Quantitative Estimation of Sensitivity of Lipolysis to Insulin

这项工作是与NIDDK临床内分泌学分支的AE Sumner博士、USC医学院的RN Bergman博士和NIDDK LBM的CC Chow博士合作进行的。 本研究的目的是定量评估FFA对胰岛素的反应。 我们假设，将血浆胰岛素测量的时间过程转换为FFA测量的时间过程的数学模型将由作为胰岛素作用调节脂解的定量测量的参数来描述。 我们考虑了几种不同的数学模型的不同的复杂性和作用机制。 我们根据模型比较的标准原则区分这些模型：（1）拟合优度，（2）描述模型所需的参数空间，（3）参数的可识别性，以及（4）生物相关性。 对数据和模型复杂性进行平衡拟合的最佳性能模型具有通过与葡萄糖最小模型的葡萄糖远端隔室不同的远端脂肪隔室的胰岛素作用。 在生理学上，胰岛素影响FFA动力学的远端脂肪区室与胰岛素调节葡萄糖水平的远端葡萄糖区室不同可能并不奇怪。胰岛素调节葡萄糖的途径涉及细胞表面的胰岛素受体，并最终涉及葡萄糖转运蛋白。相反，胰岛素通过启动导致脂解抑制的事件链，通过促进激素敏感性脂肪酶和蛋白质周脂蛋白的去磷酸化来调节脂解。 对于模型II-2的动力学，存在线性清除率（仅依赖于FFA浓度）和远程作用胰岛素对FFA外观的非线性抑制。 我们发现，一阶希尔函数足以代表相关的途径。 这可能表明，在这些途径中有一个单一的一级过程是速率限制的。 可以将Hill函数与胰岛素钳夹实验中发现的FFA Ra对胰岛素的依赖性进行比较，其中发现数据可以拟合幂律。 希尔函数可以是拟合该数据的替代参数形式，因此与钳夹结果一致。 FFA浓度的时间过程的一个方面是，最终水平几乎总是高于初始水平。 该模型能够匹配这方面的数据，虽然它没有插入一个特定的生物物理机制来解释这种影响。 相反，该模型假设FFA的初始值是一个自由参数。 在360分钟时，胰岛素浓度已恢复到基础水平，FFA达到可高于初始值的水平。 360分钟时FFA水平升高可能有多种原因，包括暴露于初始葡萄糖推注后的反弹、低血糖的影响、反调节激素或昼夜变化。 先前的研究表明，可能存在最大可抑制水平的FFA血浆出现。 这将表现为3型模型中的胰岛素非依赖性脂解速率。 然而，我们的模型评估表明，添加此参数并没有改善数据的拟合程度，不足以保证将其包含在内。 原因可能是测量的基线FFA水平的广泛变异性。 可能需要额外的数据来解析胰岛素非依赖率。 我们专门关注胰岛素对FFA水平的作用，我们发现我们的模型充分拟合数据以产生敏感性指数SFI。 因此，我们没有探讨葡萄糖对FFA水平直接作用的可能性。 葡萄糖的作用是通过其对胰岛素的作用间接解释的。 有实验证据支持我们的决定。 我们采用最小模型的理念也意味着我们没有纳入儿茶酚胺、皮质类固醇和胰高血糖素的直接作用。 据推测，这些激素有助于模型未考虑的变异性。 由于FFA促进对胰岛素调节葡萄糖能力的抵抗，该模型可能会使我们更深入地了解为什么一些肥胖患者对胰岛素对葡萄糖的影响具有抵抗力，而其他人则敏感。SFI还可以潜在地指导患者的选择，这些患者最有可能对增加脂肪组织中胰岛素敏感性的药物（如噻唑烷二酮类）有反应。SFI和脂肪量之间的显着负相关性是推测的证据，SFI最终将在指导胰岛素增敏剂治疗的价值。 我们认识到，我们开发的模型必须在其他人群中进行测试，进行重复性测试，并进行严格的验证。 提供验证的一种方法是在同一受试者上使用示踪剂（如标记的棕榈酸酯）进行IM-FSIGT和胰岛素钳夹实验，并将我们的模型参数与从钳夹中获得的参数进行比较。 钳夹实验可以给出胰岛素的FFA出现率和FFA清除率的依赖性的估计，其可以与从我们的模型导出的等效量进行比较。 当前模型的价值在于，它是FFA最小模型，似乎可以解释IM-FSIGT期间的大部分FFA水平。目前正在准备发表这些结果，以便对模型进行更广泛的研究和询问。

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 purpose of this investigation was to quantitatively assess FFA response to insulin. We postulated that a mathematical model transforming a time-course of plasma insulin measurements into a time-course of FFA measurements would be described by parameters that would serve as quantitative measures of the regulation of lipolysis by insulin action. We considered several different mathematical models of varying complexity and mechanisms of action. We discriminated between these models on the basis of standard principles of model comparison: (1) Goodness of fit, (2) Parameter space required to describe the model, (3) Identifiability of parameters, and (4) Biological relevance. The best performing model balancing fit to data and model complexity has insulin action through a remote adipose compartment that is different from the glucose remote compartment of the glucose minimal model. Physiologically, it may not be surprising that the remote adipose compartment from which insulin affects FFA dynamics is different from the remote glucose compartment from which insulin modulates glucose levels. The pathways through which insulin regulates glucose involves 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. For the kinetics of model II-2, there is a linear clearance rate (only dependent on FFA concentration) and a nonlinear suppression of FFA appearance by remote acting insulin. We found that a first order Hill function was sufficient to represent the relevant pathways. This may suggest that