Immunobiochemical Reconstruction of Influenza Lung Infection-Melanoma Skin Cancer Interactions.

It was recently reported that acute influenza infection of the lung promoted distal melanoma growth in the dermis of mice. Melanoma-specific CD8+ T cells were shunted to the lung in the presence of the infection, where they expressed high levels of inflammation-induced cell-activation blocker PD-1, and became incapable of migrating back to the tumor site. At the same time, co-infection virus-specific CD8+ T cells remained functional while the infection was cleared. It was also unexpectedly found that PD-1 blockade immunotherapy reversed this effect. Here, we proceed to ground the experimental observations in a mechanistic immunobiochemical model that incorporates T cell pathways that control PD-1 expression. A core component of our model is a kinetic motif, which we call a PD-1 Double Incoherent Feed-Forward Loop (DIFFL), and which reflects known interactions between IRF4, Blimp-1, and Bcl-6. The different activity levels of the PD-1 DIFFL components, as a function of the cognate antigen levels and the given inflammation context, manifest themselves in phenotypically distinct outcomes. Collectively, the model allowed us to put forward a few working hypotheses as follows: (i) the melanoma-specific CD8+ T cells re-circulating with the blood flow enter the lung where they express high levels of inflammation-induced cell-activation blocker PD-1 in the presence of infection; (ii) when PD-1 receptors interact with abundant PD-L1, constitutively expressed in the lung, T cells loose motility; (iii) at the same time, virus-specific cells adapt to strong stimulation by their cognate antigen by lowering the transiently-elevated expression of PD-1, remaining functional and mobile in the inflamed lung, while the infection is cleared. The role that T cell receptor (TCR) activation and feedback loops play in the underlying processes are also highlighted and discussed. We hope that the results reported in our study could potentially contribute to the advancement of immunological approaches to cancer treatment and, as well, to a better understanding of a broader complexity of fundamental interactions between pathogens and tumors.

Subharmonics and Chaos in Simple Periodically Forced Biomolecular Models.

This article uncovers a remarkable behavior in two biochemical systems that commonly appear as components of signal transduction pathways in systems biology. These systems have globally attracting steady states when unforced, so they might have been considered uninteresting from a dynamical standpoint. However, when subject to a periodic excitation, strange attractors arise via a period-doubling cascade. Quantitative analyses of the corresponding discrete chaotic trajectories are conducted numerically by computing largest Lyapunov exponents, power spectra, and autocorrelation functions. To gain insight into the geometry of the strange attractors, the phase portraits of the corresponding iterated maps are interpreted as scatter plots for which marginal distributions are additionally evaluated. The lack of entrainment to external oscillations, in even the simplest biochemical networks, represents a level of additional complexity in molecular biology, which has previously been insufficiently recognized but is plausibly biologically important.

Quorum-Sensing Synchronization of Synthetic Toggle Switches: A Design Based on Monotone Dynamical Systems Theory.

Synthetic constructs in biotechnology, biocomputing, and modern gene therapy interventions are often based on plasmids or transfected circuits which implement some form of "on-off" switch. For example, the expression of a protein used for therapeutic purposes might be triggered by the recognition of a specific combination of inducers (e.g., antigens), and memory of this event should be maintained across a cell population until a specific stimulus commands a coordinated shut-off. The robustness of such a design is hampered by molecular ("intrinsic") or environmental ("extrinsic") noise, which may lead to spontaneous changes of state in a subset of the population and is reflected in the bimodality of protein expression, as measured for example using flow cytometry. In this context, a "majority-vote" correction circuit, which brings deviant cells back into the required state, is highly desirable, and quorum-sensing has been suggested as a way for cells to broadcast their states to the population as a whole so as to facilitate consensus. In this paper, we propose what we believe is the first such a design that has mathematically guaranteed properties of stability and auto-correction under certain conditions. Our approach is guided by concepts and theory from the field of "monotone" dynamical systems developed by M. Hirsch, H. Smith, and others. We benchmark our design by comparing it to an existing design which has been the subject of experimental and theoretical studies, illustrating its superiority in stability and self-correction of synchronization errors. Our stability analysis, based on dynamical systems theory, guarantees global convergence to steady states, ruling out unpredictable ("chaotic") behaviors and even sustained oscillations in the limit of convergence. These results are valid no matter what are the values of parameters, and are based only on the wiring diagram. The theory is complemented by extensive computational bifurcation analysis, performed for a biochemically-detailed and biologically-relevant model that we developed. Another novel feature of our approach is that our theorems on exponential stability of steady states for homogeneous or mixed populations are valid independently of the number N of cells in the population, which is usually very large (N ≫ 1) and unknown. We prove that the exponential stability depends on relative proportions of each type of state only. While monotone systems theory has been used previously for systems biology analysis, the current work illustrates its power for synthetic biology design, and thus has wider significance well beyond the application to the important problem of coordination of toggle switches.

