The Neurospora photoreceptor VIVID exerts negative and positive control on light sensing to achieve adaptation.

The light response in Neurospora is mediated by the photoreceptor and circadian transcription factor White Collar Complex (WCC). The expression rate of the WCC target genes adapts in daylight and remains refractory to moonlight, despite the extraordinary light sensitivity of the WCC. To explain this photoadaptation, feedback inhibition by the WCC interaction partner VIVID (VVD) has been invoked. Here we show through data-driven mathematical modeling that VVD allows Neurospora to detect relative changes in light intensity. To achieve this behavior, VVD acts as an inhibitor of WCC-driven gene expression and, at the same time, as a positive regulator that maintains the responsiveness of the photosystem. Our data indicate that this paradoxical function is realized by a futile cycle that involves the light-induced sequestration of active WCC by VVD and the replenishment of the activatable WCC pool through the decay of the photoactivated state. Our quantitative study uncovers a novel network motif for achieving sensory adaptation and defines a core input module of the circadian clock in Neurospora.

A global circadian repressor controls antiphasic expression of metabolic genes in Neurospora.

The white-collar complex (WCC), the core transcription factor of the circadian clock of Neurospora, activates morning-specific expression of the transcription repressor CSP1. Newly synthesized CSP1 exists in a transient complex with the corepressor RCM1/RCO1 and the ubiquitin ligase UBR1. CSP1 is rapidly hyperphosphorylated and degraded via UBR1 and its ubiquitin conjugase RAD6. Genes controlled by CSP1 are rhythmically expressed and peak in the evening (i.e., in antiphase to morning-specific genes directly controlled by WCC). Rhythmic expression of these second-tier genes depends crucially on phosphorylation and rapid turnover of CSP1, which ensures tight coupling of CSP1 abundance and function to the circadian activity of WCC. Negative feedback of CSP1 on its own transcription buffers the amplitude of CSP1-dependent oscillations against fluctuations of WCC activity. CSP1 predominantly regulates genes involved in metabolism. It controls ergosterol synthesis and fatty acid desaturases and thereby modulates the lipid composition of membranes.

Circadian conformational change of the Neurospora clock protein FREQUENCY triggered by clustered hyperphosphorylation of a basic domain.

In the course of a day, the Neurospora clock protein FREQUENCY (FRQ) is progressively phosphorylated at up to 113 sites and eventually degraded. Phosphorylation and degradation are crucial for circadian time keeping, but it is not known how phosphorylation of a large number of sites correlates with circadian degradation of FRQ. We show that two amphipathic motifs in FRQ interact over a long distance, bringing the positively charged N-terminal portion in spatial proximity to the negatively charged middle and C-terminal portion of FRQ. The interaction is essential for the recruitment of casein kinase 1a (CK1a) into a stable complex with FRQ. FRQ-bound CK1a progressively phosphorylates the positively charged N-terminal domain of FRQ at up to 46 nonconsensus sites, triggering a conformational change, presumably by electrostatic repulsion, that commits the protein for degradation via the PEST1 signal in the negatively charged central portion of FRQ.

A model for cyst lumen expansion and size regulation via fluid secretion.

Many internal epithelial organs derive from cysts, which are tissues comprised of bent epithelial cell layers enclosing a lumen. Ion accumulation in the lumen drives water influx and consequently water accumulation and cyst expansion. Lumen-size recognition is important for the regulation of organ size. When lumen size and cyst size are not controlled, diseases can result; for instance, renal failure of the kidney. We develop a mechanistic mathematical model of lumen expansion in order to investigate the mechanisms for saturation of cyst growth. We include fluid accumulation in the lumen, osmotic and elastic pressure, ion transport and stretch-induced cell division. We find that the lumen volume increases in two phases: first, due to fluid accumulation stretching the cells, then in the second phase, the volume increase follows the increase in cell number until proliferation ceases as stretch forces relax. The model is quantitatively fitted to published data of in vitro cyst growth and predicts steady state lumen size as a function of the model parameters.

Inositol trisphosphate receptor and ion channel models based on single-channel data.

