Lysogeny destabilizes computationally simulated microbiomes.

Microbiomes are ecosystems, and their stability can impact the health of their hosts. Theory predicts that predators influence ecosystem stability. Phages are key predators of bacteria in microbiomes, but phages are unusual predators because many have lysogenic life cycles. It has been hypothesized that lysogeny can destabilize microbiomes, but lysogeny has no direct analog in classical ecological theory, and no formal theory exists. We studied the stability of computationally simulated microbiomes with different numbers of temperate (lysogenic) and virulent (obligate lytic) phage species. Bacterial populations were more likely to fluctuate over time when there were more temperate phages species. After disturbances, bacterial populations returned to their pre-disturbance densities more slowly when there were more temperate phage species, but cycles engendered by disturbances dampened more slowly when there were more virulent phage species. Our work offers the first formal theory linking lysogeny to microbiome stability.

Maximising the size of non-redundant protein datasets using graph theory.

Analysis of protein data sets often requires prior removal of redundancy, so that data is not biased by containing similar proteins. This is usually achieved by pairwise comparison of sequences, followed by purging so that no two pairs have similarities above a chosen threshold. From a starting set, such as the PDB or a genome, one should remove as few sequences as possible, to give the largest possible non-redundant set for subsequent analysis. Protein redundancy can be represented as a graph, with proteins as nodes connected by undirected edges, if they have a pairwise similarity above the chosen threshold. The problem is then equivalent to finding the maximum independent set (MIS), where as few nodes are removed as possible to remove all edges. We tested seven MIS algorithms, three of which are new. We applied the methods to the PDB, subsets of the PDB, various genomes and the BHOLSIB benchmark datasets. For PDB subsets of up to 1000 proteins, we could compare to the exact MIS, found by the Cliquer algorithm. The best algorithm was the new method, Leaf. This works by adding clique members that have no edges to nodes outside the clique to the MIS, starting with the smallest cliques. For PDB subsets of up to 1000 members, it usually finds the MIS and is fast enough to apply to data sets of tens of thousands of proteins. Leaf gives sets that are around 10% larger than the commonly used PISCES algorithm, that are of identical quality. We therefore suggest that Leaf should be the method of choice for generating non-redundant protein data sets, though it is ineffective on dense graphs, such as the BHOLSIB benchmarks. The Leaf algorithm is available at: https://github.com/SimonCB765/Leaf, and sets from genomes and the PDB are available at: http://www.bioinf.manchester.ac.uk/leaf/.

A systematic survey of the response of a model NF-κB signalling pathway to TNFα stimulation.

White's lab established that strong, continuous stimulation with tumour necrosis factor-α (TNFα) can induce sustained oscillations in the subcellular localisation of the transcription factor nuclear factor κB (NF-κB). But the intensity of the TNFα signal varies substantially, from picomolar in the blood plasma of healthy organisms to nanomolar in diseased states. We report on a systematic survey using computational bifurcation theory to explore the relationship between the intensity of TNFα stimulation and the existence of sustained NF-κB oscillations. Using a deterministic model developed by Ashall et al. in 2009, we find that the system's responses to TNFα are characterised by a supercritical Hopf bifurcation point: above a critical intensity of TNFα the system exhibits sustained oscillations in NF-kB localisation. For TNFα below this critical value, damped oscillations are observed. This picture depends, however, on the values of the model's other parameters. When the values of certain reaction rates are altered the response of the signalling pathway to TNFα stimulation changes: in addition to the sustained oscillations induced by high-dose stimulation, a second oscillatory regime appears at much lower doses. Finally, we define scores to quantify the sensitivity of the dynamics of the system to variation in its parameters and use these scores to establish that the qualitative dynamics are most sensitive to the details of NF-κB mediated gene transcription.

Interactions among oscillatory pathways in NF-kappa B signaling.

BACKGROUND: Sustained stimulation with tumour necrosis factor alpha (TNF-alpha) induces substantial oscillations--observed at both the single cell and population levels--in the nuclear factor kappa B (NF-kappa B) system. Although the mechanism has not yet been elucidated fully, a core system has been identified consisting of a negative feedback loop involving NF-kappa B (RelA:p50 hetero-dimer) and its inhibitor I-kappa B-alpha. Many authors have suggested that this core oscillator should couple to other oscillatory pathways. RESULTS: First we analyse single-cell data from experiments in which the NF-kappa B system is forced by short trains of strong pulses of TNF-alpha. Power spectra of the ratio of nuclear-to-cytoplasmic concentration of NF-kappa B suggest that the cells' responses are entrained by the pulsing frequency. Using a recent model of the NF-kappa B system due to Caroline Horton, we carried out extensive numerical simulations to analyze the response frequencies induced by trains of pulses of TNF-alpha stimulation having a wide range of frequencies and amplitudes. These studies suggest that for sufficiently weak stimulation, various nonlinear resonances should be observable. To explore further the possibility of probing alternative feedback mechanisms, we also coupled the model to sinusoidal signals with a wide range of strengths and frequencies. Our results show that, at least in simulation, frequencies other than those of the forcing and the main NF-kappa B oscillator can be excited via sub- and superharmonic resonance, producing quasiperiodic and even chaotic dynamics. CONCLUSIONS: Our numerical results suggest that the entrainment phenomena observed in pulse-stimulated experiments is a consequence of the high intensity of the stimulation. Computational studies based on current models suggest that resonant interactions between periodic pulsatile forcing and the system's natural frequencies may become evident for sufficiently weak stimulation. Further simulations suggest that the nonlinearities of the NF-kappa B feedback oscillator mean that even sinusoidally modulated forcing can induce a rich variety of nonlinear interactions.

Bar-like S-cone stimuli reveal the importance of an intermediate temporal filter.

The relative involvement of different temporal frequency-selective filters underlying detection of chromatic stimuli was studied. Diverse spectral stimuli were used, namely flashed blue and yellow light spots, wide bars, and narrow bars. The stimuli were temporally modulated in luminance having constant wavelength. Although the bar-like stimuli apparently reduced the sensitivity at short and long wavelengths, the cone-opponent mechanism still remained responsible for the actual stimulus detection at different temporal frequencies. The bar-like stimuli increased sensitivity for temporal frequencies around 3-6 Hz, revealing involvement of an intermediate temporal frequency-selective filter in detection, the so-called transient-1 filter. A probability summation model for the method of adjustment was developed that assumes that detection depends on the properties of the temporal filters underlying the temporal frequency-sensitivity curve. The model supports the notion that at least two temporal frequency-selective filters are necessary to account for the shape of the sensitivity curves obtained for blue bar-like stimuli.

Characterisation of congenital nystagmus waveforms in terms of periodic orbits.

Because the oscillatory eye movements of congenital nystagmus vary from cycle to cycle, there is no clear relationship between the waveform produced and the underlying abnormality of the ocular motor system. We consider the durations of successive cycles of nystagmus which could be (1) completely determined by the lengths of the previous cycles, (2) completely independent of the lengths of the previous cycles or (3) a mixture of the two. The behaviour of a deterministic system can be characterised in terms of a collection of (unstable) oscillations, referred to as periodic orbits, which make up the system. By using a recently developed technique for identifying periodic orbits in noisy data, we find evidence for periodic orbits in nystagmus waveforms, eliminating the possibility that each cycle is independent of the previous cycles. The technique also enables us to identify the waveforms which correspond to the deterministic behaviour of the ocular motor system. These waveforms pose a challenge to our understanding of the ocular motor system because none of the current extensions to models of the normal behaviour of the ocular motor system can explain the range of identified waveforms.