Search

Adaptation is used by biological sensory systems to respond to a wide range of environmental signals, by adapting their response properties to the statistics of the stimulus in order to maximize information transmission. We derive rules of optimal adaptation to changes in the mean and variance of a continuous stimulus in terms of Bayesian filters, and map them onto stochastic equations that couple the state of the environment to an internal variable controling the response function. We calculate numerical and exact results for the speed and accuracy of adaptation, and its impact on information transmission. We find that, in the regime of efficient adaptation, the speed of adaptation scales sublinearly with the rate of change of the environment. Finally, we exploit the mathematical equivalence between adaptation and stochastic thermodynamics to quantitatively relate adaptation to the irreversibility of the adaptation time course, defined by the rate of entropy production. Our results suggest a means to empirically quantify adaptation in a model-free and non-parametric way.

Key points The proton sensing ovarian cancer G protein coupled receptor 1 (OGR1, aka GPR68) promotes expression of the canonical transient receptor potential channel subunit TRPC4 in normal and transformed cerebellar granule precursor (DAOY) cells.OGR1 and TRPC4 are prominently expressed in healthy cerebellar tissue throughout postnatal development and in primary cerebellar medulloblastoma tissues.Activation of TRPC4‐containing channels in DAOY cells, but not non‐transformed granule precursor cells, results in prominent increases in [Ca2+]i and promotes cell motility in wound healing and transwell migration assays.Medulloblastoma cells not arising from granule precursor cells show neither prominent rises in [Ca2+]i nor enhanced motility in response to TRPC4 activation unless they overexpressTRPC4.Our results suggest that OGR1 enhances expression of TRPC4‐containing channels that contribute to enhanced invasion and metastasis of granule precursor‐derived human medulloblastoma. Abstract Aberrant intracellular Ca2+ signalling contributes to the formation and progression of a range of distinct pathologies including cancers. Rises in intracellular Ca2+ concentration occur in response to Ca2+ influx through plasma membrane channels and Ca2+ release from intracellular Ca2+ stores, which can be mobilized in response to activation of cell surface receptors. Ovarian cancer G protein coupled receptor 1 (OGR1, aka GPR68) is a proton‐sensing Gq‐coupled receptor that is most highly expressed in cerebellum. Medulloblastoma (MB) is the most common paediatric brain tumour that arises from cerebellar precursor cells. We found that nine distinct human MB samples all expressed OGR1. In both normal granule cells and the transformed human cerebellar granule cell line DAOY, OGR1 promoted expression of the proton‐potentiated member of the canonical transient receptor potential (TRPC) channel family, TRPC4. Consistent with a role for TRPC4 in MB, we found that all MB samples also expressed TRPC4. In DAOY cells, activation of TRPC4‐containing channels resulted in large Ca2+ influx and enhanced migration, while in normal cerebellar granule (precursor) cells and MB cells not derived from granule precursors, only small levels of Ca2+ influx and no enhanced migration were observed. Our results suggest that OGR1‐dependent increases in TRPC4 expression may favour formation of highly Ca2+‐permeable TRPC4‐containing channels that promote transformed granule cell migration. Increased motility of cancer cells is a prerequisite for cancer invasion and metastasis, and our findings may point towards a key role for TRPC4 in progression of certain types of MB., Key points The proton sensing ovarian cancer G protein coupled receptor 1 (OGR1, aka GPR68) promotes expression of the canonical transient receptor potential channel subunit TRPC4 in normal and transformed cerebellar granule precursor (DAOY) cells.OGR1 and TRPC4 are prominently expressed in healthy cerebellar tissue throughout postnatal development and in primary cerebellar medulloblastoma tissues.Activation of TRPC4‐containing channels in DAOY cells, but not non‐transformed granule precursor cells, results in prominent increases in [Ca2+]i and promotes cell motility in wound healing and transwell migration assays.Medulloblastoma cells not arising from granule precursor cells show neither prominent rises in [Ca2+]i nor enhanced motility in response to TRPC4 activation unless they overexpressTRPC4.Our results suggest that OGR1 enhances expression of TRPC4‐containing channels that contribute to enhanced invasion and metastasis of granule precursor‐derived human medulloblastoma.