Large scale chemical reaction networks are a ubiquitous phenomenon, from the metabolism of living cells to processes in planetary atmospheres and chemical technology. At least some of these networks exhibit distinctive global features such as the “small world” behavior. The systematic study of such properties, however, suffers from substantial sampling biases in the few networks that are known in detail. A computational model for generating them is therefore required. Here we present a Toy Model that provides a consistent framework in which generic properties of extensive chemical reaction networks can be explored in detail and that at the same time preserves the “look-and-feel” of chemistry:  Molecules are represented as labeled graphs, i.e., by their structural formulas; their basic properties are derived by a caricature version of the Extended Hückel MO theory that operates directly on the graphs; chemical reaction mechanisms are implemented as graph rewriting rules acting on the structural formulas; reactivities and selectivities are modeled by a variant of the Frontier Molecular Orbital Theory based on the Extended Hückel scheme. The approach is illustrated for two types of reaction networks:  Diels−Alder reactions and the formose reaction implicated in prebiotic sugar synthesis.

<p>Biochemical reaction networks with a sufficiently large number of molecules may be represented as systems of differential equations. Many networks receive inputs that fluctuate continuously in time. These networks may never settle down to a static equilibrium and are of great interest both mathematically and biologically. Biological systems receive inputs that vary on multiple time scales. Hormonal and neural inputs vary on a scale of seconds or minutes; inputs from meals and circadian rhythms vary on a scale of hours or days; and long term environmental changes (such as diet, disease, and pollution) vary on a scale of years. In this thesis, we consider the limiting behavior of networks in which the input is on a different time scale compared to the reaction kinetics within the network.</p> <p>We prove analytic results of how the variance of reaction rates within a system compares to the variance of the input when the input is on a different time scale than the reaction kinetics within the network. We consider the behavior of simple chains, single species complex networks, reversible chains, and certain classes of non-linear systems with time-scaled stochastic input, as the input speeds up and slows down. In all cases, as the input fluctuates more and more quickly, the variance of species within the system approaches to zero. As the input fluctuates more and more slowly, the variance of the species approaches the variance of the input, up to a normalization factor.</p> / Dissertation

In biochemical systems, stochastic e↵ects can be caused by the presence of small numbers of certain reactant molecules. In this setting, discrete state-space and stochastic simulation approaches were proved to be more relevant than continuous state-space and deterministic ones. These stochastic models constitute the theory of stochastic reaction networks (SRNs). Furthermore, in some cases, the dynamics of fast and slow time scales can be well separated and this is characterized by what is called sti↵ness. For such problems, the existing discrete space-state stochastic path simulation methods, such as the stochastic simulation algorithm (SSA) and the explicit tau-leap method, can be very slow. Therefore, implicit tau-leap approxima- tions were developed to improve the numerical stability and provide more e cient simulation algorithms for these systems. One of the interesting tasks for SRNs is to approximate the expected values of some observables of the process at a certain fixed time T. This is can be achieved using Monte Carlo (MC) techniques. However, in a recent work, Anderson and Higham in 2013, proposed a more computationally e cient method which combines multi-level Monte Carlo (MLMC) technique with explicit tau-leap schemes. In this MSc thesis, we propose new fast stochastic algorithm, particularly designed 5 to address sti↵ systems, for approximating the expected values of some observables of SRNs. In fact, we take advantage of the idea of MLMC techniques and drift-implicit tau-leap approximation to construct a drift-implicit MLMC tau-leap estimator. In addition to accurately estimating the expected values of a given observable of SRNs at a final time T , our proposed estimator ensures the numerical stability with a lower cost than the MLMC explicit tau-leap algorithm, for systems including simultane- ously fast and slow species. The key contribution of our work is the coupling of two drift-implicit tau-leap paths, which is the basic brick for constructing our proposed drift-implicit MLMC tau-leap estimator. As an example of sti↵ problem, we used the decaying-dimerizing reaction as a test example to show the advantage of our drift-implicit method over the explicit one. Through our numerical experiments, we checked the convergence properties of our coupling algorithm and showed that our proposed estimator is outperforming the explicit MLMC estimator about three times in terms of computational work. We also illustrated in a second example how our drift-implicit MLMC tau-leap estimator can be forty times faster than the explicit MLMC.

