Reduced plasticity in coupling strength in the SCN clock in aging as revealed by Kuramoto modelling

The mammalian circadian clock is located in the suprachiasmatic nucleus (SCN) and consist of a network of coupled neurons, which are entrained to the environmental light-dark cycle. The phase coherence of the neurons is plastic and driven by the length of the day. With aging the capacity to behaviorally adapt to changes in the light regime reduces. The mechanisms underlying photoperiodic adaptation are largely unknown, but are important to unravel for the development of novel interventions to improve the quality of life of the elderly. We analyzed the neuronal synchronization of PER2::LUC protein expression in the SCN of young and old mice entrained to either long or short photoperiod and used the synchronization levels as input for a two-community noisy Kuramoto model. With the Kuramoto model we estimated the coupling strength between and within neuronal subpopulations. The model revealed that the coupling strength between and within subpopulations contributes to photoperiod induced changes in the phase relationship among neurons. We found that the SCN of young mice adapts in coupling strength over a large range, with low coupling strength in long photoperiod and higher coupling strength in short photoperiod. In aged mice we also found low coupling strength in long photoperiod, but strongly reduced capacity to reach high coupling strength in short photoperiod. The inability to respond with an increase in coupling strength shows that manipulation of photoperiod is not a suitable strategy to enhance clock function with aging. We conclude that the inability of aged mice to reach high coupling strength makes aged mice less capable to seasonal adaptation than young mice. Author Summary Circadian clocks drive daily rhythms in physiology and behavior. In mammals the clock resides in the suprachiasmatic nucleus (SCN) of the hypothalamus. The SCN consist of a network of coupled neurons which are synchronized to produce a coherent rhythm. Due to plasticity of the network, seasonal adaptation to short winter days and long summer days occurs. Disturbances in circadian rhythmicity of the elderly have negative health effects, such as neurodegenerative diseases. With the rise in life expectancy this is becoming a major issue. In our paper, we used a model to compare the neuronal coupling in the SCN between young and old animals. We investigated whether exposure to short photoperiod can strengthen coupling among clock cells, and thereby clock function, in old animals. We observed that this is not possible, indicating that simple environmental manipulations are not an option. We suggest that receptor targeted interventions are required, setting the path for further investigation.


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How phase coherence is established at the network level is relevant for seasonal adaptation and 66 breeding, but also for understanding clock disturbance in aging [11]. Although it is known that 67 differences in the phase relationship between neurons underlie photoperiodic adaptation, the 68 mechanism is unknown. One may intuitively expect that a decrease in coupling strength leads to a 69 broadened phase distribution. Alternatively, phase differences can be driven by an active process, for 70 example due to repulsive coupling between subpopulations of SCN neurons [12]. In such a scenario, 71 coupling within these subpopulations could be equally strong in long and short photoperiod.

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Subpopulations of SCN neurons form phase clusters, that map approximately to the core and shell we can explain the changes in synchronization of the activity phase of the neurons between different 75 photoperiods by changes in coupling strength. Particularly we will investigate the ability of older mice 76 to adjust to changes in daylength.

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For optimal functioning of the SCN a combination of molecular (e.g. clock gene expression), cellular 79 (e.g. electrical activity) and network (e.g. neurotransmitters) elements are important [15].

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Neurotransmitters play a crucial role in synchronizing the neurons in the SCN. An age-related decline 81 in expression of neurotransmitters has been reported [16], probably causing reduced communication 82 among neurons in the aged SCN [17]. It has been suggested that weakened circadian rhythmicity of 83 the elderly have negative health effects, and is causal to a broad array of diseases [18]. Therefore, 84 strengthening the clock in the aged is important, and strategies to do so rely on an identification of 85 underlying mechanisms. Here we investigated whether mechanisms underlying age-related changes in 86 synchronization are the same as mechanisms underlying photoperiod induced changes in 87 synchronization.

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We used data from bioluminescence imaging of single-cell PER2::LUC gene expression rhythms as 90 input for a Kuramoto model [19,20]  We calculated the order parameter (r) and peak time dispersion from the smoothed bioluminescence 106 traces ( Fig 1A) for all SCN slices in the different experimental conditions. To test whether the order 107 parameter is an appropriate measure for synchronization we calculated the Pearson correlation 108 coefficient between r and peak time dispersion, which was taken as a measure for synchronization in 109 [7,15]. The correlation coefficient showed a strong negative correlation between r and peak time 110 dispersion (R=-0.91; Fig 1B), which is expected as high dispersion should lead to lower synchrony 111 (r). Furthermore, we compared the values of r between the different experimental conditions.

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Independent t-tests showed that the r value was always significantly higher in SP than in LP in both    slice an upper and lower bound (Fig S1). A one-sample Kolmogorov-Smirnov test showed that K and D were not normally distributed (p>0.05). To compare the bounds of K and D between the 132 experimental conditions we used non-parametric independent-samples median tests. The lower and upper bound of K is always significantly higher in SP than LP (p<0.05), except for the upper bound of 7 bound of D between the experimental conditions ( Fig S1B). Next, the ranges between the medians of 136 the upper and lower bounds for K and D in the different experimental conditions were calculated (Fig   137   2). For young mice the range for K in LP does not overlap with the range for K in SP. Therefore the 138 coupling strength is definitely higher in SP than LP in young mice. For old mice the range of K in SP 139 lies within the upper half of the range of K in LP, which indicates that K again is higher in SP than 140 LP, although this is not significant. The range between the upper and lower bound for D is larger for 141 LP than SP in both young and old mice, however the range does not differ significantly between the 142 experimental conditions. The mean value between the upper bound and lower bound of D is close to 143 one for all experimental conditions. This shows that D will not significantly impact the results of the

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Taken more general we can describe the relation between K1 and L1 as the linear line in which 2 1 1 r a r =− and b1 is only dependent on r1 in an exponential manner. Therefore, when r1 is 217 greater than r2 the slope of the line is greater than -1 and when r1 is smaller than r2 the slope of the 218 line is smaller than -1. Furthermore, when r1 increases the line shifts vertically upwards and when r1 219 decreases the line shifts vertically downwards. The relationship between K2 and L2 can be described in 220 the same way, by interchanging the role of r1 and r2.

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From our available experimental data it is difficult to obtain precise values for K1, K2, L1 and L2. We 222 found that the synchronization in the neuronal subpopulations is always higher than the 223 synchronization of the SCN as a whole and from the relation between r and K we know that K goes to 224 infinity when r reaches 1. This suggests that the coupling strength within the neuronal subpopulations 225 is higher than the coupling strength in the SCN in general. However, we were not able to measure the

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This indicates that the range over which young mice can adapt their coupling strength is larger than 235 the range over which old animals can adapt their coupling strength.

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The order parameter, representing the synchronization, was normalized to obtain a value between 0 289 and 1, in which 0 means that the phases of the single-cells are randomly distributed and 1 implies 290 perfect synchrony [26,27]. A limitation of the extended Kuramoto model is that coupling strength 291 would become infinite when the neuronal synchronization of the SCN is 100%. This problem is 292 theoretical rather than practical: due to the differences in intrinsic characteristics of the neurons and 293 noise in the system, perfect synchronization will never be reached [28].

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One unique property of the extended Kuramoto model used in this study is that the coupling strengths

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In order to find upper and lower bounds on the noise strength we will take the expectation of T  425 using two expansions of the sinusoidal function and we will take the initial phase to be zero so that