Hidden layer learns a generative model of a long sequence of spike trains.

<p>(<i>A</i>) The three neurons in layer 1 (Layer 1) are clamped to input spike trains (in this example, a random pattern with spike frequency of 0.2). During the open state, these neurons project (through synaptic weights sampled from a random uniform distribution between -1 and 1) to a much larger hidden layer (Layer 2) which in this example contains thirty neurons. Synaptic state matching in the intra-layer 2 synaptic connections (L2-L2) gives rise to an accurate predictive model within this hidden layer. Synaptic state matching of synapse projections from layer 2 to layer 1 (L2-L1) generates an accurate predictive model of the missing input at layer 1. Layer 1 neurons do not have any internal recurrent connections. (<i>B</i>) top: missing input into layer 1 during the closed state; middle: predicted pattern of missing input created by the projection of hidden layer axons to layer 1 during the closed state. The pattern is a perfect match to the missing input; bottom: the coincident activity of the 30 neurons in the hidden layer during the closed state. SSM parameter choices for both L2-L2 and L2-L1 connections were as follows: potentiation strength (α): 5×10⁻⁴, spike-rate memory (m_s): 200, potentiation memory (m_p): 50, state switching period: (Gaussian, τ_μ = 30, τ_σ = 10), neuron firing threshold (V_t): 0.5, sigmoid sharpness (S): 10, latency range (L): 20.</p

The role of SSM and STCP in the accuracy-trajectory of learning.

<p>Synaptic state matching (+SSM) is crucial for accuracy and long term stability. In the (-SSM) simulation, potentiation was unbounded (e.g. unconstrained by comparison of mean potentiation between the open and closed states). Spike-timing dependent covariance plasticity (+STCP) substantially improves convergence rate and accuracy as compared to a plasticity rule that is not modulated by spike-rate history (-STCP). In the (-STCP) simulation, Δw = +/−α. The 40 neuron SSM is trained on two alternating random spike patterns (features), each 40 time-steps long, with an intervening 20 time step quiescent period. Accuracy is a conservative measure of how well internally generated patterns match the missing input during the same time interval. It is defined as one minus the fraction of discordant spikes between the missing input spike trains and the internally generated spike trains. The value here is the average for all forty neurons. Accuracy can be negative in cases where internally generated activity is noisy and/or unstable. The accuracy does not reach maximum (1.0) because the network is unable to generate the earliest part of each random pattern due to the absence of any input during the quiescent period preceding the closed state.</p

Pattern completion in the context of moving bars across a visual field.

<p>A 400 neuron network arranged in a 20×20 sheet with topographic input from the visual field is trained on bars moving left, right, up and down (See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072865#pone.0072865.s004" target="_blank">Figure S4</a> for details). The network carries out pattern completion in response to bars moving right (top) and left (bottom). The clean input is presented with equal power random noise during the open state. The network performs perfect pattern completion during the second closed state (dashed boxes) following the presentation of a long-enough sequence of moving bars during the preceding open state. Open/closed durations are sampled from a Gaussian with a mean of 7 and sd of 2 time steps. For the sake of space, bars moving up and down are omitted and only every other time-point is shown.</p

Synaptic state matching architecture and spike-timing dependent covariance plasticity.

<p>(<i>A</i>) Dynamical architecture of synaptic state switching and state matching. Neurons continually oscillate between two global network states: activity imposed by sensory input (open) and activity generated by recurrent synaptic drive, in the absence of sensory input (closed). (<i>B</i>) synaptic plasticity rule (potentiation strength) in discrete time. X_i and X_j are binary events corresponding to pre-synaptic and post-synaptic spikes, respectively and i> and j> are their continuous valued running averages. For an activating synapse (+), a pre-synaptic spike, followed immediately by a post-synaptic spike gives rise to a potential weight increase (Δw>0). In the case of an inhibitory synapse (-), a pre-synaptic spike preceding a quiescent post-synaptic neuron gives rise to a potential weight increase (Δw<0). Potentiation can only occur following a pre-synaptic spike. Candidate potentiation events lead to synaptic strength modulation such that the mean potentiation strength is matched between the open and closed states. As mean potentiation strength is a compact measure of the locally observed spike statistics, synaptic state matching assures that recurrent synaptic drive is recapitulating the spatiotemporal dynamics of sensory input. In this example, spikes correspond to immediate pre and post-synaptic states. In principle, each synapse can have its own axonal conduction delay, in which the presynaptic action potential arrives with a distinct latency relative to the action potential originating at the soma.</p

