Reading oscillatory instructions: How cells achieve time-dependent responses to oscillating transcription factors

A transcription factor complex in Dictyostelium enables adaptive changes in macropinocytosis during the growth-to-development transition

Macropinocytosis, an evolutionarily conserved endocytic pathway, mediates nonselective bulk uptake of extracellular fluid. It is the primary route for axenic Dictyostelium cells to obtain nutrients and has also emerged as a nutrient-scavenging pathway for mammalian cells. How cells adjust macropinocytic activity in various physiological or developmental contexts remains to be elucidated. We discovered that, in Dictyostelium cells, the transcription factors Hbx5 and MybG form a functional complex in the nucleus to maintain macropinocytic activity during the growth stage. In contrast, during starvation-induced multicellular development, the transcription factor complex undergoes nucleocytoplasmic shuttling in response to oscillatory cyclic adenosine 3',5'-monophosphate (cAMP) signals, which leads to increased cytoplasmic retention of the complex and progressive downregulation of macropinocytosis. Therefore, by coupling macropinocytosis-related gene expression to the cAMP oscillation system, which facilitates long-range cell-cell communication, the dynamic translocation of the Hbx5-MybG complex orchestrates a population-level adjustment of macropinocytic activity to adapt to changing environmental conditions.

An oscillating reaction network with an exact closed form solution in the time domain

BACKGROUND

Oscillatory behavior is critical to many life sustaining processes such as cell cycles, circadian rhythms, and notch signaling. Important biological functions depend on the characteristics of these oscillations (hereafter, oscillation characteristics or OCs): frequency (e.g., event timings), amplitude (e.g., signal strength), and phase (e.g., event sequencing). Numerous oscillating reaction networks have been documented or proposed. Some investigators claim that oscillations in reaction networks require nonlinear dynamics in that at least one rate law is a nonlinear function of species concentrations. No one has shown that oscillations can be produced for a reaction network with linear dynamics. Further, no one has obtained closed form solutions for the frequency, amplitude and phase of any oscillating reaction network. Finally, no one has published an algorithm for constructing oscillating reaction networks with desired OCs.

RESULTS

This is a theoretical study that analyzes reaction networks in terms of their representation as systems of ordinary differential equations. Our contributions are: (a) construction of an oscillating, two species reaction network [two species harmonic oscillator (2SHO)] that has no nonlinearity; (b) obtaining closed form formulas that calculate frequency, amplitude, and phase in terms of the parameters of the 2SHO reaction network, something that has not been done for any published oscillating reaction network; and (c) development of an algorithm that parameterizes the 2SHO to achieve desired oscillation, a capability that has not been produced for any published oscillating reaction network.

CONCLUSIONS

Our 2SHO demonstrates the feasibility of creating an oscillating reaction network whose dynamics are described by a system of linear differential equations. Because it is a linear system, we can derive closed form expressions for the frequency, amplitude, and phase of oscillations, something that has not been done for other published reaction networks. With these formulas, we can design 2SHO reaction networks to have desired oscillation characteristics. Finally, our sensitivity analysis suggests an approach to constructing a 2SHO for a biochemical system.