Modeling clock-related metabolic syndrome due to conflicting light and food cues

Our model consists in two embedded networks: The metabolic network composed of the glucose-insulin module and the β cell circadian oscillator (Fig. 2). On one side, we model the metabolic module as follows: a 24 h forcing function representing food intake periodically increases blood glucose levels. This stimulates insulin secretion which in turn, lowers blood glucose levels by increasing its uptake by muscles and adipose tissue. On the other side, our clock network model comprises the main transcriptional translational feedback loop with the positive arm (represented by the protein BMAL1) activating the negative arm (represented by Per and Cry) which in turn shuts down the positive regulation of Bmal1. We also model the additional feedback loop between Bmal1 and Rev-Erb because several studies have highlighted the importance of this regulation in the observed phases of clock gene expression^23,24. To keep the model as simple as possible, we merge the different isoforms of the clock components into one variable and we make no distinction between cytoplasmic and nuclear proteins.

We then add the bi-directional coupling between the clock and the metabolic module. With regard to the circadian control of metabolism, Perelis et al. have shown that many transcripts of factors involved in insulin exocytosis are cycling and affected by a knockout of Bmal1¹³. This includes factors involved in diverse aspects of insulin exocytosis such as vesicule budding, transport, tethering and fusion. In particular, the authors also showed that BMAL1 and CLOCK regulate the expression of these genes by binding at distal regulatory elements. Therefore, in our model, the coupling of the β cell clock to metabolism is mainly achieved via BMAL1. More specifically, for the sake of simplicity, we only model the dynamics of one generic clock-controlled peptide involved in insulin secretion (termed as Exo mRNA and EXO protein). Furthermore, we consider that under normal physiological conditions, glucose levels and exocytosis peptide concentration are high simultaneously in order to ensure optimal insulin secretion. In other words, we consider that high insulin secretion is only possible if glucose levels and exocytosis peptide concentration are high simultaneously.

Concerning the control of the clock by metabolism, very little is known about how nutrient cues affect the β cell clock. Since increasing glucose concentration increases Per transcription in cultured rats islets²⁵, we here assume that glucose cues act on Per transcription. As we will see in the next section, the 12 h shift of Per mRNA when restricting food access to the normal rest phase can thus be explained by the 12 h shift of glucose cues.

Finally, as we aim to use the model to study what happens when light and food cues are conflicting, we must incorporate the effect of these cues in our system. Information about the feeding cues is transmitted to the system through glucose levels that rise after a meal. Light information is transmitted from the centre to the periphery through SCN-driven outputs which include endocrine, temperature and neural cues. Under daytime feeding, the time profiles of endocrine cues such as glucocorticoids (as well as those of body temperature) become bimodal, that is, one peak is shifted by 12 h and the other peak is not shifted)^6,18,26. This is probably due to the fact that these cues receive information both from the non-shifting SCN and from the shifting nutrient cues. Although glucocorticoid signalling is known to act on Per transcription²⁷, the bimodal profile does not seem to affect much Per time profile²⁶. Therefore and also because the effect of nutrient cues on Per are sufficient to explain its 12 shift, for the sake of simplicity, we do not incorporate glucocorticoid signalling in the model. Finally, very little is known about the time profile of neural cues after an inversion of the feeding schedule. To explain the partial phase shift of the other clock genes, we hypothesise that there is at least some SCN-driven signal that is not shifted when inverting the eating schedule: this could be the case of neural cues. Since the rhythm of neuronal activity peaks during the light period²⁸, we consider that it increases Rev-Erb expression because the latter is raising during the subjective day.

Figure 2 summarises the interaction network considered in our model. The model consists in 13 ordinary differential equations governing the dynamics of the key variables of our system (9 clock components, glucose, insulin and EXO mRNA/protein), as well as two periodic signals, standing for the SCN and the food cues (see Supplementary Information). In order to properly reproduce experimental time profiles of pancreatic clock gene expression and metabolic factors levels, we fit our mathematical model to published experimental data coming from mice kept under 12 h light conditions and fed ad libitum¹⁸. Figure 3 shows that the in silico time profiles correctly match the experimental ones for both metabolic and β cell clock components.

