Autocatalytic Sets and Biological Specificity

A universal feature of the biochemistry of any living system is that all the molecules and catalysts that are required for reactions of the system can be built up from an available food source by repeated application of reactions from within that system. RAF (reflexively autocatalytic and food-generated) theory provides a formal way to study such processes. Beginning with Kauffman’s notion of “collectively autocatalytic sets,” this theory has been further developed over the last decade with the discovery of efficient algorithms and new mathematical analysis. In this paper, we study how the behaviour of a simple binary polymer model can be extended to models where the pattern of catalysis more precisely reflects the ligation and cleavage reactions involved. We find that certain properties of these models are similar to, and can be accurately predicted from, the simple binary polymer model; however, other properties lead to slightly different estimates. We also establish a number of new results concerning the structure of RAFs in these systems.     

A stochastic model of autocatalytic reaction networks

Autocatalytic cycles are rather widespread in nature and in several theoretical models of catalytic reaction networks their emergence is hypothesized to be inevitable when the network is or becomes sufficiently complex. Nevertheless, the emergence of autocatalytic cycles has been never observed in wet laboratory experiments. Here, we present a novel model of catalytic reaction networks with the explicit goal of filling the gap between theoretical predictions and experimental findings. The model is based on previous study of Kauffman, with new features in the introduction of a stochastic algorithm to describe the dynamics and in the possibility to increase the number of elements and reactions according to the dynamical evolution of the system. Furthermore, the introduction of a temporal threshold allows the detection of cycles even in our context of a stochastic model with asynchronous update. In this study, we describe the model and present results concerning the effect on the overall dynamics of varying (a) the average residence time of the elements in the reactor, (b) both the composition of the firing disk and the concentration of the molecules belonging to it, (c) the composition of the incoming flux.     

Random biochemical networks: the probability of self-sustaining autocatalysis

We determine conditions under which a random biochemical system is likely to contain a subsystem that is both autocatalytic and able to survive on some ambient 'food' source. Such systems have previously been investigated for their relevance to origin-of-life models. In this paper we extend earlier work, by finding precisely the order of catalysation required for the emergence of such self-sustaining autocatalytic networks. This answers questions raised in earlier papers, yet also allows for a more general class of models. We also show that a recently described polynomial-time algorithm for determining whether a catalytic reaction system contains an autocatalytic, self-sustaining subsystem is unlikely to adapt to allow inhibitory catalysation--in this case we show that the associated decision problem is NP-complete.     

A multi-scaled approach for simulating chemical reaction systems

In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge–Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.     

Dynamics of intracellular information decoding

A variety of cellular functions are robust even to substantial intrinsic and extrinsic noise in intracellular reactions and the environment that could be strong enough to impair or limit them. In particular, of substantial importance is cellular decision-making in which a cell chooses a fate or behavior on the basis of information conveyed in noisy external signals. For robust decoding, the crucial step is filtering out the noise inevitably added during information transmission. As a minimal and optimal implementation of such an information decoding process, the autocatalytic phosphorylation and autocatalytic dephosphorylation (aPadP) cycle was recently proposed. Here, we analyze the dynamical properties of the aPadP cycle in detail. We describe the dynamical roles of the stationary and short-term responses in determining the efficiency of information decoding and clarify the optimality of the threshold value of the stationary response and its information-theoretical meaning. Furthermore, we investigate the robustness of the aPadP cycle against the receptor inactivation time and intrinsic noise. Finally, we discuss the relationship among information decoding with information-dependent actions, bet-hedging and network modularity.     

Aggregation risk prediction for antibodies and its application to biotherapeutic development

Aggregation is a common problem affecting biopharmaceutical development that can have a significant effect on the quality of the product, as well as the safety to patients, particularly because of the increased risk of immune reactions. Here, we describe a new high-throughput screening algorithm developed to classify antibody molecules based on their propensity to aggregate. The tool, constructed and validated on experimental aggregation data for over 500 antibodies, is able to discern molecules with a high aggregation propensity as defined by experimental criteria relevant to bioprocessing and manufacturing of these molecules. Furthermore, we show how this tool can be combined with other computational approaches during early drug development to select molecules with reduced risk of aggregation and optimal developability properties.     

