Modeling the kinetics of heteromeric potassium channels.

Mechanistic mathematical modeling has long been used as a tool for answering questions in cellular physiology. To mathematically describe cellular processes such as cell excitability, volume regulation, neurotransmitter release, and hormone secretion requires accurate descriptions of ion channel kinetics. One class of ion channels currently lacking a physiological model framework is the class of channels built with multiple different potassium protein subunits called heteromeric voltage gated potassium channels. Here we present a novel mathematical model for heteromeric potassium channels that captures both the number and type of protein subunits present in each channel. Key model assumptions are validated by showing our model is the reduction of a Markov model and through observations about voltage clamp data. We then show our model's success in replicating kinetic properties of concatemeric channels with different numbers of K v 1.1 and K v 1.2 subunits. Finally, through comparisons with multiple expression experiments across multiple voltage gated potassium families, we use the model to make predictions about the importance and effect of genetic mutations in heteromeric channel formation.

A mathematical model analyzing temperature threshold dependence in cold sensitive neurons.

Here we examine a class of neurons that have been recently explored, the somatosensory neuronal subclass of cold thermosensors. We create a mathematical model of a cold sensing neuron that has been formulated to understand the variety of ionic channels involved. In particular this model showcases the role of TRPM8 and voltage gated potassium channels in setting the temperature dependent activation and inactivation threshold level. Bifurcation analysis of the model demonstrates that a Hodgkin-Huxley type model with additional TRPM8 channels is sufficient to replicate observable experimental features of when different threshold level cold thermosensors turn on. Additionally, our analysis gives insight into what is happening at the temperature levels at which these neurons shut off and the role sodium and leak currents may have in this. This type of model construction and analysis provides a framework moving forward that will help tackle less well understood neuronal classes and their important ionic channels.

Changes in urban plant phenology in the Pacific Northwest from 1959 to 2016: anthropogenic warming and natural oscillation.

In the Pacific Northwest of the USA, winter and spring temperature vary with the Pacific Decadal Oscillation, making effects of anthropogenic warming difficult to detect. We sought to detect community-level signals of anthropogenic change in a legacy plant phenology dataset. We analyzed both incomplete data from 1959 to 2016 on spring phenology of 115 species and more complete 1996-2016 data on spring and fall events for 607 plant species. We used ordination of the long-term dataset to identify two major axes of community-level change in phenology among years, with the first being a trend toward earlier spring phenology in more recent years. In contrast, for the short-term dataset, variation in spring phenology was mostly PDO-driven and did not reveal a strong trend over time. At both time scales, a second axis of phenological variation reflected summer and fall events, especially earlier appearance of fall color in recent years. In univariate analysis, more than 80% of individual species' leaf out dates and first flower dates occurred earlier over time, for an average advance across all species of 2.5 days per decade from 1959 to 2016. While most events did not advance in the period 1996-2016, fall color advanced by 10.6 days per decade, suggesting that intensification of summer drought has continued regardless of the PDO cycle. While estimates of slope over time depended strongly on the time window chosen for the analysis, estimates of slope versus temperature were consistently negative regardless of time window, averaging 5-7 days per 1 °C for spring events.