Fundamental limitation of the instantaneous approximation in fold-change detection models.

The phenomenon of fold-change detection, or scale-invariance, is exhibited by a variety of sensory systems, in both bacterial and eukaryotic signalling pathways. It has been often remarked in the systems biology literature that certain systems whose output variables respond at a faster time scale than internal components give rise to an approximate scale-invariant behaviour, allowing approximate fold-change detection in stimuli. This study establishes a fundamental limitation of such a mechanism, showing that there is a minimal fold-change detection error that cannot be overcome, no matter how large the separation of time scales is. To illustrate this theoretically predicted limitation, the authors discuss two common biomolecular network motifs, an incoherent feedforward loop and a feedback system, as well as a published model of the chemotaxis signalling pathway of Dictyostelium discoideum.

The elucidation of metabolic pathways and their improvements using stable optimization of large-scale kinetic models of cellular systems.

Metabolic engineering of cellular systems to maximize reaction fluxes or metabolite concentrations still presents a significant challenge by encountering unpredictable instabilities that can be caused by simultaneous or consecutive enhancements of many reaction steps. It can therefore be important to select carefully small subsets of key enzymes for their subsequent stable modification compatible with cell physiology. To address this important problem, we introduce a general mixed integer non-linear problem (MINLP) formulation to compute automatically which enzyme levels should be modulated and which enzyme regulatory structures should be altered to achieve the given optimization goal using non-linear kinetic models of relevant cellular systems. The developed MINLP formulation directly employs a stability analysis constraint and also includes non-linear biophysical constraints to describe homeostasis conditions for metabolite concentrations and protein machinery without any preliminary model simplification (e.g. linlog kinetics approximation). The framework is demonstrated on a well-established large-scale kinetic model of the Escherichia coli central metabolism used for the optimization of the glucose uptake through the phosphotransferase transport system (PTS) and serine biosynthesis. Computational results show that substantial stable improvements can be predicted by manipulating only small subsets of enzyme levels and regulatory structures. This means that while more efforts can be required to elucidate larger stable optimal enzyme level/regulation choices, no further significant increase in the optimized fluxes can be obtained and, therefore, such choices may not be worth the effort due to the potential loss of stability properties. The source for instability through saddle-node and Hopf bifurcations is identified, and all results are contrasted with predictions from metabolic control analysis.

Nicotinamide mononucleotide synthetase is the key enzyme for an alternative route of NAD biosynthesis in Francisella tularensis.

Enzymes involved in the last 2 steps of nicotinamide adenine dinucleotide (NAD) cofactor biosynthesis, which catalyze the adenylylation of the nicotinic acid mononucleotide (NaMN) precursor to nicotinic acid dinucleotide (NaAD) followed by its amidation to NAD, constitute promising drug targets for the development of new antibiotics. These enzymes, NaMN adenylyltransferase (gene nadD) and NAD synthetase (gene nadE), respectively, are indispensable and conserved in nearly all bacterial pathogens. However, a comparative genome analysis of Francisella tularensis allowed us to predict the existence of an alternative route of NAD synthesis in this category A priority pathogen, the causative agent of tularaemia. In this route, the amidation of NaMN to nicotinamide mononucleotide (NMN) occurs before the adenylylation reaction, which converts this alternative intermediate to the NAD cofactor. The first step is catalyzed by NMN synthetase, which was identified and characterized in this study. A crystal structure of this enzyme, a divergent member of the NadE family, was solved at 1.9-A resolution in complex with reaction products, providing a rationale for its unusual substrate preference for NaMN over NaAD. The second step is performed by NMN adenylyltransferase of the NadM family. Here, we report validation of the predicted route (NaMN --> NMN --> NAD) in F. tularensis including mathematical modeling, in vitro reconstitution, and in vivo metabolite analysis in comparison with a canonical route (NaMN --> NaAD --> NAD) of NAD biosynthesis as represented by another deadly bacterial pathogen, Bacillus anthracis.

