Regulated bacterial interaction networks: A mathematical framework to describe competitive growth under inclusion of metabolite cross-feeding.

When bacterial species with the same resource preferences share the same growth environment, it is commonly believed that direct competition will arise. A large variety of competition and more general 'interaction' models have been formulated, but what is currently lacking are models that link monoculture growth kinetics and community growth under inclusion of emerging biological interactions, such as metabolite cross-feeding. In order to understand and mathematically describe the nature of potential cross-feeding interactions, we design experiments where two bacterial species Pseudomonas putida and Pseudomonas veronii grow in liquid medium either in mono- or as co-culture in a resource-limited environment. We measure population growth under single substrate competition or with double species-specific substrates (substrate 'indifference'), and starting from varying cell ratios of either species. Using experimental data as input, we first consider a mean-field model of resource-based competition, which captures well the empirically observed growth rates for monocultures, but fails to correctly predict growth rates in co-culture mixtures, in particular for skewed starting species ratios. Based on this, we extend the model by cross-feeding interactions where the consumption of substrate by one consumer produces metabolites that in turn are resources for the other consumer, thus leading to positive feedback in the species system. Two different cross-feeding options were considered, which either lead to constant metabolite cross-feeding, or to a regulated form, where metabolite utilization is activated with rates according to either a threshold or a Hill function, dependent on metabolite concentration. Both mathematical proof and experimental data indicate regulated cross-feeding to be the preferred model to constant metabolite utilization, with best co-culture growth predictions in case of high Hill coefficients, close to binary (on/off) activation states. This suggests that species use the appearing metabolite concentrations only when they are becoming high enough; possibly as a consequence of their lower energetic content than the primary substrate. Metabolite sharing was particularly relevant at unbalanced starting cell ratios, causing the minority partner to proliferate more than expected from the competitive substrate because of metabolite release from the majority partner. This effect thus likely quells immediate substrate competition and may be important in natural communities with typical very skewed relative taxa abundances and slower-growing taxa. In conclusion, the regulated bacterial interaction network correctly describes species substrate growth reactions in mixtures with few kinetic parameters that can be obtained from monoculture growth experiments.

An analog to digital converter controls bistable transfer competence development of a widespread bacterial integrative and conjugative element.

Conjugative transfer of the integrative and conjugative element ICEclc in Pseudomonas requires development of a transfer competence state in stationary phase, which arises only in 3-5% of individual cells. The mechanisms controlling this bistable switch between non-active and transfer competent cells have long remained enigmatic. Using a variety of genetic tools and epistasis experiments in P. putida, we uncovered an 'upstream' cascade of three consecutive transcription factor-nodes, which controls transfer competence initiation. One of the uncovered transcription factors (named BisR) is representative for a new regulator family. Initiation activates a feedback loop, controlled by a second hitherto unrecognized heteromeric transcription factor named BisDC. Stochastic modelling and experimental data demonstrated the feedback loop to act as a scalable converter of unimodal (population-wide or 'analog') input to bistable (subpopulation-specific or 'digital') output. The feedback loop further enables prolonged production of BisDC, which ensures expression of the 'downstream' functions mediating ICE transfer competence in activated cells. Phylogenetic analyses showed that the ICEclc regulatory constellation with BisR and BisDC is widespread among Gamma- and Beta-proteobacteria, including various pathogenic strains, highlighting its evolutionary conservation and prime importance to control the behaviour of this wide family of conjugative elements.

