Probability distributed time delays: integrating spatial effects into temporal models

Background In order to provide insights into the complex biochemical processes inside a cell, modelling approaches must find a balance between achieving an adequate representation of the physical phenomena and keeping the associated computational cost within reasonable limits. This issue is particularly stressed when spatial inhomogeneities have a significant effect on system's behaviour. In such cases, a spatially-resolved stochastic method can better portray the biological reality, but the corresponding computer simulations can in turn be prohibitively expensive. Results We present a method that incorporates spatial information by means of tailored, probability distributed time-delays. These distributions can be directly obtained by single in silico or a suitable set of in vitro experiments and are subsequently fed into a delay stochastic simulation algorithm (DSSA), achieving a good compromise between computational costs and a much more accurate representation of spatial processes such as molecular diffusion and translocation between cell compartments. Additionally, we present a novel alternative approach based on delay differential equations (DDE) that can be used in scenarios of high molecular concentrations and low noise propagation. Conclusions Our proposed methodologies accurately capture and incorporate certain spatial processes into temporal stochastic and deterministic simulations, increasing their accuracy at low computational costs. This is of particular importance given that time spans of cellular processes are generally larger (possibly by several orders of magnitude) than those achievable by current spatially-resolved stochastic simulators. Hence, our methodology allows users to explore cellular scenarios under the effects of diffusion and stochasticity in time spans that were, until now, simply unfeasible. Our methodologies are supported by theoretical considerations on the different modelling regimes, i.e. spatial vs. delay-temporal, as indicated by the corresponding Master Equations and presented elsewhere.

Inactivation of the Huntington's disease gene (Hdh) impairs anterior streak formation and early patterning of the mouse embryo

Background Huntingtin, the HD gene encoded protein mutated by polyglutamine expansion in Huntington's disease, is required in extraembryonic tissues for proper gastrulation, implicating its activities in nutrition or patterning of the developing embryo. To test these possibilities, we have used whole mount in situ hybridization to examine embryonic patterning and morphogenesis in homozygous Hdhex4/5 huntingtin deficient embryos. Results In the absence of huntingtin, expression of nutritive genes appears normal but E7.0–7.5 embryos exhibit a unique combination of patterning defects. Notable are a shortened primitive streak, absence of a proper node and diminished production of anterior streak derivatives. Reduced Wnt3a, Tbx6 and Dll1 expression signify decreased paraxial mesoderm and reduced Otx2 expression and lack of headfolds denote a failure of head development. In addition, genes initially broadly expressed are not properly restricted to the posterior, as evidenced by the ectopic expression of Nodal, Fgf8 and Gsc in the epiblast and T (Brachyury) and Evx1 in proximal mesoderm derivatives. Despite impaired posterior restriction and anterior streak deficits, overall anterior/posterior polarity is established. A single primitive streak forms and marker expression shows that the anterior epiblast and anterior visceral endoderm (AVE) are specified. Conclusion Huntingtin is essential in the early patterning of the embryo for formation of the anterior region of the primitive streak, and for down-regulation of a subset of dynamic growth and transcription factor genes. These findings provide fundamental starting points for identifying the novel cellular and molecular activities of huntingtin in the extraembryonic tissues that govern normal anterior streak development. This knowledge may prove to be important for understanding the mechanism by which the dominant polyglutamine expansion in huntingtin determines the loss of neurons in Huntington's disease.

Auditory spatial acuity approximates the resolving power of space-specific neurons

The relationship between neuronal acuity and behavioral performance was assessed in the barn owl (Tyto alba), a nocturnal raptor renowned for its ability to localize sounds and for the topographic representation of auditory space found in the midbrain. We measured discrimination of sound-source separation using a newly developed procedure involving the habituation and recovery of the pupillary dilation response. The smallest discriminable change of source location was found to be about two times finer in azimuth than in elevation. Recordings from neurons in its midbrain space map revealed that their spatial tuning, like the spatial discrimination behavior, was also better in azimuth than in elevation by a factor of about two. Because the PDR behavioral assay is mediated by the same circuitry whether discrimination is assessed in azimuth or in elevation, this difference in vertical and horizontal acuity is likely to reflect a true difference in sensory resolution, without additional confounding effects of differences in motor performance in the two dimensions. Our results, therefore, are consistent with the hypothesis that the acuity of the midbrain space map determines auditory spatial discrimination.

Spatial analysis of biomineralization associated gene expression from the mantle organ of the pearl oyster Pinctada maxima

Background: Biomineralization is a process encompassing all mineral containing tissues produced within an organism. One of the most dynamic examples of this process is the formation of the mollusk shell, comprising a variety of crystal phases and microstructures. The organic component incorporated within the shell is said to dictate this architecture. However general understanding of how this process is achieved remains ambiguous. The mantle is a conserved organ involved in shell formation throughout molluscs. Specifically the mantle is thought to be responsible for secreting the protein component of the shell. This study employs molecular approaches to determine the spatial expression of genes within the mantle tissue to further the elucidation of the shell biomineralization. Results: A microarray platform was custom generated (PmaxArray 1.0) from the pearl oyster Pinctada maxima. PmaxArray 1.0 consists of 4992 expressed sequence tags (ESTs) originating from mantle tissue. This microarray was used to analyze the spatial expression of ESTs throughout the mantle organ. The mantle was dissected into five discrete regions and analyzed for differential gene expression with PmaxArray 1.0. Over 2000 ESTs were determined to be differentially expressed among the tissue sections, identifying five major expression regions. In situ hybridization validated and further localized the expression for a subset of these ESTs. Comparative sequence similarity analysis of these ESTs revealed a number of the transcripts were novel while others showed significant sequence similarities to previously characterized shell related genes.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Patterning of tailored polycarbonate based non-chemically amplified resists using extreme ultraviolet lithography

A series of high-performance polycarbonates have been prepared with glass-transition temperatures and decomposition temperatures that are tunable by varying the repeat-unit chemical structure. Patterning of the polymers with extreme UV lithography has been achieved by taking advantage of direct photoinduced chain scission of the polymer chains, which results in a molecular-weight based solubility switch. After selective development of the irradiated regions of the polymers, feature sizes as small as 28.6 nm have been printed and the importance of resist-developer interactions for maximizing image quality has been demonstrated.

A review of locative media, mobile and embodied spatial interaction

Highlights ► Provides a review of the history and development of locative media. ► Outlines different human-computer interaction techniques applied in locative media. ► Discusses how locative media applications have changed interaction affordances in and of physical spaces. ► Discusses practices of people in urban settings that evolved through these new affordances. ► Provides an overview on methods to investigate and elaborate design principles for future locative media.