Modelling autocatalytic networks with artificial microbiology

Cells can usefully be equated to autocatalytic networks that increase in mass and then divide. To begin to model relationships between autocatalytic networks and cell division, we have written a program of artificial chemistry that simulates a cell fed by monomers. These monomers are symbols that can be assembled into linear (non-branched) polymers to give different lengths. A reaction is catalysed by a particular polymer or 'enzyme' that may itself be a reactant of that reaction (autocatalysis). These reactions are only studied within the confines of the 'cell' or 'reaction chamber'. There is a flux of material through the cell and eventually the mass of polymers reaches a threshold at which we analyse the cell. Our results indicate a similarity between the connectivity of the reaction network and that of real metabolic networks. Developing the model will entail attributing increased probabilities of reactions to polymers that are colocalised to evaluate the consequences of the dynamics of large assemblies of diverse molecules (hyperstructures) and of cell division.     

Aggregation risk prediction for antibodies and its application to biotherapeutic development

Aggregation is a common problem affecting biopharmaceutical development that can have a significant effect on the quality of the product, as well as the safety to patients, particularly because of the increased risk of immune reactions. Here, we describe a new high-throughput screening algorithm developed to classify antibody molecules based on their propensity to aggregate. The tool, constructed and validated on experimental aggregation data for over 500 antibodies, is able to discern molecules with a high aggregation propensity as defined by experimental criteria relevant to bioprocessing and manufacturing of these molecules. Furthermore, we show how this tool can be combined with other computational approaches during early drug development to select molecules with reduced risk of aggregation and optimal developability properties.     

Oscillating reactions in open systems

The probable existence of oscillating chemical reactions has been attracting some interest in recent years for their possible role in explaining certain biological phenomena. Perhaps the simplest model of oscillating reactions is that of Lotka (1910), which consists of a chain of autocatalytic reactions. Two “reactor systems” in which such a chain of reactions could take place are considered in this work and are called homogeneous and compartmental models, respectively. The differential equations governing the temporal behavior of the reacting species are solved on an analog computer, and the conditions under which sustained oscillations occur are obtained and discussed. Comparisons of the solution obtained in the two models are discussed.     

The origin of large molecules in primordial autocatalytic reaction networks

Large molecules such as proteins and nucleic acids are crucial for life, yet their primordial origin remains a major puzzle. The production of large molecules, as we know it today, requires good catalysts, and the only good catalysts we know that can accomplish this task consist of large molecules. Thus the origin of large molecules is a chicken and egg problem in chemistry. Here we present a mechanism, based on autocatalytic sets (ACSs), that is a possible solution to this problem. We discuss a mathematical model describing the population dynamics of molecules in a stylized but prebiotically plausible chemistry. Large molecules can be produced in this chemistry by the coalescing of smaller ones, with the smallest molecules, the 'food set', being buffered. Some of the reactions can be catalyzed by molecules within the chemistry with varying catalytic strengths. Normally the concentrations of large molecules in such a scenario are very small, diminishing exponentially with their size. ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population. However to reach these steady states from initial conditions that contain only the food set typically requires very large catalytic strengths, growing exponentially with the size of the catalyst molecule. We present a solution to this problem by studying 'nested ACSs', a structure in which a small ACS is connected to a larger one and reinforces it. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size (e.g., as a power law), a sparse subset of molecules including some very large molecules can come to dominate the system.     

Netscan: a procedure for generating reaction networks by size

In this paper, we describe an algorithm which can be used to generate the collection of networks, in order of increasing size, that are compatible with a list of chemical reactions and that satisfy a constraint. Our algorithm has been encoded and the software, called Netscan, can be freely downloaded from ftp://ftp.stat.ubc.ca/pub/riffraff/Netscanfiles, along with a manual, for general scientific use. Our algorithm may require pre-processing to ensure that the quantities it acts on are physically relevant and because it outputs sets of reactions, which we call canonical networks, that must be elaborated into full networks.     

Evolution of Autocatalytic Sets in Computational Models of Chemical Reaction Networks

Several computational models of chemical reaction networks have been presented in the literature in the past, showing the appearance and (potential) evolution of autocatalytic sets. However, the notion of autocatalytic sets has been defined differently in different modeling contexts, each one having some shortcoming or limitation. Here, we review four such models and definitions, and then formally describe and analyze them in the context of a mathematical framework for studying autocatalytic sets known as RAF theory. The main results are that: (1) RAF theory can capture the various previous definitions of autocatalytic sets and is therefore more complete and general, (2) the formal framework can be used to efficiently detect and analyze autocatalytic sets in all of these different computational models, (3) autocatalytic (RAF) sets are indeed likely to appear and evolve in such models, and (4) this could have important implications for a possible metabolism-first scenario for the origin of life.     

