The physics of bacterial decision making

The choice that bacteria make between sporulation and competence when subjected to stress provides a prototypical example of collective cell fate determination that is stochastic on the individual cell level, yet predictable (deterministic) on the population level. This collective decision is performed by an elaborated gene network. Considerable effort has been devoted to simplify its complexity by taking physics approaches to untangle the basic functional modules that are integrated to form the complete network: (1) A stochastic switch whose transition probability is controlled by two order parameters—population density and internal/external stress. (2) An adaptable timer whose clock rate is normalized by the same two previous order parameters. (3) Sensing units which measure population density and external stress. (4) A communication module that exchanges information about the cells' internal stress levels. (5) An oscillating gate of the stochastic switch which is regulated by the timer. The unique circuit architecture of the gate allows special dynamics and noise management features. The gate opens a window of opportunity in time for competence transitions, during which the circuit generates oscillations that are translated into a chain of short intervals with high transition probability. In addition, the unique architecture of the gate allows filtering of external noise and robustness against variations in circuit parameters and internal noise. We illustrate that a physics approach can be very valuable in investigating the decision process and in identifying its general principles. We also show that both cell-cell variability and noise have important functional roles in the collectively controlled individual decisions

A comparison of 'pruning' during multi-step planning in depressed and healthy individuals

BACKGROUND: Real-life decisions are often complex because they involve making sequential choices that constrain future options. We have previously shown that to render such multi-step decisions manageable, people 'prune' (i.e. selectively disregard) branches of decision trees that contain negative outcomes. We have theorized that sub-optimal pruning contributes to depression by promoting an oversampling of branches that result in unsavoury outcomes, which results in a negatively-biased valuation of the world. However, no study has tested this theory in depressed individuals. METHODS: Thirty unmedicated depressed and 31 healthy participants were administered a sequential reinforcement-based decision-making task to determine pruning behaviours, and completed measures of depression and anxiety. Computational, Bayesian and frequentist analyses examined group differences in task performance and relationships between pruning and depressive symptoms. RESULTS: Consistent with prior findings, participants robustly pruned branches of decision trees that began with large losses, regardless of the potential utility of those branches. However, there was no group difference in pruning behaviours. Further, there was no relationship between pruning and levels of depression/anxiety. CONCLUSIONS: We found no evidence that sub-optimal pruning is evident in depression. Future research could determine whether maladaptive pruning behaviours are observable in specific sub-groups of depressed patients (e.g. in treatment-resistant individuals), or whether misuse of other heuristics may contribute to depression

The neural basis of aversive Pavlovian guidance during planning.

Important real-world decisions are often arduous as they frequently involve sequences of choices, with initial selections affecting future options. Evaluating every possible combination of choices is computationally intractable, particularly for longer multi-step decisions. Therefore, humans frequently employ heuristics to reduce the complexity of decisions. We recently used a goal-directed planning task to demonstrate the profound behavioral influence and ubiquity of one such shortcut, namely aversive pruning, a reflexive Pavlovian process that involves neglecting parts of the decision space residing beyond salient negative outcomes. However, how the brain implements this important decision heuristic, and what underlies individual differences have hitherto remained unanswered. Therefore, we administered an adapted version of the same planning task to healthy male and female volunteers undergoing functional magnetic resonance imaging (fMRI) to determine the neural basis of aversive pruning. Through both computational and standard categorical fMRI analyses, we show that when planning was influenced by aversive pruning, the subgenual cingulate cortex was robustly recruited. This neural signature was distinct from those associated with general planning and valuation, two fundamental cognitive components elicited by our task but which are complementary to aversive pruning. Furthermore, we found that individual variation in levels of aversive pruning were associated with the responses of insula and dorsolateral prefrontal cortex to the receipt of large monetary losses, and also with sub-clinical levels of anxiety. In summary, our data reveal the neural signatures of an important reflexive Pavlovian processes that shapes goal-directed evaluations, and thereby determines the outcome of high-level sequential cognitive processes.SIGNIFICANCE STATEMENTMulti-step decisions are complex because initial choices constrain future options. Evaluating every path for long decision sequences is often impractical; thus, cognitive shortcuts are often essential. One pervasive and powerful heuristic is aversive pruning, in which potential decision-making avenues are curtailed at immediate negative outcomes. We used neuroimaging to examine how humans implement such pruning. We found it to be associated with activity in the subgenual cingulate cortex, with neural signatures that were distinguishable from those covarying with planning and valuation. Individual variations in aversive pruning levels related to sub-clinical anxiety levels and insular cortex activity. These findings reveal the neural mechanisms by which basic negative Pavlovian influences guide decision-making during planning, with implications for disrupted decision-making in psychiatric disorders

