Fig 1.
A simple stochastic model of rat feeding that uses a continuously time-varying fullness can accurately recapitulate food intake.
(A) Schematic illustration of the model, showing feeding, a short within-meal pause, a long intermeal interval, and the meal termination decision, which relies on fullness x. (B) Incorporating fullness into a stochastic model of feeding allows prediction of the intermeal interval. The model predicts a distribution over possible intermeal interval lengths (red curve in top panel, actual next mealtime shown as a dark bar). Representative sample of data showing bout-level feeding data (top panel, blue bars) and model-derived fullness (bottom panel, blue curve). Simulated trajectories of fullness are shown in the bottom panel (light red curves) alongside mean fullness (dark red curve). Inset: bout-level feeding data for the meal shown inside the dashed box. (C) Filling occurs linearly at a rate ρ that varies between bouts (see D), whereas emptying is nonlinear but has identical dynamics whenever the animal is not feeding. (D) Feeding bout duration is exponentially distributed, and rate ρ is normally distributed with mean μF and standard deviation σF. (E) Within-meal pauses are typically short compared to intermeal intervals and are distributed exponentially. Figure shows exponential distribution for representative parameter values. (F) Meal termination decisions are sigmoid in fullness x and are controlled by parameters T1 and T2. Keeping the product of these parameters fixed changes the effect of fullness on termination probability. (G) Intermeal intervals are typically long and depend on fullness x, which varies over time. Parameter L1 controls intermeal interval duration independent of fullness, and L2 measures the effect of fullness. (H) Our model accurately captures food intake: (posterior) predictive values of normalised food intake are strongly correlated with true values. Marker style indicates anorectic agent (if any) and photoperiod (see legend). Darker colours indicate higher doses; see Table 2 for concentrations. Underlying data are available in the following repository: doi:10.17632/vpm89vrz7g.1. Inference procedure described in Materials and Methods. GLP-1, glucagon-like peptide 1; PYY3-36, peptide YY3-36.
Table 1.
Summary and description of model parameters.
See Fig 1 for a graphical summary and equations.
Table 2.
Details of drug doses and administration protocols.
Light on/off times were 06:00 and 18:00, respectively. Anorectic agents were GLP-1, PYY3-36, lithium chloride (LiCl), and leptin.
Fig 2.
A two-parameter behavioural fingerprint, combining characteristic bout duration and intermeal interval parameters, accounts for a large proportion of variation both between and within groups.
Different anorectic agents drive different patterns of feeding behaviour. (A) Two parameters of the model are strongly informative regarding food intake but are only weakly correlated with one another: characteristic bout duration τF and fullness-dependent intermeal interval parameter L2. Scatter matrix of τF, L2, and normalised food intake (diagonal entries show univariate marginals) indicates substantial intergroup variation in τF and L2 correlated with changes in normalised food intake. (B) Reduced characteristic bout durations are not fully compensated for by increased feeding rate: scatter plot of individual posterior mean values coloured by normalised food intake. Dashed line indicates constant food intake contour. (C) Characteristic bout duration and feeding rate vary both within and between groups. Animals in the dark period tend to have longer, slower bouts. (D, E) PYY3-36 causes group-level variation in bout time and feeding rate. Colours as in Fig 2C. Animals recovering from an overnight fast show less variation than rats fed ad libitum. (F, G) GLP-1 produces a more pronounced effect on both bout duration and rate than PYY3-36 in rats fed ad libitum. Lithium chloride produces a stronger reduction in feeding rate than PYY3-36 in rats recovering from an overnight fast but has limited effect on bout duration. Underlying data are available in the following repository: doi:10.17632/vpm89vrz7g.1. Inference procedure described in Materials and Methods. GLP-1, glucagon-like peptide 1; IMI, intermeal interval; PYY3-36, peptide YY3-36.
Fig 3.
Fullness is predictive of intermeal interval; however, the relationship between fullness and intermeal interval varies with photoperiod, fasting status, and anorectic drug administration.
