal groove instead of a siphon and that species in the Diadematidae and Pedinidae have siphons instead of siphonal grooves. The present work shows that these claims are mistakes and confirms that Holland and Ghiselin (1970) correctly described the distribution of siphons and siphonal grooves in the Echinoidea.     

Antagonism and bistability in protein interaction networks

A protein interaction network (PIN) is a set of proteins that modulate one another's activities by regulated synthesis and degradation, by reversible binding to form complexes, and by catalytic reactions (e.g., phosphorylation and dephosphorylation). Most PINs are so complex that their dynamical characteristics cannot be deduced accurately by intuitive reasoning alone. To predict the properties of such networks, many research groups have turned to mathematical models (differential equations based on standard biochemical rate laws, e.g., mass-action, Michaelis-Menten, Hill). When using Michaelis-Menten rate expressions to model PINs, care must be exercised to avoid making inconsistent assumptions about enzyme-substrate complexes. We show that an appealingly simple model of a PIN that functions as a bistable switch is compromised by neglecting enzyme-substrate intermediates. When the neglected intermediates are put back into the model, bistability of the switch is lost. The theory of chemical reaction networks predicts that bistability can be recovered by adding specific reaction channels to the molecular mechanism. We explore two very different routes to recover bistability. In both cases, we show how to convert the original 'phenomenological' model into a consistent set of mass-action rate laws that retains the desired bistability properties. Once an equivalent model is formulated in terms of elementary chemical reactions, it can be simulated accurately either by deterministic differential equations or by Gillespie's stochastic simulation algorithm.     

Computing weakly reversible linearly conjugate chemical reaction networks with minimal deficiency

Mass-action kinetics is frequently used in systems biology to model the behavior of interacting chemical species. Many important dynamical properties are known to hold for such systems if their underlying networks are weakly reversible and have a low deficiency. In particular, the Deficiency Zero and Deficiency One Theorems guarantee strong regularity with regards to the number and stability of positive equilibrium states. It is also known that chemical reaction networks with distinct reaction structure can admit mass-action systems with the same qualitative dynamics. The theory of linear conjugacy encapsulates the cases where this relationship is captured by a linear transformation. In this paper, we propose a mixed-integer linear programming algorithm capable of determining the minimal deficiency weakly reversible reaction network which admits a mass-action system which is linearly conjugate to a given reaction network.     

Relationship between extreme pathways and structurally minimal pathways

The determination of reaction pathways is one of the most important functions that should be performed in exploring the kinetics of catalyzed chemical reactions or biochemical reactions, the latter being generally catalyzed by enzymes. It is proven that the terms, “type-I extreme pathway” and “structurally minimal pathway”, both introduced to characterize the kinetics of a catalyzed reaction are equivalent. These two terms are based on two distinct methodologies, one mainly rooted in convex analysis and the other in graph theory. The equivalence promises further even more effective methods for reaction-pathway identification by synergistic integration of existing ones.     

Passive flow through an unstalked intertidal ascidian: orientation and morphology enhance suspension feeding in Pyura stolonifera

Passive flow is believed to increase the gains and reduce the costs of active suspension feeding. We used a mixture of field and laboratory experiments to evaluate whether the unstalked intertidal ascidian Pyura stolonifera exploits passive flow. We predicted that its orientation to prevailing currents and the arrangement of its siphons would induce passive flow due to dynamic pressure at the inhalant siphon, as well as by the Bernoulli effect or viscous entrainment associated with different fluid velocities at each siphon, or by both mechanisms. The orientation of P. stolonifera at several locations along the Sydney-Illawarra coast (Australia) covering a wide range of wave exposures was nonrandom and revealed that the ascidians were consistently oriented with their inhalant siphons directed into the waves or backwash. Flume experiments using wax models demonstrated that the arrangement of the siphons could induce passive flow and that passive flow was greatest when the inhalant siphon was oriented into the flow. Field experiments using transplanted animals confirmed that such an orientation resulted in ascidians gaining food at greater rates, as measured by fecal production, than when oriented perpendicular to the wave direction. We conclude that P. stolonifera enhances suspension feeding by inducing passive flow and is, therefore, a facultatively active suspension feeder. Furthermore, we argue that it is likely that many other active suspension feeders utilize passive flow and, therefore, measurements of their clearance rates should be made under appropriate conditions of flow to gain ecologically relevant results.     