A thirty neuron SSM network trained on input spikes in the form a triangular wave.

<p>(<i>A</i>) Synaptic weight matrices for different latency conduction delays (1–5 time steps). Positive values (red) correspond to activating connections and negative values (blue) to inhibitory ones. (<i>B</i>) full pattern of activity in the sensory environment (full pattern), input activity during the open state (open), internal activity during the closed state (closed), and the combined (complete). Pattern completion during the closed state is a perfect match to the missing input. SSM parameter choices were as follows: potentiation strength (α): 4×10⁻⁵, spike-rate memory (m_s): 100, potentiation memory (m_p): 100, state switching period: (Gaussian, τ_μ = 15, τ_σ = 5), neuron firing threshold (V_t): 0.5, sigmoid sharpness (S): 10, latency range (L): 5. Spike-rate memory (m_s) and potentiation memory (m_p) are the widths of averaging time window for calculating mean spike-rate and mean potentiation, respectively. (<i>C</i>) Input synaptic drive into a single neuron for activating input (red), and inhibitory input (blue). Spikes are represented in green. The comparisons were performed after stabilization of learning. The two simulations are identical except for a thousand-fold higher potentiation scale (α). Each neuron has 290 synaptic inputs (29 neurons ×5 latencies ×2 polarities).</p

Multifactorial Competition and Resistance in a Two-Species Bacterial System

<div><p>Microorganisms exist almost exclusively in interactive multispecies communities, but genetic determinants of the fitness of interacting bacteria, and accessible adaptive pathways, remain uncharacterized. Here, using a two-species system, we studied the antagonism of <i>Pseudomonas aeruginosa</i> against <i>Escherichia coli</i>. Our unbiased genome-scale approach enabled us to identify multiple factors that explained the entire antagonism observed. We discovered both forms of ecological competition–sequestration of iron led to exploitative competition, while phenazine exposure engendered interference competition. We used laboratory evolution to discover adaptive evolutionary trajectories in our system. In the presence of <i>P</i>. <i>aeruginosa</i> toxins, <i>E</i>. <i>coli</i> populations showed parallel molecular evolution and adaptive convergence at the gene-level. The multiple resistance pathways discovered provide novel insights into mechanisms of toxin entry and activity. Our study reveals the molecular complexity of a simple two-species interaction, an important first-step in the application of systems biology to detailed molecular dissection of interactions within native microbiomes.</p></div

<i>P</i>. <i>aeruginosa</i> secreted phenazines inhibit <i>E</i>. <i>coli</i> growth.

<p><i>E</i>. <i>coli</i> cells were grown in the presence of <i>P</i>. <i>aeruginosa</i> spent media or pyocyanin, and the cell density was determined before and after 16 hours of growth. Data are the means from at least 5 replicates. Error bars represent standard deviation. <b>(A)</b> <i>E</i>. <i>coli</i> cells were grown in the presence of 20% or 50% (v/v) spent media from <i>P</i>. <i>aeruginosa</i> wild-type and phenazine mutant strains. All mutant and control data shown were significantly different from WT (<i>q</i> < 0.005) as determined by a one-sided Mann-Whitney <i>U</i> test followed by the Benjamini-Hochberg procedure for multiple testing correction (this correction included the mutant strains showed in Figs <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005715#pgen.1005715.g003" target="_blank">3B</a> and <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005715#pgen.1005715.g005" target="_blank">5</a>). <b>(B)</b> <i>E</i>. <i>coli</i> cells were grown in the presence of increasing concentrations of pyocyanin. The 50μM and 100μM data were significantly different from the immediately lower concentration (25μM and 50μM, respectively) as determined by a one-sided Mann-Whitney <i>U</i> test followed by the Benjamini-Hochberg procedure for multiple testing correction (<i>q</i> < 0.01), but the 25μM data was not significantly different from the 0μM data (<i>q</i> > 0.5).</p

<i>P</i>. <i>aeruginosa</i> spent media induces iron transport pathways.

