Expanding Metabolic Networks: Scopes of Compounds, Robustness, and Evolution

A new method for the mathematical analysis of large metabolic networks is presented. Based on the fact that the occurrence of a metabolic reaction generally requires the existence of other reactions providing its substrates, series of metabolic networks are constructed. In each step of the corresponding expansion process those reactions are incorporated whose substrates are made available by the networks of the previous generations. The method is applied to the set of all metabolic reactions included in the KEGG database. Starting with one or more seed compounds, the expansion results in a final network whose compounds define the scope of the seed. Scopes of all metabolic compounds are calculated and it is shown that large parts of cellular metabolism can be considered as the combined scope of simple building blocks. Analyses of various expansion processes reveal crucial metabolites whose incorporation allows for the increase in network complexity. Among these metabolites are common cofactors such as NAD⁺, ATP, and coenzyme A. We demonstrate that the outcome of network expansion is in general very robust against elimination of single or few reactions. There exist, however, crucial reactions whose elimination results in a dramatic reduction of scope sizes. It is hypothesized that the expansion process displays characteristics of the evolution of metabolism such as the temporal order of the emergence of metabolic pathways. [Reviewing Editor : Dr. David Pollock]     

siMS Score: Simple Method for Quantifying Metabolic Syndrome

Objective

To evaluate siMS score and siMS risk score, novel continuous metabolic syndrome scores as methods for quantification of metabolic status and risk.

Materials and Methods

Developed siMS score was calculated using formula: siMS score = 2*Waist/Height + Gly/5.6 + Tg/1.7 + TA_systolic/130—HDL/1.02 or 1.28 (for male or female subjects, respectively). siMS risk score was calculated using formula: siMS risk score = siMS score * age/45 or 50 (for male or female subjects, respectively) * family history of cardio/cerebro-vascular events (event = 1.2, no event = 1). A sample of 528 obese and non-obese participants was used to validate siMS score and siMS risk score. Scores calculated as sum of z-scores (each component of metabolic syndrome regressed with age and gender) and sum of scores derived from principal component analysis (PCA) were used for evaluation of siMS score. Variants were made by replacing glucose with HOMA in calculations. Framingham score was used for evaluation of siMS risk score.

Results

Correlation between siMS score with sum of z-scores and weighted sum of factors of PCA was high (r = 0.866 and r = 0.822, respectively). Correlation between siMS risk score and log transformed Framingham score was medium to high for age groups 18+,30+ and 35+ (0.835, 0.707 and 0.667, respectively).

Conclusions

siMS score and siMS risk score showed high correlation with more complex scores. Demonstrated accuracy together with superior simplicity and the ability to evaluate and follow-up individual patients makes siMS and siMS risk scores very convenient for use in clinical practice and research as well.     

On the Use of a Simple Physical System Analogy to Study Robustness Features in Animal Sciences

Environmental perturbations can affect the health, welfare, and fitness of animals. Being able to characterize and phenotype adaptive capacity is therefore of growing scientific concern in animal ecology and in animal production sciences. Terms borrowed from physics are commonly used to describe adaptive responses of animals facing an environmental perturbation, but no quantitative characterization of these responses has been made. Modeling the dynamic responses to an acute challenge was used in this study to facilitate the characterization of adaptive capacity and therefore robustness. A simple model based on a spring and damper was developed to simulate the dynamic responses of animals facing an acute challenge. The parameters characterizing the spring and the damper can be interpreted in terms of stiffness and resistance to the change of the system. The model was tested on physiological and behavioral responses of rainbow trout facing an acute confinement challenge. The model has proven to properly fit the different responses measured in this study and to quantitatively describe the different temporal patterns for each statistical individual in the study. It provides therefore a new way to explicitly describe, analyze and compare responses of individuals facing an acute perturbation. This study suggests that such physical models may be usefully applied to characterize robustness in many other biological systems.     

Isotope Chirality and Asymmetric Autocatalysis: A Possible Entry to Biological Chirality

Natural-abundance isotopic substitution in isotopically prochiral groups of otherwise achiral molecules can provide stochastically formed enantiomeric excesses which exceed the sensitivity threshold of sensitive asymmetric autocatalytic (Soai-type) reactions. This kind of induction of chirality should be taken into consideration in in vitro model experiments and offer a new kind of entry into primary prebiotic or early biotic enantioselection in the earliest stages of molecular evolution.     

