How to get Oscillators in a Multicellular Clock to Agree on the Right Period

Circadian clocks generate nearly 24-h rhythms that regulate many physiological behaviors of organisms throughout the kingdoms of life. A clock’s complexity varies with the complexity of the organism. For simple organisms, rhythms are generated by a gene regulatory network within a single cell. For higher organisms (such as mammals and flies), the clockworks reside in multiple cells: each cell contains a genetic oscillator and intercellular signaling synchronizes the cellular rhythms, forming coherent, high-amplitude oscillations. Clocks in organisms at all levels of complexity have at their core a negative feedback loop. They differ in many details, such as the number of genes, the mechanisms involved in the regulation, and posttranslational modifications. Kim et al. (1) have identified the negative regulation term as key to clock functionality and provide an explanation as to why unicellular and multicellular clocks rely on different mechanisms. They do so by connecting protein sequestration within each cell to the emergent behavior of the synchronized multicellular oscillator in the mammalian clock. In mammals, the gene regulatory network within each cell is relatively well understood (2) and it has been fruitful to develop mechanistic mathematical models of the network that capture both the mRNA and protein interactions within each cell and the effects of intercellular signaling (3,4). Model analyses are helping us to understand how it is possible for a network of weak, heterogeneous oscillators to form a reliable clock. For example, it has been shown that tissues are more likely to synchronize if they are composed of single cells that operate close to a bifurcation boundary (5) and that networks with weak oscillators at network hubs are more easily synchronized than those with strong oscillators at hubs (3). Further, the phenomenon of amplitude expansion allows for cells with low amplitude to collectively increase their amplitudes and become less sensitive to external perturbations (6). In addition to understanding how the circadian clock achieves high-amplitude synchrony, we want to know how the period of the population is determined by the periods of the constituent cells (7). Experimental data show that the period of the synchronized clock is close to the mean intrinsic periods of its cells (8,9). Kim et al. (1) address the question of period-determination, in particular of how the population period ends up being very close to the mean of the individual periods. They construct a clear chain of mathematical reasoning that leads us from a particular mechanism within a cell to emergent behavior at the population level—that of the period of oscillation (see Fig. 1). They identify the expression controlling transcriptional regulation as key (10), show that protein sequestration is the appropriate mechanism, relate it to the alternative (and more popular) Hill kinetics, and explain the response of the transcription rate to the regulators. They then relate the transcription rate’s response to the phase response. Using the phase response and techniques from the theory of weakly connected neural networks (11), they derive formulae for predicting the period of the population. They simulate a simple (three-equation) model to demonstrate the accuracy of their predictions and show that their reasoning does not depend on the specific choice of parameters. This is important, because it suggests that their observations apply to broader contexts. Figure 1 Tracing the effects of protein sequestration as the mechanism for transcriptional regulation to the period of the synchronized network of oscillators in Kim et al. (1). (A) Within each cell, a key gene is downregulated when the activator (A) and ... Connecting individual cell properties to network-level behavior is complicated—not only does the behavior of oscillators affect the network, but the network affects the oscillators. In other words, context is critical. Do insights drawn from the model of Kim et al. (1) extend to models of multicellular clocks that are more complex, and, more importantly, do they explain the mechanisms in vivo? Previous modeling work has shown that the traditional Hill kinetics for transcriptional regulation tends to predict population periods that differ from the mean intrinsic periods of the constituent cells (12–14). However, in the future, it will be necessary to conduct formal analyses of models involving more processes to see if those additional processes, such as posttranslational modification, in some way compensate for or negate the effects of the term controlling transcriptional regulation. It will also be important to determine whether Kim et al. (1) have uncovered an evolutionary principle: Have multicellular organisms evolved to include protein-sequestration-based regulation as a critical modulator of circadian clock function? If so, we now know why.