This work was performed in collaboration with Dr. AE Sumner of the Clinical Endocrinology Branch, NIDDK, Dr. RN Bergman of the USC Medical School and Dr. CC Chow of LBM, NIDDK. ? ? The effects of insulin on the suppression of lipolysis are neither fully understood nor quantified. We examined a variety of mathematical models analogous to the minimal model of glucose disposal (MMG) to quantify the combined influence of insulin on lipolysis and glucose disposal during an insulin-modified frequently sampled intravenous glucose tolerance test. The tested models, which include two previously published ones, consisted of separate compartments for plasma free fatty acids (FFA), glucose and insulin. They differed in the number of compartments and in the action of insulin to suppress lipolysis that decreased the plasma FFA level. In one category of models, a single insulin compartment (X models) acted on both glucose and FFA simultaneously. In a second category, there were two insulin compartments (Y models), each acting on FFA and glucose independently. For each of these two categories, we tested 11 variations of how insulin suppressed lipolysis. We also tested a model with an additional glucose compartment that acted on FFA. These 23 models were fit to the plasma FFA and glucose concentrations of 102 subjects individually. Using Bayesian model comparison methods, the model that best balanced fit and minimized model complexity was selected. In the best model, insulin suppressed lipolysis via a Hill function through a remote compartment that acted on both glucose and FFA simultaneously and glucose dynamics obeyed the classic MMG. ? ? Hill function models clearly outperformed all other models, both in terms of fit ? and Bayes factor. Among the top performing models, the analysis selected the X Hill function model (XH) as ? the best model. However, given the small margin of victory, we feel that a ? superior model is not unambiguously decided by this data set. In model XH, ? lipolysis is suppressed by insulin through a Hill function with a nonzero minimal ? rate, and insulin acts on lipolysis through the glucose remote compartment of the ? glucose minimal model. ? ? Physiologically, it may be surprising that insulin affects FFA dynamics from the ? remote glucose compartment from which insulin modulates glucose levels. The ? pathways through which insulin regulates glucose involve the insulin receptor on ? the cell surface and ultimately glucose transporters. In contrast insulin regulates ? lipolysis by initiating a chain of events that leads to inhibition of lipolysis, by ? promoting the dephosphorylation of both hormone sensitive lipase and the protein ? perilipin (30). However, models YH and XH had nearly identical Bayes factors, ? implying that both remote compartments had similar enough dynamics that one ? could serve for the other with little effect on the model fit. This may be because ? insulin action in the remote compartment is a rate-limiting step so that adipose ? tissue and muscle in close proximity would receive similar signals. Alternatively, ? it may indicate that the physiology of glucose and FFA regulation may have ? unknown mechanisms ensuring coordinated insulin response even though the ? pathways are prima facie distinct. ? ? Previous studies indicate that there may be a maximally suppressible level of FFA ? plasma appearance. This would be manifested as a nonzero ? insulin independent lipolysis rate (i.e. l0≠0). Our model confirms this claim ? although weakly. Fixing the minimal rate to zero only reduced the Bayes factor ? marginally. Additional data may be required to fully resolve the insulin ? independent minimum rate. ? ? Our model predicts that the lipolysis rate during an insulin clamp will depend on ? insulin via a Hill function. Jensen and Nielsen showed that their clamped ? lipolysis rate could be fit by a power law function and the properties of this ? function such as the ED50 might be a measure of the sensitivity of insulins action ? on lipolysis. Since a power law function is a special case of our function (with ? Hill constant zero), our model is consistent with the clamp results. Hence, our ? minimal FFA model provides a possible means to obtain the dependence of ? lipolysis for step-wise clamped insulin levels with a dynamic IM-FSIGT. ? Analogously, the parameters of the lipolysis function describing insulins ? influence on lipolysis might provide a measure for the sensitivity of lipolysis on ? insulin. For example, we can derive an effective ED50 for insulins action on ? lipolysis. The model derived ED50 would be a prediction for the ED50 that would ? be measured from an insulin clamp experiment on the same subject. We note that ? the ED50 could not be predicted from the data without the benefit of a model. ? Future studies are required to test whether our predicted rate of lipolysis function ? and ED50 matches the result obtained during an insulin clamp in the same subject. ? ? We focused primarily on fit to data with minimal complexity and did not address ? issues of identifiability of the parameters. Some of the parameters in the models ? had fairly broad posterior distributions indicating that multiple parameter sets ? could possibly fit the data equally well. This may be indicative of an interaction ? between parameters. For example the exponent A can be partially compensated ? by the offset X2. Future work is required to optimize the model for identifiability ? of parameters. ? ? We did not explore the possibility of direct action of glucose on FFA levels. ? There is some experimental evidence supporting our decision . We also did ? not include the direct effects of insulin or glucose on FFA clearance. Although it ? has been found that FFA uptake increases with glucose infusion, we note that ? in the minimal model framework an increase in clearance is not distinguishable ? from a decrease in appearance. Thus this effect is partially accounted for by our ? rate of lipolysis function. Future modeling work could incorporate these effects ? explicitly. Our philosophy of employing a minimal model also meant that we did ? not incorporate the direct effects of catecholamines, corticosteroids and glucagon. ? Presumably, these hormones contribute to the variability not accounted for by the ? model. As FFA promote resistance to insulins ability to regulate glucose (5, 23), ? this model could potentially lead to a greater insight into our understanding for ? why some individuals with obesity are resistant to insulins effect on glucose and ? others are sensitive. ? ? Perspectives and Significance ? ? The ability of insulin to modulate glucose and free fatty acid (FFA) levels has a ? major impact on many disease processes including diabetes, heart disease and ? cancer. In contrast to our ability to assess the effect on insulin on glucose ? disposal, there is no clinically relevant tool to assess the effect of insulin on FFA. ? To close this gap we examined a variety of mathematical models analogous to the ? minimal model of glucose disposal to quantify the combined influence of insulin ? on lipolysis and glucose disposal during an insulin-modified frequently sampled ? intravenous glucose tolerance test. With insulin as the input and FFA as the ? output and employing Bayesian model comparison methods we identified a ? single model which best balanced fit and minimized model complexity. For the ? model to have clinical relevance, an index of FFA sensitivity needs to be derived.
