Effects of noise on models of spiny dendrites

We study the effects of noise in two models of spiny dendrites. Through the introduction of different types of noise to both the Spike-diffuse-spike (SDS) and Baer–Rinzel (BR) models we investigate the change in behaviour of the travelling wave solution present in both deterministic systems, as noise intensity increases. We show that the speed of wave propagation in both the SDS and BR models respectively differs as the noise intensity in the spine heads increases. In contrast the cable is very robust to noise and as such the speed shows very little variation from the deterministic system. We introduce a space-dependent spine density, ρ(x), to the original Baer–Rinzel model and show how this modified model can mimic behaviour (under influence of noise) of both original systems, through variation of one parameter. We also show that the correlation time and length scales of the noise can enhance propagation of travelling wave solutions where the white noise dominates the underlying signal and produces noise induced phenomena.     

Extrinsic noise passing through a Michaelis-Menten reaction: A universal response of a genetic switch

The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system through a nonlinear uptake reaction which acts as a nonlinear filter. Varying input noise intensity varies the mean of the noise after the passage through the filter, which changes the stability properties of the system. The steady-state displacement due to small noise is independent on the kinetics of the system but it only depends on the nonlinearity of the input function.For monotonically increasing and concave input functions such as the Michaelis-Menten uptake rate, we give a simple argument based on the small-noise expansion, which enables qualitative predictions of the steady-state displacement only by inspection of experimental data: when weak and rapid noise enters the system through a Michaelis-Menten reaction, then the graph of the system's steady states vs. the mean of the input signal always shifts to the right as noise intensity increases.We test the predictions on two models of lac operon, where TMG/lactose uptake is driven by a Michaelis-Menten enzymatic process. We show that as a consequence of the steady state displacement due to fluctuations in extracellular TMG/lactose concentration the lac switch responds in an asymmetric manner: as noise intensity increases, switching off lactose metabolism becomes easier and switching it on becomes more difficult.     

Increased Noise Levels Have Different Impacts on the Anti-Predator Behaviour of Two Sympatric Fish Species

Animals must avoid predation to survive and reproduce, and there is increasing evidence that man-made (anthropogenic) factors can influence predator−prey relationships. Anthropogenic noise has been shown to have a variety of effects on many species, but work investigating the impact on anti-predator behaviour is rare. In this laboratory study, we examined how additional noise (playback of field recordings of a ship passing through a harbour), compared with control conditions (playback of recordings from the same harbours without ship noise), affected responses to a visual predatory stimulus. We compared the anti-predator behaviour of two sympatric fish species, the three-spined stickleback (Gasterosteus aculeatus) and the European minnow (Phoxinus phoxinus), which share similar feeding and predator ecologies, but differ in their body armour. Effects of additional-noise playbacks differed between species: sticklebacks responded significantly more quickly to the visual predatory stimulus during additional-noise playbacks than during control conditions, while minnows exhibited no significant change in their response latency. Our results suggest that elevated noise levels have the potential to affect anti-predator behaviour of different species in different ways. Future field-based experiments are needed to confirm whether this effect and the interspecific difference exist in relation to real-world noise sources, and to determine survival and population consequences.     

Subtle interplay of stochasticity and deterministic dynamics pervades an evolutionary plausible genetic circuit for Bacillus subtilis competence

Here we study the interplay of stochastic and deterministic dynamics in an evolutionary plausible candidate core genetic circuit for Bacillus subtilis competence. We find that high noise would not necessarily be detrimental to the circuit’s ability to deliver the phenotype, due to an unexpected built-in robustness that we further investigate. Also, we find that seemingly subtle deterministic dynamical features of the regulation, unstable and stable limit cycles, while in the presence of biochemical noise, would result in a distinctive new observable in the phenotype. We conduct mathematical analyses of the system’s stability at the fixed points and derive some general model-independent consequences. We also show how imperfect time-scale separation in the system would result in observables detrimental to the phenotype, that nature could have harnessed for selection.     