The inositol trisphosphate receptor (IPR) plays an important role in controlling the dynamics of intracellular Ca(2+). Single-channel patch-clamp recordings are a typical way to study these receptors as well as other ion channels. Methods for analyzing and using this type of data have been developed to fit Markov models of the receptor. The usual method of parameter fitting is based on maximum-likelihood techniques. However, Bayesian inference and Markov chain Monte Carlo techniques are becoming more popular. We describe the application of the Bayesian methods to real experimental single-channel data in three ion channels: the ryanodine receptor, the K(+) channel, and the IPR. One of the main aims of all three studies was that of model selection with different approaches taken. We also discuss the modeling implications for single-channel data that display different levels of channel activity within one recording.

A kinetic model of the inositol trisphosphate receptor based on single-channel data.

In many cell types, the inositol trisphosphate receptor is one of the important components controlling intracellular calcium dynamics, and an understanding of this receptor is necessary for an understanding of calcium oscillations and waves. Based on single-channel data from the type-I inositol trisphosphate receptor, and using a Markov chain Monte Carlo approach, we show that the most complex time-dependent model that can be unambiguously determined from steady-state data is one with three closed states and one open state, and we determine how the rate constants depend on calcium. Because the transitions between these states are complex functions of calcium concentration, each model state must correspond to a group of physical states. We fit two different topologies and find that both models predict that the main effect of [Ca(2+)] is to modulate the probability that the receptor is in a state that is able to open, rather than to modulate the transition rate to the open state.

Markov chain Monte Carlo fitting of single-channel data from inositol trisphosphate receptors.

In many cell types, the inositol trisphosphate receptor (IPR) is one of the important components that control intracellular calcium dynamics, and an understanding of this receptor (which is also a calcium channel) is necessary for an understanding of calcium oscillations and waves. Recent advances in experimental techniques now allow for the measurement of single-channel activity of the IPR in conditions similar to its native environment, and these data can be used to determine the rate constants in Markov models of the IPR. We illustrate a parameter estimation method based on Markov chain Monte Carlo, which can be used to fit directly to single-channel data, and determining, as an intrinsic part of the fit, the times at which the IPR is opening and closing. We show, using simulated data, the most complex Markov model that can be unambiguously determined from steady-state data and show that non-steady-state data is required to determine more complex models.

A mathematical model of fluid secretion from a parotid acinar cell.

Salivary fluid secretion is crucial for preventing problems such as dryness of mouth, difficulty with mastication and swallowing, as well as oral pain and dental cavities. Fluid flow is driven primarily by the transepithelial movement of chloride and sodium ions into the parotid acinus lumen. The activation of Cl(-) channels is calcium dependent, with the average elevated calcium concentration during calcium oscillations increasing the conductance of the channels, leading to an outflow of Cl(-). The accumulation of NaCl in the lumen drives water flow by osmosis. We construct a mathematical model of the calcium concentration oscillations and couple this to a model for Cl(-) efflux. We also construct a model governing fluid flow in an isolated parotid acinar cell, which includes a description of the rate of change of intracellular ion concentrations, cell volume, membrane potential and water flow rate. We find that [Ca(2+)] oscillations lead to oscillations in fluid flow, and that the rate of fluid flow is regulated by the average calcium concentration and not the frequency of the oscillations.

A bifurcation analysis of calcium buffering.

Many mathematical models of calcium oscillations model buffering implicitly by using a rapid buffering approximation. This approximation assumes that separate time scales can be distinguished, with the buffer reactions occurring on a faster time scale than the other calcium fluxes. The rapid buffering approximation is convenient as it reduces the model to a single transport equation for calcium, but buffering is not always so fast. We investigated what happens if such an assumption is made for slower buffers for parameter values typical of both endogenous and exogenous buffers. We found that no qualitative differences are introduced to the bifurcation structure, i.e. there are no anomalous behaviour or artifacts in the dynamics when a rapid buffering approximation is used compared with including buffering explicitly in the model. We found that there exist distinct buffer parameter regions in which either the rapid buffering approximation or an assumption of no buffering could be used. Separating the two regions was a small transition region of buffer parameters for which care needs to be taken in modelling buffers. However, overall, the qualitative behaviour in all three regions was similar.