Modeling of 2D diffusion processes based on microscopy data: parameter estimation and practical identifiability analysis.

BACKGROUND: Diffusion is a key component of many biological processes such as chemotaxis, developmental differentiation and tissue morphogenesis. Since recently, the spatial gradients caused by diffusion can be assessed in-vitro and in-vivo using microscopy based imaging techniques. The resulting time-series of two dimensional, high-resolutions images in combination with mechanistic models enable the quantitative analysis of the underlying mechanisms. However, such a model-based analysis is still challenging due to measurement noise and sparse observations, which result in uncertainties of the model parameters. METHODS: We introduce a likelihood function for image-based measurements with log-normal distributed noise. Based upon this likelihood function we formulate the maximum likelihood estimation problem, which is solved using PDE-constrained optimization methods. To assess the uncertainty and practical identifiability of the parameters we introduce profile likelihoods for diffusion processes. RESULTS AND CONCLUSION: As proof of concept, we model certain aspects of the guidance of dendritic cells towards lymphatic vessels, an example for haptotaxis. Using a realistic set of artificial measurement data, we estimate the five kinetic parameters of this model and compute profile likelihoods. Our novel approach for the estimation of model parameters from image data as well as the proposed identifiability analysis approach is widely applicable to diffusion processes. The profile likelihood based method provides more rigorous uncertainty bounds in contrast to local approximation methods.

Sharpening of expression domains induced by transcription and microRNA regulation within a spatio-temporal model of mid-hindbrain boundary formation.

BACKGROUND: The establishment of the mid-hindbrain region in vertebrates is mediated by the isthmic organizer, an embryonic secondary organizer characterized by a well-defined pattern of locally restricted gene expression domains with sharply delimited boundaries. While the function of the isthmic organizer at the mid-hindbrain boundary has been subject to extensive experimental studies, it remains unclear how this well-defined spatial gene expression pattern, which is essential for proper isthmic organizer function, is established during vertebrate development. Because the secreted Wnt1 protein plays a prominent role in isthmic organizer function, we focused in particular on the refinement of Wnt1 gene expression in this context. RESULTS: We analyzed the dynamics of the corresponding murine gene regulatory network and the related, diffusive signaling proteins using a macroscopic model for the biological two-scale signaling process. Despite the discontinuity arising from the sharp gene expression domain boundaries, we proved the existence of unique, positive solutions for the partial differential equation system. This enabled the numerically and analytically analysis of the formation and stability of the expression pattern. Notably, the calculated expression domain of Wnt1 has no sharp boundary in contrast to experimental evidence. We subsequently propose a post-transcriptional regulatory mechanism for Wnt1 miRNAs which yields the observed sharp expression domain boundaries. We established a list of candidate miRNAs and confirmed their expression pattern by radioactive in situ hybridization. The miRNA miR-709 was identified as a potential regulator of Wnt1 mRNA, which was validated by luciferase sensor assays. CONCLUSION: In summary, our theoretical analysis of the gene expression pattern induction at the mid-hindbrain boundary revealed the need to extend the model by an additional Wnt1 regulation. The developed macroscopic model of a two-scale process facilitate the stringent analysis of other morphogen-based patterning processes.

Exposure of the snail Potamopyrgus antipodarum to herbicide boosts output and survival of parasite infective stages.

Anthropogenic stressors such as pollutants can modulate levels of parasitic infections in aquatic animals by suppressing host immunity or through some other mechanisms. One such mechanism could involve increases in either the quantity or quality of infective stages produced by parasites. We investigated the effect of exposure of infected snails, Potamopyrgus antipodarum, to different concentrations of the widely-used herbicide glyphosate, on (i) the production of infective cercariae by three trematode species, Coitocaecum parvum, Apatemon sp. and an undescribed renicolid, and (ii) the survival of cercariae of the latter species. For all three trematode species, infected snails exposed over a month to low (0.36 mg a.i. L(-1)) or medium (3.6 mg a.i. L(-1)) formulated glyphosate concentrations released between 1.5 and 3 times more cercariae per day than snails under control conditions. The similar pattern seen in all trematodes suggests a general weakening of the host benefiting any of its parasites rather than some parasite species-specific mechanism. In addition, the survival of renicolid cercariae improved with increasing glyphosate concentrations, with cercariae living about 50% longer in the medium concentration (3.6 mg a.i. L(-1)) than in control conditions. Our results demonstrate a clear interaction between glyphosate pollution and parasitism by trematodes in freshwater systems, occurring at glyphosate concentrations recorded in aquatic habitats, and within the environmental exposure limit allowed in New Zealand freshwaters. Future risk assessments and toxicity tests need to consider indirect impacts resulting from infections to invertebrate and vertebrate species penetrated by cercariae and serving as second intermediate hosts of trematodes.