Coexistence of competitors mediated by nonlinear noise

Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative models such as Fokker- Planck diffusion is not less convincing, movement of populations is most commonly modelled using the diffusion law due to Fick. An interesting feature of Fokker-Planck diffusion is the fact that for spatially varying diffusion coefficients the stationary solution is not a homogeneous distribution – in contrast to Fick’s law of diffusion. Instead, concentration accumulates in regions of low diffusivity and tends to lower levels for areas of high diffusivity. Thus, we may interpret the stationary distribution of the Fokker-Planck diffusion as a reflection of different levels of habitat quality. Moreover, the most common model for environmental fluctuations, linear multiplicative noise, is based on the assumption that individuals respond independently to stochastic environmental fluctuations. For large population densities the assumption of independence is debatable and the model further implies that noise intensities can increase to arbitrarily high levels. Therefore, instead of the commonly used linear multiplicative noise model, we implement environmental variability by an alternative nonlinear noise term which never exceeds a certain maximum noise intensity. With Fokker-Planck diffusion and the nonlinear noise model replacing the classical approaches we investigate a simple invasive system based on the Lotka-Volterra competition model. We observe that the heterogeneous stationary distribution generated by Fokker-Planck diffusion generally facilitates the formation of segregated habitats of resident and invader. However, this segregation can be broken by nonlinear noise leading to coexistence of resident and invader across the whole spatial domain, an effect that would not be possible in the non-spatial version of the competition model for the parameters considered here

Polysomal mRNA Association and Gene Expression in <i>Trypanosoma brucei</i>

Background: The contrasting physiological environments of Trypanosoma brucei procyclic (insect vector) and bloodstream (mammalian host) forms necessitates deployment of different molecular processes and, therefore, changes in protein expression. Transcriptional regulation is unusual in T. brucei because the arrangement of genes is polycistronic; however, genes which are transcribed together are subsequently cleaved into separate mRNAs by trans-splicing. Following pre-mRNA processing, the regulation of mature mRNA stability is a tightly controlled cellular process. While many stage-specific transcripts have been identified, previous studies using RNA-seq suggest that changes in overall transcript level do not necessarily reflect the abundance of the corresponding protein. Methods: To better understand the regulation of gene expression in T. brucei, we performed a bioinformatic analysis of RNA-seq on total, sub-polysomal, and polysomal mRNA samples. We further cross-referenced our dataset with a previously published proteomics dataset to identify new protein coding sequences. Results: Our analyses showed that several long non-coding RNAs are more abundant in the sub-polysome samples, which possibly implicates them in regulating cellular differentiation in T. brucei. We also improved the annotation of the T.brucei genome by identifying new putative protein coding transcripts that were confirmed by mass spectrometry data. Conclusions: Several long non-coding RNAs are more abundant in the sub-polysome cellular fractions and might pay a role in the regulation of gene expression. We hope that these data will be of wide general interest, as well as being of specific value to researchers studying gene regulation expression and life stage transitions in T. brucei