In systems biology, models often contain a large number of unknown or only roughly known parameters that must be estimated through the fitting of data. This work examines the question of whether or not these parameters can in fact be estimated from available measurements. Structural or a priori identifiability of unknown parameters in biochemical reaction networks is considered. Such systems consist of continuous time, nonlinear differential equations. Several methods for analyzing identifiability of such systems exist, most of which restate the question as one of observability by expanding the state space to include parameters. However, these existing methods were not developed with biological systems in mind, so do not necessarily address the specific challenges posed by this type of problem. In this work, such methods are considered for the analysis of a representative biological system, the NF-kappaB signal transduction pathway. It is shown that existing observability-based strategies, which rely on finding an analytical solution, require significant simplifications to be applicable to systems biology problems that are seldom feasible. The analytical nature of the solution imposes restrictions on the size and complexity of systems that these methods can handle. This conflicts with the fact that most currently studied systems biology models are rather large networks containing many states and parameters. In this thesis, a new simulation based method using an empirical observability Gramian for determining identifiability is proposed. Computational and numerical sensitivity issues for this method are considered. An algorithm, based on this method, is developed and demonstrated on a simple biological example of microbial growth with Michaelis-Menten kinetics. The new method is applied to the motivating NF-kappaB example to show its suitability for use in systems biology. / Thesis (Master, Chemical Engineering) -- Queen's University, 2008-08-05 22:20:32.561

Stochastic models of biochemical reaction networks are used for understanding the properties of molecular regulatory circuits in living cells. The state of the cell is defined by the number of copies of each molecular species in the model. The chemical master equation (CME) governs the time evolution of the the probability density function of the often high-dimensional state space. The CME is approximated by a partial differential equation (PDE), the Fokker-Planck equation and solved numerically. Direct solution of the CME rapidly becomes computationally expensive for increasingly complex biological models, since the state space grows exponentially with the number of dimensions. Adaptive numerical methods can be applied in time and space in the PDE framework, and error estimates of the approximate solutions are derived. A method for splitting the CME operator in order to apply the PDE approximation in a subspace of the state space is also developed. The performance is compared to the most widely spread alternative computational method.

Recent advances in systems biology have uncovered detailed mechanisms of  biological processes such as the cell cycle, circadian rhythms, and signaling pathways.  These mechanisms are modeled by chemical reaction networks (CRNs) which are typically simulated by converting to ordinary differential equations (ODEs), so that the goal is to closely reproduce the observed quantitative and qualitative behaviors of the modeled process. This thesis proposes two algorithmic problems related to the construction and comprehension of CRN models. The first problem focuses on reconstructing CRNs from given time series. Given multivariate time course data obtained by perturbing a given CRN, how can we systematically deduce the interconnections between the species of the network? We demonstrate how this problem can be modeled as, first, one of uncovering conditional independence relationships using buffering experiments and, second, of determining the properties of the individual chemical reactions. Experimental results demonstrate the effectiveness of our approach on both synthetic and real CRNs. The second problem this work focuses on is to aid in network comprehension, i.e., to understand the motifs underlying complex dynamical behaviors of CRNs. Specifically, we  focus on bistability---an important dynamical property of a CRN---and propose algorithms to identify the core structures responsible for conferring bistability. The approach we take is to systematically infer the instability causing structures (ICSs) of a CRN and use machine learning techniques to relate properties of the CRN to the presence of such ICSs. This work has the potential to aid in not just network comprehension but also model simplification, by helping  reduce the complexity of known bistable systems. / Ph. D.

Oxidative coupling of methane (OCM) represents a potentially viable method to convert methane directly into more desirable products such as ethane, and ethylene. In this dissertation, a comprehensive kinetic study of oxidative coupling of methane was performed over La2O3-based catalysts. An accurate and reliable gas-phase model is critical for the entire mechanism. The gas-phase kinetics was first studied using a jet-stirred reactor without catalyst. Both experiments and simulations were conducted under various operating conditions using different gas-phase models. Quantities of interest and rate of production analyses on hydrocarbon products were also performed to evaluate the models. NUIGMech1.1 was selected as the most comprehensive model to describe the OCM gas-phase kinetics and used for the next study. Next, microkinetic analysis on La2O3-based catalysts with different dopants was performed. The Ce addition has the greatest boost over the performance. The kinetics at low conversion regimes were analyzed and correlated to the catalysts’ properties. The activation energy for methane hydrogen abstraction was estimated, with the formation rate of primary products, which suggested that the initiation reaction steps were similar for La2O3-based catalyst. A homogeneous-heterogeneous kinetic model for La2O3/CeO2 catalyst was then constructed. By applying in situ XRD, the doping of CeO2 not only enhanced catalytic performance but also improved catalyst stability from CO2 and H2O. A wide range of operating conditions was investigated experimentally and numerically, where a packed bed reactor model was constructed based on the dimensions of experimental setup and catalyst characterization. The rate of production (ROP) was also performed to identify the important reactions and prove the necessity of surface reactions for the OCM process. Laser-induced fluorescence was implemented to directly observe the presence of formaldehyde. The last section includes the implementation of in situ laser diagnosis techniques at the near-surface region to solve the existing challenges. Raman scattering was implemented to quantitate the concentration profiles of major stable species near the surface and measure the in situ local temperatures at different heights above the catalyst surface, to study the kinetics transiting from the surface edge to the near-surface gas phase and provide a new perspective in OCM kinetic studies.