Bistability: Requirements on Cell-Volume,Protein Diffusion,and Thermodynamics

Bistability is considered wide-spread among bacteria and eukaryotic cells, useful e.g. for enzyme induction, bet hedging, and epigenetic switching. However, this phenomenon has mostly been described with deterministic dynamic or well-mixed stochastic models. Here, we map known biological bistable systems onto the well-characterized biochemical Schlögl model, using analytical calculations and stochastic spatiotemporal simulations. In addition to network architecture and strong thermodynamic driving away from equilibrium, we show that bistability requires fine-tuning towards small cell volumes (or compartments) and fast protein diffusion (well mixing). Bistability is thus fragile and hence may be restricted to small bacteria and eukaryotic nuclei, with switching triggered by volume changes during the cell cycle. For large volumes, single cells generally loose their ability for bistable switching and instead undergo a first-order phase transition.     

A Mathematical Model of the Human Metabolic System and Metabolic Flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.     

Bistability, bifurcations, and Waddington's epigenetic landscape

Waddington's epigenetic landscape is probably the most famous and most powerful metaphor in developmental biology. Cells, represented by balls, roll downhill through a landscape of bifurcating valleys. Each new valley represents a possible cell fate and the ridges between the valleys maintain the cell fate once it has been chosen. Here I examine models of two important developmental processes - cell-fate induction and lateral inhibition - and ask whether the landscapes for these models at least qualitatively resemble Waddington's picture. For cell-fate induction, the answer is no. The commitment of a cell to a new fate corresponds to the disappearance of a valley from the landscape, not the splitting of one valley into two, and it occurs through a type of bifurcation - a saddle-node bifurcation - that possesses an intrinsic irreversibility that is missing from Waddington's picture. Lateral inhibition, a symmetrical cell-cell competition process, corresponds better to Waddington's picture, with one valley reversibly splitting into two through a pitchfork bifurcation. I propose an alternative epigenetic landscape that has numerous valleys and ridges right from the start, with the process of cell-fate commitment corresponding to the irreversible disappearance of some of these valleys and ridges, via cell-fate induction, complemented by the creation of new valleys and ridges through processes like cell-cell competition.     

Multiple Kinases and System Robustness: A Link Between Cdc37 and Genome Integrity

We identified 38 genes as having a genetic interaction with a mutant form of the kinase specific chaperone, Cdc37, using a genome-wide synthetic screening approach. The identified genes included a sub-network of highly interacting genes enriched for functions in genome integrity and comprising multiple components of several discrete molecular machines. A network analysis approach related these machines to a small group of cell cycle checkpoint kinases.     

Melanopsin Bistability: A Fly's Eye Technology in the Human Retina

In addition to rods and cones, the human retina contains light-sensitive ganglion cells that express melanopsin, a photopigment with signal transduction mechanisms similar to that of invertebrate rhabdomeric photopigments (IRP). Like fly rhodopsins, melanopsin acts as a dual-state photosensitive flip-flop in which light drives both phototransduction responses and chromophore photoregeneration that bestows independence from the retinoid cycle required by rods and cones to regenerate photoresponsiveness following bleaching by light. To explore the hypothesis that melanopsin in humans expresses the properties of a bistable photopigment in vivo we used the pupillary light reflex (PLR) as a tool but with methods designed to study invertebrate photoreceptors. We show that the pupil only attains a fully stabilized state of constriction after several minutes of light exposure, a feature that is consistent with typical IRP photoequilibrium spectra. We further demonstrate that previous exposure to long wavelength light increases, while short wavelength light decreases the amplitude of pupil constriction, a fundamental property of IRP difference spectra. Modelling these responses to invertebrate photopigment templates yields two putative spectra for the underlying R and M photopigment states with peaks at 481 nm and 587 nm respectively. Furthermore, this bistable mechanism may confer a novel form of “photic memory” since information of prior light conditions is retained and shapes subsequent responses to light. These results suggest that the human retina exploits fly-like photoreceptive mechanisms that are potentially important for the modulation of non-visual responses to light and highlights the ubiquitous nature of photoswitchable photosensors across living organisms.     