Mobile DNA elements are pieces of genetic material that can jump from one bacterium to another, and even across species. They are often useful to their host, for example carrying genes that allow bacteria to resist antibiotics. One example of bacterial mobile DNA is the ICEclc element. Usually, ICEclc sits passively within the bacterium's own DNA, but in a small number of cells, it takes over, hijacking its host to multiply and to get transferred to other bacteria. Cells that can pass on the elements cannot divide, and so this ability is ultimately harmful to individual bacteria. Carrying ICEclc can therefore be positive for a bacterium but passing it on is not in the cell's best interest. On the other hand, mobile DNAs like ICEclc have evolved to be disseminated as efficiently as possible. To shed more light on this tense relationship, Carraro et al. set out to identify the molecular mechanisms ICEclc deploys to control its host. Experiments using mutant bacteria revealed that for ICEclc to successfully take over the cell, a number of proteins needed to be produced in the correct order. In particular, a protein called BisDC triggers a mechanism to make more of itself, creating a self-reinforcing 'feedback loop'. Mathematical simulations of the feedback loop showed that it could result in two potential outcomes for the cell. In most of the 'virtual cells', ICEclc ultimately remained passive; however, in a few, ICEclc managed to take over its hosts. In this case, the feedback loop ensured that there was always enough BisDC to maintain ICEclc's control over the cell. Further analyses suggested that this feedback mechanism is also common in many other mobile DNA elements, including some that help bacteria to resist drugs. These results are an important contribution to understand how mobile DNAs manipulate their bacterial host in order to propagate and disperse. In the future, this knowledge could help develop new strategies to combat the spread of antibiotic resistance.

Extending the Mathematical Palette for Developmental Pattern Formation: Piebaldism.

Here, we present a theoretical investigation with potential insights on developmental mechanisms. Three biological factors, consisting of two diffusing factors and a cell-autonomous immobile transcription factor are combined with different feedback mechanisms. This results in four different situations or fur patterns. Two of them reproduce classical Turing patterns: (1) regularly spaced spots, (2) labyrinth patterns or straight lines with an initial slope in the activation of the transcription factor. The third situation does not lead to patterns, but results in different homogeneous color tones. Finally, the fourth one sheds new light on the possible mechanisms leading to the formation of piebald patterns exemplified by the random patterns on the fur of some cows' strains and Dalmatian dogs. Piebaldism is usually manifested as white areas of fur, hair, or skin due to the absence of pigment-producing cells in those regions. The distribution of the white and colored zones does not reflect the classical Turing patterns. We demonstrate that these piebald patterns are of transient nature, developing from random initial conditions and relying on a system's bistability. We show numerically that the presence of a cell-autonomous factor not only expands the range of reaction diffusion parameters in which a pattern may arise, but also extends the pattern-forming abilities of the reaction-diffusion equations.

Statistical modelling of navigational decisions based on intensity versus directionality in Drosophila larval phototaxis.

Organisms use environmental cues for directed navigation. Understanding the basic logic behind navigational decisions critically depends on the complexity of the nervous system. Due to the comparably simple organization of the nervous system of the fruit fly larva, it stands as a powerful model to study decision-making processes that underlie directed navigation. We have quantitatively measured phototaxis in response to well-defined sensory inputs. Subsequently, we have formulated a statistical stochastic model based on biased Markov chains to characterize the behavioural basis of negative phototaxis. Our experiments show that larvae make navigational decisions depending on two independent physical variables: light intensity and its spatial gradient. Furthermore, our statistical model quantifies how larvae balance two potentially-contradictory factors: minimizing exposure to light intensity and at the same time maximizing their distance to the light source. We find that the response to the light field is manifestly non-linear, and saturates above an intensity threshold. The model has been validated against our experimental biological data yielding insight into the strategy that larvae use to achieve their goal with respect to the navigational cue of light, an important piece of information for future work to study the role of the different neuronal components in larval phototaxis.

The feasibility of equilibria in large ecosystems: A primary but neglected concept in the complexity-stability debate.

The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive abundances. However, this key assumption has not been tested. We provide analytical results complemented by simulations which show that equilibrium feasibility vanishes in species rich systems. This result leaves us in the uncomfortable situation in which the existence of a feasible equilibrium assumed in local stability criteria is far from granted. We extend our analyses by changing interaction structure and intensity, and find that feasibility and stability is warranted irrespective of species richness with weak interactions. Interestingly, we find that the dynamical behaviour of ecologically inspired architectures is very different and richer than that of unstructured systems. Our results suggest that a general understanding of ecosystem dynamics requires focusing on the interplay between interaction strength and network architecture.