Regeneration of lost siphon tissues in the tellinacean bivalve Nuttallia olivacea

The inhalant siphon of the tellinacean bivalve Nuttallia olivacea is an important prey item for juvenile stone flounder Platichthys bicoloratus in estuaries in Japan. We examined quantitative siphon regeneration of N. olivacea in rearing experiments of siphon-removed bivalves (> 30 mm shell length) both in the laboratory and in their natural habitat. Under laboratory conditions, siphon-removed bivalves regenerated lost tissues quantitatively at 15 and 25 °C 1 mo after siphon removal, although regeneration was incomplete. A 3-mo caging experiment in the field showed that great regeneration occurred in siphon-removed bivalves. However, the siphon weight of removed bivalves was significantly smaller than that of non-amputated bivalves, suggesting the incomplete regeneration. In a 1-mo caging experiment, bivalves that had approximately 15% of their siphons amputated were selected at some intervals to illustrate the quantitative regeneration process. Estimated daily siphon production was remarkably high only a few days after amputation. It decreased greatly thereafter, but regeneration was not completed within 30 d. These results indicate that bivalves regenerate siphons rapidly just after losing siphon tissues and then regeneration is slowed down before it is completed.     

Reaction routes in biochemical reaction systems: algebraic properties,validated calculation procedure and example from nucleotide metabolism

 Elementary flux modes (direct reaction routes) are minimal sets of enzymes that can operate at steady state, with all irreversible reactions used in the appropriate direction. They can be interpreted as component pathways of a (bio)chemical reaction network. Here, two different definitions of elementary modes are given and their equivalence is proved. Several algebraic properties of elementary modes are then presented and proved. This concerns, amongst other features, the minimal number of enzymes of the network not used in an elementary mode and the situations where irreversible reactions are replaced by reversible ones. Based on these properties, a refined algorithm is presented, and it is formally proved that this algorithm will exclusively generate all the elementary flux modes of an arbitrary network containing reversible or irreversible reactions or both. The algorithm is illustrated by a biochemical example relevant in nucleotide metabolism. The computer implementation in two different programming languages is discussed. Received: 1 January 2001 / Revised version: 17 December 2001 / Published online: 17 July 2002     

Pathology of acute poisoning with the insecticide Sevin in the bent-nosed clam, Macoma nasuta

Toxicity tests of 96-hr duration of the insecticide Sevin were done with adult bent-nosed clams, Macoma nasuta. Sevin concentrations of 15, 20, 25, and 30 mg/liter were used in duplicate tests. The criterion of “death” was the inability of clams to retract siphons or to close valves. About half of the animals so affected were removed from the test solutions and returned to clean sea water to observe if recovery occurred, and others were preserved for histological examination.No “dead” clams recovered within 96 hr after return to clean water. The histopathology consisted primarily of necrosis of epithelial tissue of the gill, mantle, siphon, and suprabranchial gland, and the severity of damage was directly related to the test concentrations. Vacuolization, rupture, and pycnosis of cells occurred. The gills were the most severely affected organs. Epithelial cells of the gill filaments bearing the frontal, laterofrontal, and lateral cilia were sloughed as early as 24 hr after the beginning of exposure to Sevin. About 50% of the exposed clams had lost one or both siphons and also the epithelia on still attached segments within 96 hr of exposure. There were no deaths of control clams, and their tissues were normal.     

Thermodynamics of Random Reaction Networks

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.     