Designing ecological corridors in a fragmented landscape: A fuzzy approach to circuit connectivity analysis

Landscape connectivity analysis is a major tool in supporting biodiversity conservation. Several methodologies have been developed to tackle it by following two main paths. The first path exploits graph approaches and models focal nodes’ connections on a resistance/conductance matrix depending on focal species’ movement potential. The second path considers geometrical pattern analyses based on the calculation of structural landscape metrics. These approaches separately investigate functional and structural features of the landscape, and may come short of a total definition if used separately. Here we propose a new scalable, modular, participative and open-source procedure based on Fuzzy logic to combine the functional and structural aspects of connectivity. We applied this method on the highly fragmented landscape of the Po Plain, focusing on its rare and endangered plain springs named fontanili. We identified an expert panel and involved it in the assignation of permeability values of land use classes with respect to the capacity of movement of animal species typical of fontanili. We concurrently performed a quantitative evaluation of the landscape fragmentation with a moving window. We found that the functional and structural evaluations were poorly correlated in the area under study (Pearson's r = −0.35, p < 0.001). We thus integrated these two non-overlapping analyses of the landscape by Fuzzy logic using thresholds and combination weights obtained from questionnaires proposed to the expert panel. The resulting index, termed Fuzzy Functionality Index (FFI), improved the level of information associated with landscape classification. By merging functional and structural aspects of the landscape, the FFI allowed us to discriminate different functional values of equally permeable parcels and vice versa. We demonstrate that FFI may act as a conductance measure in a circuit theory approach, highlighting ecological corridors between focal points of species’ distribution. We present FFI as an effective predictive index to inspect complex and non-linear landscape dynamics.     

System-level design of bacterial cell cycle control

Understanding of the cell cycle control logic in Caulobacter has progressed to the point where we now have an integrated view of the operation of an entire bacterial cell cycle system functioning as a state machine. Oscillating levels of a few temporally-controlled master regulator proteins in a cyclical circuit drive cell cycle progression. To a striking degree, the cell cycle regulation is a whole cell phenomenon. Phospho-signaling proteins and proteases dynamically deployed to specific locations on the cell wall are vital. An essential phospho-signaling system integral to the cell cycle circuitry is central to accomplishing asymmetric cell division.     

Coding of time-dependent stimuli in homogeneous and heterogeneous neural populations

We compare the information transmission of a time-dependent signal by two types of uncoupled neuron populations that differ in their sources of variability: i) a homogeneous population whose units receive independent noise and ii) a deterministic heterogeneous population, where each unit exhibits a different baseline firing rate (’disorder’). Our criterion for making both sources of variability quantitatively comparable is that the interspike-interval distributions are identical for both systems. Numerical simulations using leaky integrate-and-fire neurons unveil that a non-zero amount of both noise or disorder maximizes the encoding efficiency of the homogeneous and heterogeneous system, respectively, as a particular case of suprathreshold stochastic resonance. Our findings thus illustrate that heterogeneity can render similarly profitable effects for neuronal populations as dynamic noise. The optimal noise/disorder depends on the system size and the properties of the stimulus such as its intensity or cutoff frequency. We find that weak stimuli are better encoded by a noiseless heterogeneous population, whereas for strong stimuli a homogeneous population outperforms an equivalent heterogeneous system up to a moderate noise level. Furthermore, we derive analytical expressions of the coherence function for the cases of very strong noise and of vanishing intrinsic noise or heterogeneity, which predict the existence of an optimal noise intensity. Our results show that, depending on the type of signal, noise as well as heterogeneity can enhance the encoding performance of neuronal populations.     

Implementing conventional logic unconventionally: photochromic molecular populations as registers and logic gates

In this paper we detail experimental methods to implement registers, logic gates and logic circuits using populations of photochromic molecules exposed to sequences of light pulses. Photochromic molecules are molecules with two or more stable states that can be switched reversibly between states by illuminating with appropriate wavelengths of radiation. Registers are implemented by using the concentration of molecules in each state in a given sample to represent an integer value. The register's value can then be read using the intensity of a fluorescence signal from the sample. Logic gates have been implemented using a register with inputs in the form of light pulses to implement 1-input/1-output and 2-input/1-output logic gates. A proof of concept logic circuit is also demonstrated; coupled with the software workflow describe the transition from a circuit design to the corresponding sequence of light pulses.     