Quantitative chemical biosensing by bacterial chemotaxis in microfluidic chips.

Whole-cell bacterial bioreporters are proposed as alternatives to chemical analysis of, for example, pollutants in environmental compartments. Commonly based on reporter gene induction, bioreporters produce a detectable signal within 30 min to a few hours after exposure to the chemical target, which is impractical for applications aiming at a fast response. In an attempt to attain faster readout but maintain flexibility of chemical targeting, we explored the concept for quantitative chemical sensing by bacterial chemotaxis. Chemotaxis was quantified from enrichment of cells across a 600 µm-wide chemical gradient stabilized by parallel flow in a microfluidic chip, further supported by transport and chemotaxis steady state and kinetic modelling. As proof-of-concept, we quantified Escherichia coli chemotaxis towards serine, aspartate and methylaspartate as a function of attractant concentration and exposure time. E. coli chemotaxis enrichment increased sharply between 0 and 10 µM serine, before saturating at 100 µM. The chemotaxis accumulation rate was maximal at 10 µM serine, leading to observable cell enrichment within 5 min. The potential application for biosensing of environmental toxicants was investigated by quantifying chemotaxis of Cupriavidus pinatubonensis JMP134 towards the herbicide 2,4-dichlorophenoxyacetate. Our results show that bacterial chemotaxis can be quantified on a scale of minutes and may be used for developing faster bioreporter assays.

The Effect of Gap Junctional Coupling on the Spatiotemporal Patterns of Ca2+ Signals and the Harmonization of Ca2+-Related Cellular Responses.

Calcium ions (Ca2+) are important mediators of a great variety of cellular activities e.g. in response to an agonist activation of a receptor. The magnitude of a cellular response is often encoded by frequency modulation of Ca2+ oscillations and correlated with the stimulation intensity. The stimulation intensity highly depends on the sensitivity of a cell to a certain agonist. In some cases, it is essential that neighboring cells produce a similar and synchronized response to an agonist despite their different sensitivity. In order to decipher the presumed function of Ca2+ waves spreading among connecting cells, a mathematical model was developed. This model allows to numerically modifying the connectivity probability between neighboring cells, the permeability of gap junctions and the individual sensitivity of cells to an agonist. Here, we show numerically that strong gap junctional coupling between neighbors ensures an equilibrated response to agonist stimulation via formation of Ca2+ phase waves, i.e. a less sensitive neighbor will produce the same or similar Ca2+ signal as its highly sensitive neighbor. The most sensitive cells within an ensemble are the wave initiator cells. The Ca2+ wave in the cytoplasm is driven by a sensitization wave front in the endoplasmic reticulum. The wave velocity is proportional to the cellular sensitivity and to the strength of the coupling. The waves can form different patterns including circular rings and spirals. The observed pattern depends on the strength of noise, gap junctional permeability and the connectivity probability between neighboring cells. Our simulations reveal that one highly sensitive region gradually takes the lead within the entire noisy system by generating directed circular phase waves originating from this region.

Matching-centrality decomposition and the forecasting of new links in networks.

Networks play a prominent role in the study of complex systems of interacting entities in biology, sociology, and economics. Despite this diversity, we demonstrate here that a statistical model decomposing networks into matching and centrality components provides a comprehensive and unifying quantification of their architecture. The matching term quantifies the assortative structure in which node makes links with which other node, whereas the centrality term quantifies the number of links that nodes make. We show, for a diverse set of networks, that this decomposition can provide a tight fit to observed networks. Then we provide three applications. First, we show that the model allows very accurate prediction of missing links in partially known networks. Second, when node characteristics are known, we show how the matching-centrality decomposition can be related to this external information. Consequently, it offers us a simple and versatile tool to explore how node characteristics explain network architecture. Finally, we demonstrate the efficiency and flexibility of the model to forecast the links that a novel node would create if it were to join an existing network.

Self-organization of plant vascular systems: claims and counter-claims about the flux-based auxin transport model.