PSAMM: A Portable System for the Analysis of Metabolic Models

The genome-scale models of metabolic networks have been broadly applied in phenotype prediction, evolutionary reconstruction, community functional analysis, and metabolic engineering. Despite the development of tools that support individual steps along the modeling procedure, it is still difficult to associate mathematical simulation results with the annotation and biological interpretation of metabolic models. In order to solve this problem, here we developed a Portable System for the Analysis of Metabolic Models (PSAMM), a new open-source software package that supports the integration of heterogeneous metadata in model annotations and provides a user-friendly interface for the analysis of metabolic models. PSAMM is independent of paid software environments like MATLAB, and all its dependencies are freely available for academic users. Compared to existing tools, PSAMM significantly reduced the running time of constraint-based analysis and enabled flexible settings of simulation parameters using simple one-line commands. The integration of heterogeneous, model-specific annotation information in PSAMM is achieved with a novel format of YAML-based model representation, which has several advantages, such as providing a modular organization of model components and simulation settings, enabling model version tracking, and permitting the integration of multiple simulation problems. PSAMM also includes a number of quality checking procedures to examine stoichiometric balance and to identify blocked reactions. Applying PSAMM to 57 models collected from current literature, we demonstrated how the software can be used for managing and simulating metabolic models. We identified a number of common inconsistencies in existing models and constructed an updated model repository to document the resolution of these inconsistencies.     

Factors Affecting Autocatalysis of Botulinum A Neurotoxin Light Chain*

The light chain of botulinum neurotoxin serotype A undergoes autocatalytic fragmentation into two major peptides during purification and storage (Ahmed S. A. et al. 2001, J. Protein Chem. 20:221–231) by both intermolecular and intramolecular mechanisms (Ahmed S. A. etal. 2003, Biochemistry 42:12539–12549). In this study, we investigated the effects of buffers and salts on this autocatalytic reaction in the presence and absence of zinc chloride. In the presence of zinc chloride, the fragmentation reaction was enhanced in each of acetate, MES, HEPES and phosphate buffers with maximum occurring in acetate when compared to those in the absence of zinc chloride. Adding sodium chloride in phosphate buffer in the presence of zinc chloride increased the extent of proteolysis. Irrespective of the presence of zinc chloride, adding sodium chloride or potassium chloride in phosphate buffer elicited an additional proteolytic reaction. Higher concentrations of sodium phosphate buffer enhanced the autocatalytic reaction in the absence of zinc chloride. In contrast, in the presence of zinc chloride, higher concentrations of sodium phosphate decreased the autocatalytic reaction. Optimum pH of autocatalysis was not affected significantly by the absence or presence of zinc chloride. Like zinc chloride, other chlorides of divalent metals, such as magnesium, cobalt, iron and calcium also enhanced the autocatalytic reaction. Polyols such as ethylene glycol protected the light chain from fragmentation. Exposure of light chain to UV radiation led to enhanced fragmentation. In order to avoid fragmentation, the protein should be stored frozen in a low concentration buffer of neutral or higher pH devoid of any metal. Our results provide a choice of buffers and salts for isolation, purification and storage of intact botulinum neurotoxin serotype A light chain.     

Robustness in Regulatory Networks: A Multi-Disciplinary Approach

We give in this paper indications about the dynamical impact (as phenotypic changes) coming from the main sources of perturbation in biological regulatory networks. First, we define the boundary of the interaction graph expressing the regulations between the main elements of the network (genes, proteins, metabolites, ...). Then, we search what changes in the state values on the boundary could cause some changes of states in the core of the system (robustness to boundary conditions). After, we analyse the role of the mode of updating (sequential, block sequential or parallel) on the asymptotics of the network, essentially on the occurrence of limit cycles (robustness to updating methods). Finally, we show the influence of some topological changes (e.g. suppression or addition of interactions) on the dynamical behaviour of the system (robustness to topology perturbations).     

A Simple and Automatic Leaflet Movement-monitoring System

A simple and automatic leaflet movement-monitoring system using phototransistors is described for Albizzia julibrissin.     

A Simple Exoskeleton That Assists Plantarflexion Can Reduce the Metabolic Cost of Human Walking

Background

Even though walking can be sustained for great distances, considerable energy is required for plantarflexion around the instant of opposite leg heel contact. Different groups attempted to reduce metabolic cost with exoskeletons but none could achieve a reduction beyond the level of walking without exoskeleton, possibly because there is no consensus on the optimal actuation timing. The main research question of our study was whether it is possible to obtain a higher reduction in metabolic cost by tuning the actuation timing.