The autocatalytic step is an integral part of the hydrogenase cycle

We earlier proved the involvement of an autocatalytic step in the oxidation of H₂ by HynSL hydrogenase from Thiocapsa roseopersicina, and demonstrated that two enzyme forms interact in this step. Using a modified thin-layer reaction chamber which permits quantitative analysis of the concentration of the reaction product (reduced benzyl viologen) in the reaction volume during the oxidation of H₂, we now show that the steady-state concentration of the product displays a strong enzyme concentration dependence. This experimental fact can be explained only if the previously detected autocatalytic step occurs inside the catalytic enzyme-cycle and not in the enzyme activation process. Consequently, both interacting enzyme forms should participate in the catalytic cycle of the enzyme. As far as we are aware, this is the first experimental observation of such a phenomenon resulting in an apparent inhibition of the enzyme. It is additionally concluded that the interaction of the two enzyme forms should result in a conformational change in the enzyme–substrate form. This scheme is very similar to that of prion reactions. Since merely a few molecules are involved at some point of the reaction, this process is entirely stochastic in nature. We have therefore developed a stochastic calculation method, calculations with which lent support to the conclusion drawn from the experiment.     

An Auto-Catalytic Surface for Conformational Replication of Amyloid Fibrils—Genesis of an Amyloid World?

Amyloid fibrils are composed of self assembled stacked peptide or protein molecules folded and trapped in a stable cross-beta-sheet conformation. The amyloid fibrillation mechanism represents an intriguing self-catalyzed process rendering replication of a molecular conformational memory of interest for prebiotic chemistry. Herein we describe how a solid surface can be rendered auto-catalytic for fibrillation of a protein solution. We have discovered that a hydrophobic silicon or glass surface can be made to continuously fibrillate solutions of insulin monomers under stressed conditions (pH 1.6, 65°C). It was found that the surface acts as a platform for the formation of nascent seeds that induce fibril replication on and at the surface. This autocatalytic effect stems from a layer a few insulin molecules thick representing an oligomeric layer of misfolded, conformationally trapped, insulin molecules that rapidly through epitaxial growth catalyze the rate determining step (nucleation) during fibril replication. This autocatalytic layer is generated by the protein-solid surface interaction and conformational changes of the adsorbed protein during exposure at the air-water interface. The resulting autocatalytic surface thus both initiates local conformational molecular self-replication and acts as a reservoir for fibril seeds budding off into solution spreading fibril replication entities to the surrounding medium. The possibility of catalysis of the conformational replication process by minute amounts of nucleation sites located on a recruiting surface can evade the issue of dramatic concentration dependence of amyloidogenesis.     

A Structural and Functional Comparison Between Infectious and Non-Infectious Autocatalytic Recombinant PrP Conformers

Infectious prions contain a self-propagating, misfolded conformer of the prion protein termed PrP^Sc. A critical prediction of the protein-only hypothesis is that autocatalytic PrP^Sc molecules should be infectious. However, some autocatalytic recombinant PrP^Sc molecules have low or undetectable levels of specific infectivity in bioassays, and the essential determinants of recombinant prion infectivity remain obscure. To identify structural and functional features specifically associated with infectivity, we compared the properties of two autocatalytic recombinant PrP conformers derived from the same original template, which differ by >10⁵-fold in specific infectivity for wild-type mice. Structurally, hydrogen/deuterium exchange mass spectrometry (DXMS) studies revealed that solvent accessibility profiles of infectious and non-infectious autocatalytic recombinant PrP conformers are remarkably similar throughout their protease-resistant cores, except for two domains encompassing residues 91-115 and 144-163. Raman spectroscopy and immunoprecipitation studies confirm that these domains adopt distinct conformations within infectious versus non-infectious autocatalytic recombinant PrP conformers. Functionally, in vitro prion propagation experiments show that the non-infectious conformer is unable to seed mouse PrP^C substrates containing a glycosylphosphatidylinositol (GPI) anchor, including native PrP^C. Taken together, these results indicate that having a conformation that can be specifically adopted by post-translationally modified PrP^C molecules is an essential determinant of biological infectivity for recombinant prions, and suggest that this ability is associated with discrete features of PrP^Sc structure.     