The plant hormone auxin plays a central role in growth and morphogenesis. In shoot apical meristems, auxin flux is polarized through its interplay with PIN proteins. Concentration-based mathematical models of the flux can explain some aspects of phyllotaxis for the L1 surface layer, where auxin accumulation points act as sinks and develop into primordia. The picture differs in the interior of the meristem, where the primordia act as auxin sources, leading to the initiation of the vascular system. Self-organization of the auxin flux involves large numbers of molecules and is difficult to treat by intuitive reasoning alone; mathematical models are therefore vital to understand these phenomena. We consider a leading computational model based on the so-called flux hypothesis. This model has been criticized and extended in various ways. One of the basic counter-arguments is that simulations yield auxin concentrations inside canals that are lower than those seen experimentally. Contrary to what is claimed in the literature, we show that the model can lead to higher concentrations within canals for significant parameter regimes. We then study the model in the usual case where the response function Φ defining the model is quadratic and unbounded, and show that the steady state vascular patterns are formed of loopless directed trees. Moreover, we show that PIN concentrations can diverge in finite time, thus explaining why previous simulation studies introduced cut-offs which force the system to have bounded PIN concentrations. Hence, contrary to previous claims, extreme PIN concentrations are not due to numerical problems but are intrinsic to the model. On the other hand, we show that PIN concentrations remain bounded for bounded Φ, and simulations show that in this case, loops can emerge at steady state.

High-level transgene expression by homologous recombination-mediated gene transfer.

Gene transfer and expression in eukaryotes is often limited by a number of stably maintained gene copies and by epigenetic silencing effects. Silencing may be limited by the use of epigenetic regulatory sequences such as matrix attachment regions (MAR). Here, we show that successive transfections of MAR-containing vectors allow a synergistic increase of transgene expression. This finding is partly explained by an increased entry into the cell nuclei and genomic integration of the DNA, an effect that requires both the MAR element and iterative transfections. Fluorescence in situ hybridization analysis often showed single integration events, indicating that DNAs introduced in successive transfections could recombine. High expression was also linked to the cell division cycle, so that nuclear transport of the DNA occurs when homologous recombination is most active. Use of cells deficient in either non-homologous end-joining or homologous recombination suggested that efficient integration and expression may require homologous recombination-based genomic integration of MAR-containing plasmids and the lack of epigenetic silencing events associated with tandem gene copies. We conclude that MAR elements may promote homologous recombination, and that cells and vectors can be engineered to take advantage of this property to mediate highly efficient gene transfer and expression.

Nuclear factor I revealed as family of promoter binding transcription activators.

BACKGROUND: Multiplex experimental assays coupled to computational predictions are being increasingly employed for the simultaneous analysis of many specimens at the genome scale, which quickly generates very large amounts of data. However, inferring valuable biological information from the comparisons of very large genomic datasets still represents an enormous challenge. RESULTS: As a study model, we chose the NFI/CTF family of mammalian transcription factors and we compared the results obtained from a genome-wide study of its binding sites with chromatin structure assays, gene expression microarray data, and in silico binding site predictions. We found that NFI/CTF family members preferentially bind their DNA target sites when they are located around transcription start sites when compared to control datasets generated from the random subsampling of the complete set of NFI binding sites. NFI proteins preferably associate with the upstream regions of genes that are highly expressed and that are enriched in active chromatin modifications such as H3K4me3 and H3K36me3. We postulate that this is a causal association and that NFI proteins mainly act as activators of transcription. This was documented for one member of the family (NFI-C), which revealed as a more potent gene activator than repressor in global gene expression analysis. Interestingly, we also discovered the association of NFI with the tri-methylation of lysine 9 of histone H3, a chromatin marker previously associated with the protection against silencing of telomeric genes by NFI. CONCLUSION: Taken together, we illustrate approaches that can be taken to analyze large genomic data, and provide evidence that NFI family members may act in conjunction with specific chromatin modifications to activate gene expression.