Methodology/Principal Findings

We measured metabolic cost by means of respiratory gas analysis. Test subjects walked with a simple pneumatic exoskeleton that assists plantarflexion with different actuation timings. We found that the exoskeleton can reduce metabolic cost by 0.18±0.06 W kg⁻¹ or 6±2% (standard error of the mean) (p = 0.019) below the cost of walking without exoskeleton if actuation starts just before opposite leg heel contact.

Conclusions/Significance

The optimum timing that we found concurs with the prediction from a mathematical model of walking. While the present exoskeleton was not ambulant, measurements of joint kinetics reveal that the required power could be recycled from knee extension deceleration work that occurs naturally during walking. This demonstrates that it is theoretically possible to build future ambulant exoskeletons that reduce metabolic cost, without power supply restrictions.     

Robustness, evolvability, and neutrality

Biological systems, from macromolecules to whole organisms, are robust if they continue to function, survive, or reproduce when faced with mutations, environmental change, and internal noise. I focus here on biological systems that are robust to mutations and ask whether such systems are more or less evolvable, in the sense that they can acquire novel properties. The more robust a system is, the more mutations in it are neutral, that is, without phenotypic effect. I argue here that such neutral change--and thus robustness--can be a key to future evolutionary innovation, if one accepts that neutrality is not an essential feature of a mutation. That is, a once neutral mutation may cause phenotypic effects in a changed environment or genetic background. I argue that most, if not all, neutral mutations are of this sort, and that the essentialist notion of neutrality should be abandoned. This perspective reconciles two opposing views on the forces dominating organismal evolution, natural selection and random drift: neutral mutations occur and are especially abundant in robust systems, but they do not remain neutral indefinitely, and eventually become visible to natural selection, where some of them lead to evolutionary innovations.     

Bistability in a Metabolic Network Underpins the De Novo Evolution of Colony Switching in Pseudomonas fluorescens

Phenotype switching is commonly observed in nature. This prevalence has allowed the elucidation of a number of underlying molecular mechanisms. However, little is known about how phenotypic switches arise and function in their early evolutionary stages. The first opportunity to provide empirical insight was delivered by an experiment in which populations of the bacterium Pseudomonas fluorescens SBW25 evolved, de novo, the ability to switch between two colony phenotypes. Here we unravel the molecular mechanism behind colony switching, revealing how a single nucleotide change in a gene enmeshed in central metabolism (carB) generates such a striking phenotype. We show that colony switching is underpinned by ON/OFF expression of capsules consisting of a colanic acid-like polymer. We use molecular genetics, biochemical analyses, and experimental evolution to establish that capsule switching results from perturbation of the pyrimidine biosynthetic pathway. Of central importance is a bifurcation point at which uracil triphosphate is partitioned towards either nucleotide metabolism or polymer production. This bifurcation marks a cell-fate decision point whereby cells with relatively high pyrimidine levels favour nucleotide metabolism (capsule OFF), while cells with lower pyrimidine levels divert resources towards polymer biosynthesis (capsule ON). This decision point is present and functional in the wild-type strain. Finally, we present a simple mathematical model demonstrating that the molecular components of the decision point are capable of producing switching. Despite its simple mutational cause, the connection between genotype and phenotype is complex and multidimensional, offering a rare glimpse of how noise in regulatory networks can provide opportunity for evolution.     

Fatal or Harmless: Extreme Bistability Induced by Sterilizing,Sexually Transmitted Pathogens

Models of sexually transmitted infections have become a fixture of mathematical epidemiology. A common attribute of all these models is treating reproduction and mating, and hence pathogen transmission, as uncoupled events. This is fine for humans, for example, where only a tiny fraction of sexual intercourses ends up with having a baby. But it can be a deficiency for animals in which mating and giving birth are tightly coupled, and mating thus mediates both reproduction and pathogen transmission. Here, we model dynamics of sterilizing, sexually transmitted infections in such animals, assuming structural consistency between the processes of reproduction and pathogen transmission. We show that highly sterilizing, sexually transmitted pathogens trigger bistability in the host population. In particular, the host population can end up in two extreme alternative states, disease-free persistence and pathogen-driven extinction, depending on its initial state. Given that sterilizing, sexually transmitted infections that affect animals are abundant, our results might implicate an effective pest control tactic that consists of releasing the corresponding pathogens, possibly after genetically enhancing their sterilization power.