Aggregation Patterns in Stressed Bacteria

We study the formation of spot patterns seen in a variety of bacterial species when the bacteria are subjected to oxidative stress due to hazardous byproducts of respiration. Our approach consists of coupling the cell density field to a chemoattractant concentration as well as to nutrient and waste fields. The latter serves as a triggering field for emission of chemoattractant. Important elements in the proposed model include the propagation of a front of motile bacteria radially outward form an initial site, a Turing instability of the uniformly dense state and a reduction of motility for cells sufficiently far behind the front. The wide variety of patterns seen in the experiments is explained as being due the variation of the details of the initiation of the chemoattractant emission as well as the transition to a non-motile phase.Comment: 4 pages, REVTeX with 4 postscript figures (uuencoded) Figures 1a and 1b are available from the authors; paper submitted to PRL

Novel type of phase transition in a system of self-driven particles

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation ($\eta$) added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $| {\bf v}_a | =0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since $| {\bf v}_a |$ is found to scale as $(\eta_c-\eta)^\beta$ with $\beta\simeq 0.45$

Towards developmental modelling of tree root systems

Knowledge of belowground structures and processes is essential for understanding and predicting ecosystem functioning, and consequently in the development of adaptive strategies to safeguard production from trees and woody plants into the future. In the past, research has mainly been concentrated on growth models for the prediction of agronomic or forest production. Newly emerging scientific challenges, e.g. climate change and sustainable development, call for new integrated predictive methods where root systems development will become a key element for understanding global biological systems. The types of input data available from the various branches of woody root research, including biomass allocation, architecture, biomechanics, water and nutrient supply, are discussed with a view to the possibility of incorporating them into a more generic developmental model. We discuss here the main focus of root system modelling to date, including a description of simple allometric biomass models, and biomechanical stress models, and then build in complexity through static growth models towards architecture models. The next progressive and logical step in developing an inclusive developmental model that integrates these modelling approaches is discussed.Knowledge of belowground structures and processes is essential for understanding and predicting ecosystem functioning, and consequently in the development of adaptive strategies to safeguard production from trees and woody plants into the future. In the past, research has mainly been concentrated on growth models for the prediction of agronomic or forest production. Newly emerging scientific challenges, e.g. climate change and sustainable development, call for new integrated predictive methods where root systems development will become a key element for understanding global biological systems. The types of input data available from the various branches of woody root research, including biomass allocation, architecture, biomechanics, water and nutrient supply, are discussed with a view to the possibility of incorporating them into a more generic developmental model. We discuss here the main focus of root system modelling to date, including a description of simple allometric biomass models, and biomechanical stress models, and then build in complexity through static growth models towards architecture models. The next progressive and logical step in developing an inclusive developmental model that integrates these modelling approaches is discussed.Knowledge of belowground structures and processes is essential for understanding and predicting ecosystem functioning, and consequently in the development of adaptive strategies to safeguard production from trees and woody plants into the future. In the past, research has mainly been concentrated on growth models for the prediction of agronomic or forest production. Newly emerging scientific challenges, e.g. climate change and sustainable development, call for new integrated predictive methods where root systems development will become a key element for understanding global biological systems. The types of input data available from the various branches of woody root research, including biomass allocation, architecture, biomechanics, water and nutrient supply, are discussed with a view to the possibility of incorporating them into a more generic developmental model. We discuss here the main focus of root system modelling to date, including a description of simple allometric biomass models, and biomechanical stress models, and then build in complexity through static growth models towards architecture models. The next progressive and logical step in developing an inclusive developmental model that integrates these modelling approaches is discussed.Peer reviewe