Challenging the concept of "recycling" as a mechanism for the evolution of homochirality in chemical reactions

The concept that "recycling" of reactants may be key to the spontaneous generation of a homochiral state in closed autocatalytic reaction networks has recently been introduced and has been supported by computer simulations of such reaction networks. It has been suggested that unidirectional cycles maintained away from equilibrium may avoid the inevitable establishment of a racemic state, and under such conditions the explicit reverse reactions dictated by microscopic reversibility may be all be treated as having negligible rates. We show here that because the equilibrium constants in a recycled network are interdependent, it is not valid to neglect all reverse reactions simultaneously; a very low value for the rate constant of one reverse reaction in the network dictates that another reverse reaction in the same network will exhibit a large rate constant. This conclusion is general and applies to any closed mass system where the energy input is subject to microscopic reversibility. Therefore, chemical reversibility cannot be invoked as a mechanism for the evolution of a single chiral molecular state in thermally activated reactions.     

Translated Chemical Reaction Networks

Many biochemical and industrial applications involve complicated networks of simultaneously occurring chemical reactions. Under the assumption of mass action kinetics, the dynamics of these chemical reaction networks are governed by systems of polynomial ordinary differential equations. The steady states of these mass action systems have been analyzed via a variety of techniques, including stoichiometric network analysis, deficiency theory, and algebraic techniques (e.g., Gröbner bases). In this paper, we present a novel method for characterizing the steady states of mass action systems. Our method explicitly links a network’s capacity to permit a particular class of steady states, called toric steady states, to topological properties of a generalized network called a translated chemical reaction network. These networks share their reaction vectors with their source network but are permitted to have different complex stoichiometries and different network topologies. We apply the results to examples drawn from the biochemical literature.     

Tellegen's theorem for bond graphs its relevance to chemical networks

Amongst the available graph theories the one making use of “bond graphs” has been considered the most suitable in network thermodynamics for representing a wide range of physico-chemical processes in the form of networks.In this article a complete representation of chemical reactions, both far from- and near-equilibrium, by bond graphs, is proposed. In addition, a new proof of the Tellegen theorem is given, derived directly from the properties of bond graphs. A new insight into the general meaning of Tellegen's theorem in variable networks and its relevance to biological networks is thus provided. The structure of the network being represented by new elements — i.e. the junctions — in bond graphs, time variations of these elements have the meaning of changes in the structure itself, to that the Tellegen theorem appears as an invariance relation in networks where the structure is allowed to change.     

Recovery from Siphon Damage in Donax vittatus (Da Costa) (Bivalvia: Donacidae)

Between 2.5% and 18% of Donax vittatus from a natural populationon West Sands beach, St Andrews on the Scottish east coast showeddamage to the siphons caused by non-lethal predation by juvenileflatfishes. The percentage with damaged siphons was greatestin summer. Either inhalant or exhalant siphons were affected,in varying proportions, or in some cases, both siphons. In experimentalaquaria, Donax vittatus that suffered non-lethal attack by juvenileplaice which resulted in their removal from the sand, rapidlyresumed normal activity as evidenced by reburrowing. Wound healing,followed by re-differentiation of siphonal tentacles, took placerapidly following experimental amputation of siphon tips, withthe newly-formed tentacles appearing almost normal after 10days. Re-differentiation of the siphonal tentacles was accompaniedby the development of their complement of three types of ciliated senseorgans. (Received 11 May 1998; accepted 9 July 1998)     

Reaction networks and evolutionary game theory

The powerful mathematical tools developed for the study of large scale reaction networks have given rise to applications of this framework beyond the scope of biochemistry. Recently, reaction networks have been suggested as an alternative way to model social phenomena. In this “socio-chemical metaphor” molecular species play the role of agents’ decisions and their outcomes, and chemical reactions play the role of interactions among these decisions. From here, it is possible to study the dynamical properties of social systems using standard tools of biochemical modelling. In this work we show how to use reaction networks to model systems that are usually studied via evolutionary game theory. We first illustrate our framework by modeling the repeated prisoners’ dilemma. The model is built from the payoff matrix together with assumptions of the agents’ memory and recognizability capacities. The model provides consistent results concerning the performance of the agents, and allows for the examination of the steady states of the system in a simple manner. We further develop a model considering the interaction among Tit for Tat and Defector agents. We produce analytical results concerning the performance of the strategies in different situations of agents’ memory and recognizability. This approach unites two important theories and may produce new insights in classical problems such as the evolution of cooperation in large scale systems.     