Analysis of noise in quorum sensing

Noise may play a pivotal role in gene circuit functionality, as demonstrated for the genetic switch in the bacterial phage lambda. Like the lambda switch, bacterial quorum sensing (QS) systems operate within a population and contain a bistable switching element, making it likely that noise plays a functional role in QS circuit operation. Therefore, a detailed analysis of the noise behavior of QS systems is needed. We have developed a set of tools generally applicable to the analysis of gene circuits, with an emphasis on investigations in the frequency domain (FD), that we apply here to the QS system in the marine bacterium Vibrio fischeri. We demonstrate that a tight coupling between exact stochastic simulation and FD analysis provides insights into the structure/function relationships in the QS circuit. Furthermore, we argue that a noise analysis is incomplete without consideration of the power spectral densities (PSDs) of the important molecular output signals. As an example we consider reversible reactions in the QS circuit, and show through analysis and exact stochastic simulation that these circuits make significant and dynamic modifications to the noise spectra. In particular, we demonstrate a "whitening" effect, which occurs as the noise is processed through these reversible reactions.     

Noise Expands the Response Range of the Bacillus subtilis Competence Circuit

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit.     

Statistical interpretation of the interplay between noise and chaos in the stochastic logistic map

A recurring problem in population biology - as well as other stochastic dynamical systems in biology, the physical and social sciences - is the distinction between the ‘true’ dynamics of a system and observational noise: i.e. can we from present data reliably infer e.g. biological mechanisms, or are signals swamped by noise.Here, we approach this problem using the canonical model for simple systems that exhibit complex behaviour, the logistic map. At each time-point noise is added, which allows us to study the long-term behaviour of a system which exhibits both non-linear dynamics and intrinsic noise.We show that the interplay between deterministic non-linear dynamics and simple Gaussian noise results in a perplexingly simple system when viewed statistically.In particular we show that for the case of Gaussian noise it is possible to derive at very reliable approximations for the time until the system has reached an absorbing state. This generic model allows us, for example, to study the life-time of molecular species involved in noisy feedback loops.     

Constructive effects of environmental noise in an excitable prey–predator plankton system with infected prey

An excitable model of fast phytoplankton and slow zooplankton dynamics is considered for the case of lysogenic viral infection of the phytoplankton population. The phytoplankton population is split into a susceptible (S) and an infected (I) part. Both parts grow logistically, limited by a common carrying capacity. Zooplankton (Z) is grazing on susceptibles and infected, following a Holling-type III functional response. The local analysis of the S–I–Z differential equations yields a number of stationary and/or oscillatory regimes and their combinations. Correspondingly interesting is the behaviour under multiplicative noise, modelled by stochastic differential equations. The external noise can enhance the survival of susceptibles and infected, respectively, that would go extinct in a deterministic environment. In the parameter range of excitability, noise can induce prey–predator oscillations and coherence resonance (CR). In the spatially extended case, synchronized global oscillations can be observed for medium noise intensities. Higher values of noise give rise to the formation of stationary spatial patterns.     

Random perturbations of spiking activity in a pair of coupled neurons

We examine the effects of stochastic input currents on the firing behaviour of two coupled Type 1 or Type 2 neurons. In Hodgkin–Huxley model neurons with standard parameters, which are Type 2, in the bistable regime, synaptic transmission can initiate oscillatory joint spiking, but white noise can terminate it. In Type 1 cells (models), typified by a quadratic integrate and fire model, synaptic coupling can cause oscillatory behaviour in excitatory cells, but Gaussian white noise can again terminate it. We locally determine an approximate basin of attraction, of the periodic orbit and explain the firing behaviour in terms of the effects of noise on the probability of escape of trajectories from      

Evaluation of the Oscillatory Interference Model of Grid Cell Firing through Analysis and Measured Period Variance of Some Biological Oscillators

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5µ ³ /(4πσ) ² seconds where µ is the mean period of an oscillator in seconds and σ² its variance in seconds². We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed.     