<p><i>E</i>. <i>coli</i> cells were grown in the presence of 20% (v/v) <i>P</i>. <i>aeruginosa</i> spent media for 20min, and the transcriptional response was measured compared to unexposed cells. The genes were ordered by their fold-induction and divided into 10 equal sized bins, which are represented in the 10 columns. The range of log₁₀ (fold-change) is shown on the top left of the heat-map. The global change in gene expression was analyzed using iPAGE [<a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005715#pgen.1005715.ref013" target="_blank">13</a>], which identifies the functional GO categories significantly enriched and depleted across the bins, as depicted in the heat map. The colors show the significance, with red representing the negative of log₁₀ of the over-representation <i>p</i>-values, and blue representing the log₁₀ of the under-representation <i>p</i>-values.</p

Iron-limitation by <i>P</i>. <i>aeruginosa</i> siderophores inhibits <i>E</i>. <i>coli</i> growth.

<p><i>E</i>. <i>coli</i> cells were grown in the presence of <i>P</i>. <i>aeruginosa</i> spent media and the cell density was determined before and after 16 hours of growth. Data are the means from at least 5 replicates. Error bars represent standard deviation. <b>(A)</b> <i>E</i>. <i>coli</i> cells were grown in the presence of 50% (v/v) <i>P</i>. <i>aeruginosa</i> spent media supplemented with increasing levels of ferric citrate. Data from each concentration were significantly different from the preceding concentration (<i>q</i> < 0.005) as determined by a one-sided Mann-Whitney <i>U</i> test followed by the Benjamini-Hochberg procedure for multiple testing correction. <b>(B)</b> <i>E</i>. <i>coli</i> cells were grown in the presence of 20% or 50% (v/v) spent media from various <i>P</i>. <i>aeruginosa</i> wild-type and mutant strains. All mutant and control data shown (except for Δ<i>pchE</i> at 20%) were significantly different from WT (<i>q</i> < 0.005) as determined by a one-sided Mann-Whitney <i>U</i> test followed by the Benjamini-Hochberg procedure for multiple testing correction (this correction included the mutant strains showed in Figs <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005715#pgen.1005715.g005" target="_blank">5</a> and <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005715#pgen.1005715.g007" target="_blank">7A</a>). Spent media from the Δ<i>pvdJ</i> and the Δ<i>pvdJ</i> Δ<i>pchE</i> mutants supported more growth than the media salts base control, likely due to the presence of unused nutrients or <i>P</i>. <i>aeruginosa</i> signaling molecules in the spent media.</p

The PQS pathway response in <i>P</i>. <i>aeruginosa</i> is important for <i>E</i>. <i>coli</i> growth inhibition.

<p><i>E</i>. <i>coli</i> cells were grown in the presence of 20% or 50% (v/v) spent media from either WT <i>P</i>. <i>aeruginosa</i> or various PQS pathway mutants, and the cell density was determined before and after 16 hours of growth. Data are the means from at least 5 replicates. Error bars represent standard deviation. All mutant and control data shown were significantly different from WT (<i>q</i> < 0.005) as determined by a one-sided Mann-Whitney <i>U</i> test followed by the Benjamini-Hochberg procedure for multiple testing correction (this correction included the mutant strains showed in Figs <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005715#pgen.1005715.g003" target="_blank">3B</a> and <a href="http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1005715#pgen.1005715.g007" target="_blank">7A</a>).</p