Statistically validated networks in bipartite complex systems

Many complex systems present an intrinsic bipartite nature and are often described and modeled in terms of networks [1-5]. Examples include movies and actors [1, 2, 4], authors and scientific papers [6-9], email accounts and emails [10], plants and animals that pollinate them [11, 12]. Bipartite networks are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set. When one constructs a projected network with nodes from only one set, the system heterogeneity makes it very difficult to identify preferential links between the elements. Here we introduce an unsupervised method to statistically validate each link of the projected network against a null hypothesis taking into account the heterogeneity of the system. We apply our method to three different systems, namely the set of clusters of orthologous genes (COG) in completely sequenced genomes [13, 14], a set of daily returns of 500 US financial stocks, and the set of world movies of the IMDb database [15]. In all these systems, both different in size and level of heterogeneity, we find that our method is able to detect network structures which are informative about the system and are not simply expression of its heterogeneity. Specifically, our method (i) identifies the preferential relationships between the elements, (ii) naturally highlights the clustered structure of investigated systems, and (iii) allows to classify links according to the type of statistically validated relationships between the connected nodes.Comment: Main text: 13 pages, 3 figures, and 1 Table. Supplementary information: 15 pages, 3 figures, and 2 Table

Distinguishing mechanisms underlying EMT tristability

Abstract Background The Epithelial-Mesenchymal Transition (EMT) endows epithelial-looking cells with enhanced migratory ability during embryonic development and tissue repair. EMT can also be co-opted by cancer cells to acquire metastatic potential and drug-resistance. Recent research has argued that epithelial (E) cells can undergo either a partial EMT to attain a hybrid epithelial/mesenchymal (E/M) phenotype that typically displays collective migration, or a complete EMT to adopt a mesenchymal (M) phenotype that shows individual migration. The core EMT regulatory network - miR-34/SNAIL/miR-200/ZEB1 - has been identified by various studies, but how this network regulates the transitions among the E, E/M, and M phenotypes remains controversial. Two major mathematical models – ternary chimera switch (TCS) and cascading bistable switches (CBS) - that both focus on the miR-34/SNAIL/miR-200/ZEB1 network, have been proposed to elucidate the EMT dynamics, but a detailed analysis of how well either or both of these two models can capture recent experimental observations about EMT dynamics remains to be done. Results Here, via an integrated experimental and theoretical approach, we first show that both these two models can be used to understand the two-step transition of EMT - E→E/M→M, the different responses of SNAIL and ZEB1 to exogenous TGF-β and the irreversibility of complete EMT. Next, we present new experimental results that tend to discriminate between these two models. We show that ZEB1 is present at intermediate levels in the hybrid E/M H1975 cells, and that in HMLE cells, overexpression of SNAIL is not sufficient to initiate EMT in the absence of ZEB1 and FOXC2. Conclusions These experimental results argue in favor of the TCS model proposing that miR-200/ZEB1 behaves as a three-way decision-making switch enabling transitions among the E, hybrid E/M and M phenotypes

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

Charge Solitons in 1-D Arrays of Serially Coupled Josephson Junctions

We study a 1-D array of Josephson coupled superconducting grains with kinetic inductance which dominates over the Josephson inductance. In this limit the dynamics of excess Cooper pairs in the array is described in terms of charge solitons, created by polarization of the grains. We analyze the dynamics of these topological excitations, which are dual to the fluxons in a long Josephson junction, using the continuum sine-Gordon model. We find that their classical relativistic motion leads to saturation branches in the I-V characteristic of the array. We then discuss the semi-classical quantization of the charge soliton, and show that it is consistent with the large kinetic inductance of the array. We study the dynamics of a quantum charge soliton in a ring-shaped array biased by an external flux through its center. If the dephasing length of the quantum charge soliton is larger than the circumference of the array, quantum phenomena like persistent current and coherent current oscillations are expected. As the characteristic width of the charge soliton is of the order of 100 microns, it is a macroscopic quantum object. We discuss the dephasing mechanisms which can suppress the quantum behaviour of the charge soliton.Comment: 26 pages, LaTex, 7 Postscript figure