As the world turns: short-term human spatial memory in egocentric and allocentric coordinates.

We aimed to determine whether human subjects' reliance on different sources of spatial information encoded in different frames of reference (i.e., egocentric versus allocentric) affects their performance, decision time and memory capacity in a short-term spatial memory task performed in the real world. Subjects were asked to play the Memory game (a.k.a. the Concentration game) without an opponent, in four different conditions that controlled for the subjects' reliance on egocentric and/or allocentric frames of reference for the elaboration of a spatial representation of the image locations enabling maximal efficiency. We report experimental data from young adult men and women, and describe a mathematical model to estimate human short-term spatial memory capacity. We found that short-term spatial memory capacity was greatest when an egocentric spatial frame of reference enabled subjects to encode and remember the image locations. However, when egocentric information was not reliable, short-term spatial memory capacity was greater and decision time shorter when an allocentric representation of the image locations with respect to distant objects in the surrounding environment was available, as compared to when only a spatial representation encoding the relationships between the individual images, independent of the surrounding environment, was available. Our findings thus further demonstrate that changes in viewpoint produced by the movement of images placed in front of a stationary subject is not equivalent to the movement of the subject around stationary images. We discuss possible limitations of classical neuropsychological and virtual reality experiments of spatial memory, which typically restrict the sensory information normally available to human subjects in the real world.

Modeling food webs: exploring unexplained structure using latent traits.

Several stochastic models have tried to capture the architecture of food webs. This approach is interesting, but it is limited by the fact that different assumptions can yield similar results. To overcome this limitation, we develop a purely statistical approach. Body size in terms of an optimal ratio between prey and predator is used as explanatory variable. In 12 observed food webs, this model predicts, on average, 20% of interactions. To analyze the unexplained part, we introduce a latent term: each species is described by two latent traits, foraging and vulnerability, that represent nonmeasured characteristics of species once the optimal body size has been accounted for. The model now correctly predicts an average of 73% of links. The key features of our approach are that latent traits quantify the structure that is left unexplained by the explanatory variable and that this quantification allows a test of whether independent biological information, such as microhabitat use, camouflage, or phylogeny, explains this structure. We illustrate this method with phylogeny and find that it is linked to one or both latent traits in nine of 12 food webs. Our approach opens the door to the formulation of more complex models that can be applied to any kind of biological network.

Stochastic models and numerical algorithms for a class of regulatory gene networks.

Regulatory gene networks contain generic modules, like those involving feedback loops, which are essential for the regulation of many biological functions (Guido et al. in Nature 439:856-860, 2006). We consider a class of self-regulated genes which are the building blocks of many regulatory gene networks, and study the steady-state distribution of the associated Gillespie algorithm by providing efficient numerical algorithms. We also study a regulatory gene network of interest in gene therapy, using mean-field models with time delays. Convergence of the related time-nonhomogeneous Markov chain is established for a class of linear catalytic networks with feedback loops.

Clonidine as an adjuvant to intrathecal local anesthetics for surgery: systematic review of randomized trials.

BACKGROUND AND OBJECTIVES: Clonidine is added to intrathecal local anesthetics to improve intraoperative analgesia and to increase the duration of sensory and motor block. The aim of this systematic review is to quantify beneficial and harmful effects of clonidine when used as an adjuvant to intrathecal local anesthetics for surgery. METHODS: We included data from 22 randomized trials (1,445 patients) testing a large variety of doses of clonidine, added to intrathecal bupivacaine, mepivacaine, prilocaine, or tetracaine. RESULTS: Clonidine 15 to 150 microg prolonged in a linear, dose-dependent manner, the time to 2 segment regression (range of means, 14 to 75 minutes) and the time to regression to L2 (range of means, 11 to 128 minutes). The time to first analgesic request (median 101 minutes, range 35 to 310) and of motor block (median 47 minutes, range 6 to 131) was prolonged without evidence of dose-responsiveness. Time to achieve complete sensory or motor block, and extent of cephalic spread remained unchanged. There were fewer episodes of intraoperative pain with clonidine (relative risk, 0.24; 95% confidence interval [CI], 0.09-0.64; number needed to treat, 13) but more episodes of arterial hypotension (relative risk, 1.81; 95% CI 1.44-2.28; number needed to harm, 8) without evidence of dose-responsiveness. The risk of bradycardia was unchanged. CONCLUSIONS: This study may serve as a rational basis to help clinicians decide whether or not to combine clonidine with an intrathecal local anesthetic for surgery. The optimal dose of clonidine, however, remains unknown.