As good as dead? Sublethal predation facilitates lethal predation on an intertidal clam

Although ecologists have speculated that sublethal predation can impact prey dynamics, consequences of these predator effects have seldom been experimentally tested. In soft‐sediment marine communities, fishes crop extended feeding siphons of buried clams, potentially causing clams to reduce their burial depth, thereby enhancing their susceptibility to excavating lethal predators. We simulated cropping of the confamilial clams, Protothaca staminea and Venerupis philippinarum, by removing the top 40% of siphons, which caused each species to burrow 33–50% shallower than conspecifics with intact siphons. To examine subsequent consequences of reduced burial depth, we exposed cropped and intact clams to natural levels of predation in the field. Because of a naturally longer siphon, Protothaca, even after cropping, remained at relatively safe burial depths. In contrast, siphon cropping nearly doubled the mortality rate of Venerupis. Thus, while sublethal predation facilitates lethal predation, this linkage depends on specific life history characteristics, even among ecologically similar species.     

Reconsidering Darwin’s “Several Powers”

Contemporary textbooks often define evolution in terms of the replication, mutation, and selective retention of DNA sequences, ignoring the contribution of the physical processes involved. In the closing line of The Origin of Species, however, Darwin recognized that natural selection depends on prior more basic living functions, which he merely described as life’s “several powers.” For Darwin these involved the organism’s capacity to maintain itself and to reproduce offspring that preserve its critical functional organization. In modern terms we have come to recognize that this involves the continual generation of complex organic molecules in complex configurations accomplished with the aid of persistent far-from-equilibrium chemical self-organizing and self-assembling processes. But reliable persistence and replication of these processes also requires constantly available constraints and boundary conditions. Organism autonomy further requires that these constraints and co-dependent dynamics are reciprocally produced, each by the other. In this paper I argue that the different constraint-amplifying dynamics of two or more self-organizing processes can be coupled so that they reciprocally generate each other’s critical supportive boundary conditions. This coupling is a higher-order constraint (which can be distributed among components or offloaded onto molecular structures) that effectively constitutes a sign vehicle “interpreted” by the synergistic dynamics of these co-dependent self-organizing process so that they reconstitute this same semiotic-dynamic relationship and its self-reconstituting potential in new substrates. This dynamical co-dependence constitutes Darwin’s “several powers” and is the basis of the biosemiosis that enables evolution.     

Neural mechanisms of persistent aggression

While aggression is often conceptualized as a highly stereotyped, innate behavior, individuals within a species exhibit a surprising amount of variability in the frequency, intensity, and targets of their aggression. While differences in genetics are a source of some of this variation across individuals (estimates place the heritability of behavior at around 25–30%), a critical driver of variability is previous life experience. A wide variety of social experiences, including sexual, parental, and housing experiences can facilitate “persistent” aggressive states, suggesting that these experiences engage a common set of synaptic and molecular mechanisms that act on dedicated neural circuits for aggression. It has long been known that sex steroid hormones are powerful modulators of behavior, and also, that levels of these hormones are themselves modulated by experience. Several recent studies have started to unravel how experience-dependent hormonal changes during adulthood can create a cascade of molecular, synaptic, and circuit changes that enable behavioral persistence through circuit level remodeling. Here, we propose that sex steroid hormones facilitate persistent aggressive states by changing the relationship between neural activity and an aggression “threshold”.