there is a single first order process within these pathways that is rate limiting. The Hill function could be compared to the FFA Ra dependence on insulin as found in insulin clamp experiments, where it was found that the data could be fit to a power law. A Hill function could be an alternative parametric form for a fit to this data and is thus consistent with the clamp results. One aspect of the time course of FFA concentration is that the final level is almost always higher than the initial level. The model is able to match this aspect of the data although it does not insert a specific biophysical mechanism to account for this effect. Instead, the model assumes that the initial value of FFA is a free parameter. At 360 minutes, insulin concentration has returned to basal levels and FFA attains a level that can be higher than the initial value. The elevation in FFA levels at 360 minutes may occur for several reasons, including the rebound after exposure to the initial bolus of glucose, the effect of hypoglycemia, counter regulatory hormones, or diurnal variation. Previous studies indicate that there may be a maximally suppressible level of FFA plasma appearance. This would be manifested as the insulin independent lipolysis rate in the Type 3 models. However, our model evaluation showed that adding this parameter did not improve the fit to the data enough to warrant its inclusion. The reason may be the wide variability in the measured baseline FFA levels. Additional data may be required to resolve the insulin independent rate. We focused exclusively on the action of insulin on FFA levels and we found that our models adequately fit to the data to produce a sensitivity index SFI. As a result we did not explore the possibility of direct action of glucose on FFA levels. The action of glucose is indirectly accounted for through its effect on insulin. There is experimental evidence supporting our decision. 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, 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. The SFI could also potentially guide the selection of patients that are most likely to respond to agents which increase insulin sensitivity in adipose tissues such as thiazolidinediones. The significant negative correlation between SFI and fat mass is presumptive evidence that SFI will ultimately be of value in guiding therapy with insulin sensitizers. We recognize that the model we developed must be tested in other populations, be tested for reproducibility and undergo rigorous validation. One means of providing validation is to perform an IM-FSIGT and an insulin clamp experiment with a tracer such as labeled palmitate on the same subject and compare our model parameters to those derived from the clamp. The clamp experiments can give an estimate of the dependence on FFA rate of appearance on insulin and the rate of FFA clearance, which can be compared to the equivalent quantities derived from our model. The value of the current model is that it is a FFA minimal model that appears to explain most of the FFA levels during the IM-FSIGT. These results are being prepared for publication now to allow the models to be subject to wider study and interrogation.