Statistical significance of quantitative PCR.

BACKGROUND: PCR has the potential to detect and precisely quantify specific DNA sequences, but it is not yet often used as a fully quantitative method. A number of data collection and processing strategies have been described for the implementation of quantitative PCR. However, they can be experimentally cumbersome, their relative performances have not been evaluated systematically, and they often remain poorly validated statistically and/or experimentally. In this study, we evaluated the performance of known methods, and compared them with newly developed data processing strategies in terms of resolution, precision and robustness. RESULTS: Our results indicate that simple methods that do not rely on the estimation of the efficiency of the PCR amplification may provide reproducible and sensitive data, but that they do not quantify DNA with precision. Other evaluated methods based on sigmoidal or exponential curve fitting were generally of both poor resolution and precision. A statistical analysis of the parameters that influence efficiency indicated that it depends mostly on the selected amplicon and to a lesser extent on the particular biological sample analyzed. Thus, we devised various strategies based on individual or averaged efficiency values, which were used to assess the regulated expression of several genes in response to a growth factor. CONCLUSION: Overall, qPCR data analysis methods differ significantly in their performance, and this analysis identifies methods that provide DNA quantification estimates of high precision, robustness and reliability. These methods allow reliable estimations of relative expression ratio of two-fold or higher, and our analysis provides an estimation of the number of biological samples that have to be analyzed to achieve a given precision.

Stochastic gene expression in switching environments.

Organisms are known to adapt to regularly varying environments. However, in most cases, the fluctuations of the environment are irregular and stochastic, alternating between favorable and unfavorable regimes, so that cells must cope with an uncertain future. A possible response is population diversification. We assume here that the cell population is divided into two groups, corresponding to two phenotypes, having distinct growth rates, and that cells can switch randomly their phenotypes. In static environments, the net growth rate is maximized when the population is homogeneously composed of cells having the largest growth rate. In random environments, growth rates fluctuate and observations reveal that sometimes heterogeneous populations have a larger net growth rate than homogeneous ones, a fact illustrated recently through Monte-Carlo simulations based on a birth and migration process in a random environment. We study this process mathematically by focusing on the proportion f(t) of cells having the largest growth rate at time t, and give explicitly the related steady state distribution pi. We also prove the convergence of empirical averages along trajectories to the first moment E(pi) (f), and provide efficient numerical methods for computing E(pi) (f).

Strand separation in negatively supercoiled DNA.

We consider Benham's model for strand separation in negatively supercoiled circular DNA, and study denaturation as function of the linking difference density kappa<0. We propose a statistical version of this model, based on bayesian segmentation methods of current use in bioinformatics; this leads to new algorithms with priors adapted to supercoiled DNA, taking into account the random nature of the free energies needed to denature base pairs.

On the Storage Capacity of Nonlinear Neural Networks.

We consider the Hopfield associative memory for storing m patterns xi(r) in { - 1, + 1}(n), r = 1, em leader,m. The weights are given by the scalar product model w(ij)=(m/n)G,i not equal j,w(ii) identical with 0, where G:R --> R is some nonlinear function, like G(x) z.tbnd6; Sgn(x), which is used in hardware implementation of associative memories. We give a rigorous lower bound for the memory size of this (ANN) by using large deviations estimates. Our main results states that retrieval without errors occurs when m(n) --> infinity as n --> infinity in such a way that m(n) < (n/2log(n))q(G), where 0 < q(G): = E(NG)N))(2)/E(G(N)(2)))