We then investigate the effect of restricting food access to the light period. We simulate this perturbation by shifting the phase of the forcing function representing food intake by 12 h while leaving the one representing SCN-driven cues unchanged (Fig. 4A,B). Our hypothesis is that the resulting conflict between nutrient and SCN-driven inputs driving the local clock could explain the observed differential phase shift in clock gene expression. We were able to find a set of parameter values that qualitatively reproduce experimental data: Per expression shifts by 11.63 h while the phase shift of the other clock genes (Bmal1, Rev-Erb and Cry mRNAs) lies between 7 and 9 h (Figs 4 and S1). This differential phase shift suggests that the phase relationship between the positive and the negative arm of the clock is not preserved when several systemic inputs are conflicting.

To test this more systematically, we progressively increase the strength of SCN-driven cues and compare the phase shift of several clock components when inverting the eating schedule (Fig. 5A). In the absence of SCN-driven cues, the whole clock shifts by 12 h. When increasing the strength of SCN-driven cues, the simulations show that the different clock components do not shift in the same way. Indeed, the negative element Per, which receives information about food intake (through Glucose cues), shifts by almost 12 h regardless of the strength of the SCN cue. On the other hand, the positive element Bmal1, which also integrates the unchanged SCN-driven cues through Rev-Erbα, undergoes smaller phase shifts as the strength of the SCN cues increases. As we will see in the next section, this can impact the phase and amplitude of clock-controlled physiological outputs.

One might wonder if this “differential phase shift” property depends on a specific parameter set. A further analysis shows how the phase shift of Bmal1 and Per is influenced by the variations of a few relevant parameters (see supplementary material, section 3.2 and Fig. S2). This analysis indicates that this “differential phase shift” property does not depend on a specific set of parameter values and suggests that it could be more general for the described model.

Until now, we have considered large perturbations such as a 12 h phase shift in food intake. We then investigate the effect of smaller perturbations in the eating schedule: The simulations show that the phase difference between different clock components is only slightly changed for a short advance or delay in food intake (Fig.). Altogether, the equilibrium between the positive and the negative arm can be strongly affected by large chronic perturbations. S3A,B

In order to ensure a timely insulin secretion, the clock-controlled protein machinery participating in insulin exocytosis has to be present when nutrients (glucose) are ingested. Therefore, we assume that a high insulin exocytosis requires the concomitance between glucose and clock-controlled exocytosis cues. This condition is integrated in the model by describing the time evolution of insulin levels as (see also Eq.in the Suppl. Mat.) S17

where the first term of the right hand side represents insulin secretion and the second term, insulin clearance. The kinetic constant k_i is the maximal secretion rate and d_i is the clearance constant. The function f_exo = f(clock) represents the effect of clock-controlled exocytosis cues on insulin secretion and its dynamics is mainly driven by BMAL1 while f_glu = f(glucose) corresponds to the effect of glucose on insulin secretion (see Table S2 in Supplementary Information for the exact expressions of these functions (f_Ins,EXO and f_Ins,glucose)).

Thus, under normal feeding conditions, the peak in the concentration of factors involved in insulin exocytosis is concomitant with the peak in blood glucose levels, thereby ensuring optimal insulin secretion (Fig. 5B, upper panel). However, disturbing the phase relation between the different core clock genes can strongly affect the phase of clock-controlled outputs. Indeed, our simulations show that the partial shift of some clock components following a reversal of the eating schedule also results in an incomplete inversion of the clock-controlled expression of exocytosis peptides. Consequently, the rise in the concentration of the factors involved in insulin exocytosis is now delayed and no longer concomitant with the rise in blood glucose levels (Fig. 5B, lower panel). This results in a reduced insulin secretion and consequent increase in blood glucose levels (Fig. 4C,F). Thus our model shows that the metabolic syndrome (hypoinsulinemia and hyperglycemia) observed during restricted feeding can be explained by a disruption of the coincidence mechanism between clock-controlled and nutrient cues due to upstream conflicts between SCN-driven and nutrient cues (Fig. 5C). Our simulations also predict that there is no significative amplitude change in insulin secretion for smaller shifts in the eating schedule (Fig. S3C,D).

We further use the model to test what happens when peripheral clocks completely uncouple from the central when food intake is inverted, as it was earlier assumed⁶. The model predicts that in this case, all genes would shift by 12 h when inverting the eating schedule and that insulin levels would not be reduced, which is not what is observed experimentally (Fig. S4). Thus, the hypothesis of a complete uncoupling from the SCN fails to reproduce the differential phase shift in clock gene expression as well as the metabolic syndrome.