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method.

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.

A computational procedure for optimal engineering interventions using kinetic models of metabolism.

The identification of optimal intervention strategies is a key step in designing microbial strains with enhanced capabilities. In this paper, we propose a general computational procedure to determine which genes/enzymes should be eliminated, repressed or overexpressed to maximize the flux through a product of interest for general kinetic models. The procedure relies on the generalized linearization of a kinetic description of the investigated metabolic system and the iterative application of mixed-integer linear programming (MILP) optimization to hierarchically identify all engineering interventions allowing for reaction eliminations and/or enzyme level modulations. The effect of the magnitude of the allowed changes in concentrations and enzyme levels is investigated, and a variant of the method to explore high-fold changes in enzyme levels is also analyzed. The proposed framework is demonstrated using a kinetic model modeling part of the central carbon metabolism of E. coli for serine overproduction. The proposed computational procedure is a general approach that can be applied to any metabolic system for which a kinetic description is provided.

Elucidation and structural analysis of conserved pools for genome-scale metabolic reconstructions.

In this article, we introduce metabolite concentration coupling analysis (MCCA) to study conservation relationships for metabolite concentrations in genome-scale metabolic networks. The analysis allows the global identification of subsets of metabolites whose concentrations are always coupled within common conserved pools. Also, the minimal conserved pool identification (MCPI) procedure is developed for elucidating conserved pools for targeted metabolites without computing the entire basis conservation relationships. The approaches are demonstrated on genome-scale metabolic reconstructions of Helicobacter pylori, Escherichia coli, and Saccharomyces cerevisiae. Despite significant differences in the size and complexity of the examined organism's models, we find that the concentrations of nearly all metabolites are coupled within a relatively small number of subsets. These correspond to the overall exchange of carbon molecules into and out of the networks, interconversion of energy and redox cofactors, and the transfer of nitrogen, sulfur, phosphate, coenzyme A, and acyl carrier protein moieties among metabolites. The presence of large conserved pools can be viewed as global biophysical barriers protecting cellular systems from stresses, maintaining coordinated interconversions between key metabolites, and providing an additional mode of global metabolic regulation. The developed approaches thus provide novel and versatile tools for elucidating coupling relationships between metabolite concentrations with implications in biotechnological and medical applications.

Flux coupling analysis of genome-scale metabolic network reconstructions.

In this paper, we introduce the Flux Coupling Finder (FCF) framework for elucidating the topological and flux connectivity features of genome-scale metabolic networks. The framework is demonstrated on genome-scale metabolic reconstructions of Helicobacter pylori, Escherichia coli, and Saccharomyces cerevisiae. The analysis allows one to determine whether any two metabolic fluxes, v(1) and v(2), are (1) directionally coupled, if a non-zero flux for v(1) implies a non-zero flux for v(2) but not necessarily the reverse; (2) partially coupled, if a non-zero flux for v(1) implies a non-zero, though variable, flux for v(2) and vice versa; or (3) fully coupled, if a non-zero flux for v(1) implies not only a non-zero but also a fixed flux for v(2) and vice versa. Flux coupling analysis also enables the global identification of blocked reactions, which are all reactions incapable of carrying flux under a certain condition; equivalent knockouts, defined as the set of all possible reactions whose deletion forces the flux through a particular reaction to zero; and sets of affected reactions denoting all reactions whose fluxes are forced to zero if a particular reaction is deleted. The FCF approach thus provides a novel and versatile tool for aiding metabolic reconstructions and guiding genetic manipulations.