The satiety ratio fails to capture the effect of feeding on intermeal interval because it neglects feeding prior to the most recent meal. (A) Intermeal interval parameters are affected strongly by refeeding status, photoperiod, and anorectic drug administration. Intermeal intervals of rats in the light period are strongly affected by fullness, whereas rats in the dark period have briefer intermeal intervals that are less strongly affected by fullness. Rats given lithium chloride behave similarly in the light and dark period. Rats given PYY3-36 behave more like fasted rats, whereas rats given GLP-1 and leptin have intermeal interval parameters similar to those of rats fed ad libitum. Inset figures show how parameter variation affects intermeal interval. (B) Intermeal interval parameters are strongly associated with variation in food intake: animals with lower parameters eat more. Points coloured by normalised food intake. (C) Mean (solid red line) and 95% posterior predictive interval for rats fed ad libitum given saline in the light period. Intermeal interval tracks gut emptying. Although fullness is indicative of intermeal interval, the predictive window is relatively wide. Blue circles are group data, and black line is moving window average. (D) Satiety-ratio–based predictions of intermeal interval from meal size are inaccurate. Solid red line shows satiety ratio prediction, blue circles are group data, and black line is moving window average. (E) Fullness at meal termination is poorly correlated with meal size, leading to poor predictive ability. Underlying data are available in the following repository: doi:10.17632/vpm89vrz7g.1. Inference procedure described in Materials and Methods. a.u., arbitrary unit; GLP-1, glucagon-like peptide 1; IMI, intermeal interval; PYY3-36, peptide YY3-36.
Fig 4.
Meal termination decisions vary strongly across experimental conditions; however, the effectiveness of altering meal termination decisions to reduce food intake is complex.
(A) Aversive agents (LiCl and high-dose PYY3-36) lead to meal termination at lower fullness, indicated by a move downwards and to the right. Leptin has a contrasting effect—rats given leptin are more likely to terminate meals at low fullness and are largely indifferent to fullness in their meal termination decisions. Meal termination is postponed in the dark period, consistent with increased meal size. Individual posterior mean values for fullness-independent and fullness-dependent meal termination parameters T1 and T2. Insets show posterior mean decision function for representative individuals. (B) Extreme values of either T1 or T2 are associated with decreased food intake. (C, D) Simulated food intake distributions show that the effectiveness of altering the fullness-dependent meal termination parameter T2 varies strongly with the other parameter values (baseline distribution in blue, altered parametrisation in red). Food intake is largely unchanged in simulated rats given leptin when T2 is increased; however, food intake increases substantially in simulated controls. (E–I) Alterations in multiple parameters simultaneously can produce substantial changes in the microstructure of feeding without affecting overall food intake. Altering mean feeding rate μF, T1, and T2 produces an alteration of feeding microstructure similar to that seen in recent studies on CGRP neuron silencing: meals are enlarged and extended (F, G) but intermeal interval is elongated (H) and meal count decreased (I) to fully compensate over 24 hours of feeding. Underlying data for Figures A–D are available in the following repository: doi:10.17632/vpm89vrz7g.1. Inference procedure described in Materials and Methods. Details of simulation procedure for Figures E–I in S1 Text. a.u., arbitrary unit; CGRP, Calcitonin Gene-Related Peptide; GLP-1, glucagon-like peptide 1; PYY3-36, peptide YY3-36.
Fig 5.
Model-based in silico experimentation allows investigation of the effects of parameter changes, design of optimal dosing protocols, and testing of behavioural interventions.
(A) Schematic of refractory period experiment: following meal termination, access to food is prevented for a length of time (the refractory period). This is modelled by enforcing the intermeal interval to be at least the refractory period in length. (B) Introducing a refractory period into feeding behaviour reduces food intake to a similar degree as the administration of a high dose of PYY3-36 in simulated rats fed ad libitum in the dark period. (C) Food intake reduction occurs before the mean intermeal interval is substantially reduced, with a surprising dip in the intermeal interval when a short refractory period is introduced. (D) Schematic of optimal dosing experiment. All permutations of drug administrations, including at least 2 doses of saline, were tested with 10,000 in silico repeats. (E) Optimising drug administration schedules can reduce food intake by an additional 7% when feeding with zero initial fullness. Ad libitum-fed high-dose GLP-1, PYY3-36, and saline parameter values were used to simulate feeding behaviour with drug administration at different times. Error bars indicate standard error of the mean with 10,000 samples. Horizontal lines compare to refractory period reductions in food intake: dash-dotted and dashed lines indicate 15-minute and 30-minute refractory period food intakes for rats given saline, respectively. (F) The main effect of the optimal schedule is to reduce food intake once refed. Blue and red lines correspond to simulations using optimal administration protocol and control parameters, respectively. Shaded area indicates 95th percentile window of fullness. (G) Altering fullness decrease parameter k powerfully reduces food intake once refeeding is complete. A one-third reduction in k reduced 12-hour food intake by over 10 grams in simulated rats fed ad libitum given saline in the dark period. (H) Altering k over a plausible range linearly reduces food intake in simulated rats fed ad libitum given saline in the dark period. Dashed horizontal line indicates food intake typical of rats given high-dose PYY3-36. (I, J) Simplifying the model to predict meal termination with a sigmoid and intermeal interval with a linear regression (red lines) against fullness at meal termination shows good agreement with model-derived predictions (black lines). Details of simulation procedure in S1 Text. GLP-1, glucagon-like peptide 1; PYY3-36, peptide YY3-36.