It is commonly assumed that the cross-talk between clock and metabolic pathways enables the anticipation of the “daily” (periodic) arrival of food. This raises the question of whether this property can be observed in clock-controlled metabolic outputs and how it is affected upon ill-timed feeding. Under normal (nighttime) feeding conditions, we notice that experimental profiles of insulin levels display a slope rupture (Fig. 6A). Indeed, prior to food intake, the slope of the insulin profile rises slowly, while it increases steeply after meal ingestion. The same feature is reproduced in our simulations (Fig. 6B). Interestingly, this slope rupture is lost in both in silico and in experimental data when restricting food access to the light period (Fig. 6D,E). This can be interpreted as follows: in physiological conditions, the clock induces the expression of exocytosis peptides in anticipation of the forthcoming arrival of food, leading to a slow increase of insulin secretion. This is followed by a fast increase in insulin secretion after food intake. When inverting the eating schedule, the clock control of exocytosis is delayed and therefore fails to induce peptides synthesis prior to food intake: this situation corresponds to a passive response to meal ingestion (no anticipatory rise) similar to what would happen in the absence of any clock (see next section). This suggests that the slope rupture observed in physiological metabolic time profiles can be seen as the hallmark of a food anticipatory behaviour due to the circadian control of metabolism.

Finally, our mathematical model allows us to discuss the implications of the circadian control of metabolism. A way to gain insight into the properties of a particular physiological network is to compare it to alternative architectures, a task for which mathematical modelling is particularly well-suited. In this regard, here we compare the physiological architecture described above (a local clock driven by SCN cues and coupled to a metabolic cycle) to two alternatives: the case where the metabolic module is only controlled by the local clock (that is, without any rhythmic cues from the SCN informing about the light-dark cycle) and the case where the metabolic module is not controlled by any clock. We refer to the first situation as “physiological case” (Fig. 7A), the second one as “no central clock” (Fig. 7C) and the last one as “no clock at all” (Fig. 7E). The absence of a central clock is simulated by replacing the SCN-driven rhythm by its mean value. Similarly, we mimic the absence of a local clock by replacing the circadian transcription of the factor involved in exocytosis (here Exo mRNA) by its mean value (see Supplementary Information).

Having a clock system that is sensitive to light cues and nutrient cues (physiological and “no central clock” cases) enables the anticipation of predictable environmental changes. By having a local clock that is sensitive to nutrient cues and controls metabolic outputs, organisms are able to anticipate food availability and metabolise the ingested nutrients optimally (Fig. 6A,B). In the absence of any clock, they can only passively respond to food intake (no anticipation): this is characterised by an absence of food anticipatory rise in metabolic time profiles (Fig. 6C). In addition, having a light anticipatory mechanism as in the physiological case enables the organism to keep track of the alternation between active and rest phases so that starving animals can still look for food during the appropriate phase of the cycle¹⁸.

However, this anticipation property comes with a cost: as we have seen in the previous sections, in physiological conditions, the organism is not able to completely adapt to large chronic perturbations in food intake, which creates metabolic syndrome-like pathology. Figure 7B summarises this prediction with a circular plot representation: an inverted eating schedule leads to a differential phase shift in clock gene expression and to subsequent hypoinsulinemia. Conversely, in the absence of light information from the SCN (“no central clock” architecture), the system would completely adapt to the new feeding schedule because the local clock would not be twisted by conflicting light and food cues. This is illustrated in Fig. 7D (no differential phase shift of clock components and similar insulin levels during nighttime and daytime feeding). But the adaptation of such a system is predicted to take some time because of the inertia of the local clock (Fig. S5A,B and E). In contrast, in the absence of any clock (“no clock at all” situation), the metabolic response to large chronic changes in food availability is immediate (Fig. S5C–E). Altogether, these observations suggest that there is a tradeoff between the ability to sense light and nutrient cues (which leads to anticipation) and the ability to fully adapt to chronic perturbations in one of these inputs.

The system of 13 ordinary differential equations (+2 ordinary differential equations for food intake) was implemented in MATLAB R2015a (MathWorks, https://nl.mathworks.com↗) and solved with ode15s. In order to reproduce expression and metabolic time profiles, the values of the parameters of the model were fitted by the Hooke & Jeeves pattern search optimisation method using COPASI 4.20³⁶. The published time profiles come from mice kept under 12 h light conditions and fed ad libitum (for the restricted feeding conditions, mice could access food only during the light phase)¹⁸. These raw data were interpolated with Fourier series in order to facilitate the adjustment with in silico time profiles. More detailed information can be found in Supplementary Information.

The authors declare no competing interests.