Epidemics have shaped, sometimes more than wars and natural disasters, demo- graphic aspects of human populations around the world, their health habits and their economies. Ebola and the Middle East Respiratory Syndrome (MERS) are clear and current examples of potential hazards at planetary scale. During the spread of an epidemic disease, there are phenomena, like the sudden extinction of the epidemic, that can not be captured by deterministic models. As a consequence, stochastic models have been proposed during the last decades. A typical forward problem in the stochastic setting could be the approximation of the expected number of infected individuals found in one month from now. On the other hand, a typical inverse problem could be, given a discretely observed set of epidemiological data, infer the transmission rate of the epidemic or its basic reproduction number. Markovian epidemic models are stochastic models belonging to a wide class of pure jump processes known as Stochastic Reaction Networks (SRNs), that are intended to describe the time evolution of interacting particle systems where one particle interacts with the others through a finite set of reaction channels. SRNs have been mainly developed to model biochemical reactions but they also have applications in neural networks, virus kinetics, and dynamics of social networks, among others. 4 This PhD thesis is focused on novel fast simulation algorithms and statistical inference methods for SRNs. Our novel Multi-level Monte Carlo (MLMC) hybrid simulation algorithms provide accurate estimates of expected values of a given observable of SRNs at a prescribed final time. They are designed to control the global approximation error up to a user-selected accuracy and up to a certain confidence level, and with near optimal computational work. We also present novel dual-weighted residual expansions for fast estimation of weak and strong errors arising from the MLMC methodology. Regarding the statistical inference aspect, we first mention an innovative multi- scale approach, where we introduce a deterministic systematic way of using up-scaled likelihoods for parameter estimation while the statistical fittings are done in the base model through the use of the Master Equation. In a di↵erent approach, we derive a new forward-reverse representation for simulating stochastic bridges between con- secutive observations. This allows us to use the well-known EM Algorithm to infer the reaction rates. The forward-reverse methodology is boosted by an initial phase where, using multi-scale approximation techniques, we provide initial values for the EM Algorithm.

Large chemical reaction networks often exhibit distinctive features that can be interpreted as higher-level structures. Prime examples are metabolic pathways in a biochemical context. We review mathematical approaches that exploit the stoichiometric structure, which can be seen as a particular directed hypergraph, to derive an algebraic picture of chemical organizations. We then give an alternative interpretation in terms of set-valued set functions that encapsulate the production rules of the individual reactions. From the mathematical point of view, these functions define generalized topological spaces on the set of chemical species. We show that organization-theoretic concepts also appear in a natural way in the topological language. This abstract representation in turn suggests the exploration of the chemical meaning of well-established topological concepts. As an example, we consider connectedness in some detail.

A possible mechanism to explain the origin of around 35 neutron–deficient stable isotopes with mass A≥75 between 74 Se and 196 Hg, known as the p–nuclei is the nucleosynthesis in the proton–rich neutrino–driven winds of core–collapse supernovae via the νp–process. However this production scenario is very sensitive to the underlying supernova dynamics and the nuclear physics input. As far as nuclear uncertainties are concerned, the breakout reaction from the pp-chains, 7Be(α, γ)11C, has been identified as an important link which can influence the nuclear flow and therefore the efficiency of the νp–process. However its reaction rate is not well known over the relevant energy range (T9 = 1.5–3). In this thesis we report on the direct first measurement of two resonances of the 7Be(α, γ)11 C reaction with previously unknown strengths using an intense radioactive 7Be beam from ISAC and the DRAGON recoil separator in inverse kinematics. Since resonance strength measurements with low mass beams using recoil separators depend strongly on the recoil angular distribution, which can exceed the acceptance of the separator, we first performed a proof–of–principle test by measuring a known resonance of the 6Li(α, γ)10B reaction, which also presents a similar challenge. Our results from the 6Li(α, γ)10B reaction are in agreement with literature, showing that DRAGON can measure resonance strengths of reactions for which the maximum momentum cone of the recoils exceeds its acceptance. From the newly measured 7Be(α, γ)11C resonance strengths we calculated the new reaction rate which is lower than the current recommended by 10–50% and constrained to 5–10% in the relevant temperature region. Using this new rate, we performed detailed nucleosynthesis calculations which suggest that there is no effect the production of light p–nuclei, but a production increase for CNO elements of up to an order of magnitude is observed. / Dissertation / Doctor of Philosophy (PhD)