Experimentally increased noise levels change spatial and singing behaviour

The reasons why animal populations decline in response to anthropogenic noise are still poorly understood. To understand how populations are affected by noise, we must understand how individuals are affected by noise. By modifying the acoustic environment experimentally, we studied the potential relationship between noise levels and both spatial and singing behaviour in the European robin (Erithacus rubecula). We found that with increasing noise levels, males were more likely to move away from the noise source and changed their singing behaviour. Our results provide the first experimental evidence in a free ranging species, that not merely the presence of noise causes changes in behaviour and distribution, but that the level of noise pollution plays a crucial role as well. Our results have important implications for estimating the impact of infrastructure which differs in the level of noise produced. Thus, governmental planning bodies should not only consider the physical effect on the landscape when assessing the impact of new infrastructure, but also the noise levels emitted, which may reduce the loss of suitable habitats available for animals.     

Regulation of vocal amplitude by the blue-throated hummingbird, Lampornis clemenciae

Animals that rely on vocal communication must broadcast sound so that a perceptible signal is transmitted over an appropriate distance. We found that male blue-throated hummingbirds modified the amplitude of their vocalizations in response to both naturally occurring and experimenter-controlled changes in ambient noise levels. This phenomenon is known as the Lombard effect and may increase the efficiency of acoustic signalling. This study demonstrates the effect under natural field conditions and documents the first hummingbird species (Apodiformes: Trochilidae) to show this behaviour. We measured sound pressure levels (SPLs) of Serial Chip territorial advertisement calls across a natural range of ambient noise, primarily due to creeks within male territories. We found a significant correlation between the amplitude of Serial Chips and the amplitude of background noise. To test this relationship, we broadcast recordings of creek noise at high and low amplitudes while target individuals were producing Serial Chip vocalizations. We measured vocal SPLs before and during the playback. Individuals responded to changes in playback creek noise by changing the amplitude of Serial Chip production. We also measured transmission properties of Serial Chip calls through natural habitat to calculate the approximate amplitude of vocalizations at the position of the calling bird. We suggest that amplitude regulation of vocalizations contibutes to signal transmission distance along with the established relationships between singing behaviour, acoustic structure and habitat. Copyright 2003 Published by Elsevier Ltd on behalf of The Association for the Study of Animal Behaviour.     

Kinetic modeling and exploratory numerical simulation of chloroplastic starch degradation

Background

The chemotaxis pathway in the bacterium Escherichia coli allows cells to detect changes in external ligand concentration (e.g. nutrients). The pathway regulates the flagellated rotary motors and hence the cells' swimming behaviour, steering them towards more favourable environments. While the molecular components are well characterised, the motor behaviour measured by tethered cell experiments has been difficult to interpret.

Results

We study the effects of sensing and signalling noise on the motor behaviour. Specifically, we consider fluctuations stemming from ligand concentration, receptor switching between their signalling states, adaptation, modification of proteins by phosphorylation, and motor switching between its two rotational states. We develop a model which includes all signalling steps in the pathway, and discuss a simplified version, which captures the essential features of the full model. We find that the noise characteristics of the motor contain signatures from all these processes, albeit with varying magnitudes.

Conclusions

Our analysis allows us to address how cell-to-cell variation affects motor behaviour and the question of optimal pathway design. A similar comprehensive analysis can be applied to other two-component signalling pathways.     

Emergence of complex behaviour from simple circuit structures

The set of (feedback) circuits of a complex system is the machinery that allows the system to be aware of the levels of its crucial constituents. Circuits can be identified without ambiguity from the elements of the Jacobian matrix of the system. There are two types of circuits: positive if they comprise an even number of negative interactions, negative if this number is odd. The two types of circuits play deeply different roles: negative circuits are required for homeostasis, with or without oscillations, positive circuits are required for multistationarity, and hence, in biology, for differentiation and memory. In non-linear systems, a circuit can positive or negative (an 'ambiguous circuit', depending on the location in phase space. Full circuits are those circuits (or unions of disjoint circuits) that imply all the variables of the system. There is a tight relation between circuits and steady states. Each full circuit, if isolated, generates steady state(s) whose nature (eigenvalues) is determined by the structure of the circuit. Multistationarity requires the presence of at least two full circuits of opposite Eisenfeld signs, or else, an ambiguous circuit. We show how a significant part of the dynamical behaviour of a system can be predicted by a mere examination of its Jacobian matrix. We also show how extremely complex dynamics can be generated by such simple logical structures as a single (full and ambiguous) circuit.