Quantification of Interactions between Dynamic Cellular Network Functionalities by Cascaded Layering

Large, naturally evolved biomolecular networks typically fulfil multiple functions. When modelling or redesigning such systems, functional subsystems are often analysed independently first, before subsequent integration into larger-scale computational models. In the design and analysis process, it is therefore important to quantitatively analyse and predict the dynamics of the interactions between integrated subsystems; in particular, how the incremental effect of integrating a subsystem into a network depends on the existing dynamics of that network. In this paper we present a framework for simulating the contribution of any given functional subsystem when integrated together with one or more other subsystems. This is achieved through a cascaded layering of a network into functional subsystems, where each layer is defined by an appropriate subset of the reactions. We exploit symmetries in our formulation to exhaustively quantify each subsystem’s incremental effects with minimal computational effort. When combining subsystems, their isolated behaviour may be amplified, attenuated, or be subject to more complicated effects. We propose the concept of mutual dynamics to quantify such nonlinear phenomena, thereby defining the incompatibility and cooperativity between all pairs of subsystems when integrated into any larger network. We exemplify our theoretical framework by analysing diverse behaviours in three dynamic models of signalling and metabolic pathways: the effect of crosstalk mechanisms on the dynamics of parallel signal transduction pathways; reciprocal side-effects between several integral feedback mechanisms and the subsystems they stabilise; and consequences of nonlinear interactions between elementary flux modes in glycolysis for metabolic engineering strategies. Our analysis shows that it is not sufficient to just specify subsystems and analyse their pairwise interactions; the environment in which the interaction takes place must also be explicitly defined. Our framework provides a natural representation of nonlinear interaction phenomena, and will therefore be an important tool for modelling large-scale evolved or synthetic biomolecular networks.     

Kinetic analysis of artificial peptide self-replication. Part II: the heterochiral case

A kinetic model has been designed to describe and to analyze the stereoselective behavior of a recently discovered heterochiral template-directed peptide self-replicator by Ghadiri and co-workers [Nature 409 (2001) 797-801]. It turned out that previous assumptions stating that exclusively homochiral species participate in a stereoselective and autocatalytic pathway and that heterochiral species originate only from uncatalyzed background reactions could not be validated by our model. On the contrary, excellent fitting of experimental data indicated that the whole combinatorial variety of possible cross-catalytic processes involving L- and D- peptide species play an important role and need to be taken into account. The system shows no net creation of chiral matter but only a redistribution of the initially present chiral material. Both, the separation of an optically inactive meso-type template dimer and a slight chiroselective autocatalytic effect, contribute to a predicted amplification of enantiomeric excess that, in some cases, can simultaneously result in a substantial amount of optically active matter.     

Linear systems approach to analysis of complex dynamic behaviours in biochemical networks

Central functions in the cell are often linked to complex dynamic behaviours, such as sustained oscillations and multistability, in a biochemical reaction network. Determination of the specific mechanisms underlying such behaviours is important, e.g. to determine sensitivity, robustness, and modelling requirements of given cell functions. In this work we adopt a systems approach to the analysis of complex behaviours in intracellular reaction networks, described by ordinary differential equations with known kinetic parameters. We propose to decompose the overall system into a number of low complexity subsystems, and consider the importance of interactions between these in generating specific behaviours. Rather than analysing the network in a state corresponding to the complex non-linear behaviour, we move the system to the underlying unstable steady state, and focus on the mechanisms causing destabilisation of this steady state. This is motivated by the fact that all complex behaviours in unforced systems can be traced to destabilisation (bifurcation) of some steady state, and hence enables us to use tools from linear system theory to qualitatively analyse the sources of given network behaviours. One important objective of the present study is to see how far one can come with a relatively simple approach to the analysis of highly complex biochemical networks. The proposed method is demonstrated by application to a model of mitotic control in Xenopus frog eggs, and to a model of circadian oscillations in Drosophila. In both examples we are able to identify the subsystems, and the related interactions, which are instrumental in generating the observed complex non-linear behaviours.