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.

Correlation of the expression of human kallikrein-related peptidases 4 and 7 with the prognosis in oral squamous cell carcinoma

Background Very few articles have been written about the expression of kallikreins (KLK4 and KLK7) in oral cancers. Therefore, the purpose of this study was to examine and report on their prognostic potential. Methods Eighty archival blocks of primary oral cancers were sectioned and stained for KLK4 and KLK7 by immunohistochemistry. The percentage and the intensity of malignant keratinocyte staining were correlated with patient survival using Cox regression analysis. Results Both kallikreins were expressed strongly in the majority of tumor cells in 68 of 80 cases: these were mostly moderately or poorly differentiated neoplasms. Staining was particularly intense at the infiltrating front. Patients with intense staining had significantly shorter overall survival (p < .05). Conclusion This is the first observation on the patient survival influenced by kallikrein expression in oral carcinoma. The findings are consistent with those for carcinomas at other sites, in particular the prostate and ovary. KLK4 and/or KLK7 immunohistochemistry seems to have diagnostic and prognostic potential in this 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.