Tøndel Kristin, Niederer Steven A, Land Sander, Smith Nicolas P
Department of Biomedical Engineering, King's College London, St, Thomas' Hospital, Westminster Bridge Road, London SE1 7EH, UK.
BMC Syst Biol. 2014 May 20;8:59. doi: 10.1186/1752-0509-8-59.
Striking a balance between the degree of model complexity and parameter identifiability, while still producing biologically feasible simulations using modelling is a major challenge in computational biology. While these two elements of model development are closely coupled, parameter fitting from measured data and analysis of model mechanisms have traditionally been performed separately and sequentially. This process produces potential mismatches between model and data complexities that can compromise the ability of computational frameworks to reveal mechanistic insights or predict new behaviour. In this study we address this issue by presenting a generic framework for combined model parameterisation, comparison of model alternatives and analysis of model mechanisms.
The presented methodology is based on a combination of multivariate metamodelling (statistical approximation of the input-output relationships of deterministic models) and a systematic zooming into biologically feasible regions of the parameter space by iterative generation of new experimental designs and look-up of simulations in the proximity of the measured data. The parameter fitting pipeline includes an implicit sensitivity analysis and analysis of parameter identifiability, making it suitable for testing hypotheses for model reduction. Using this approach, under-constrained model parameters, as well as the coupling between parameters within the model are identified. The methodology is demonstrated by refitting the parameters of a published model of cardiac cellular mechanics using a combination of measured data and synthetic data from an alternative model of the same system. Using this approach, reduced models with simplified expressions for the tropomyosin/crossbridge kinetics were found by identification of model components that can be omitted without affecting the fit to the parameterising data. Our analysis revealed that model parameters could be constrained to a standard deviation of on average 15% of the mean values over the succeeding parameter sets.
Our results indicate that the presented approach is effective for comparing model alternatives and reducing models to the minimum complexity replicating measured data. We therefore believe that this approach has significant potential for reparameterising existing frameworks, for identification of redundant model components of large biophysical models and to increase their predictive capacity.
在模型复杂度和参数可识别性之间取得平衡,同时仍能通过建模产生生物学上可行的模拟,这是计算生物学中的一项重大挑战。虽然模型开发的这两个要素紧密相关,但传统上从测量数据进行参数拟合和对模型机制进行分析是分别且按顺序进行的。这个过程会在模型和数据复杂度之间产生潜在的不匹配,从而可能损害计算框架揭示机制性见解或预测新行为的能力。在本研究中,我们通过提出一个用于组合模型参数化、比较模型备选方案和分析模型机制的通用框架来解决这个问题。
所提出的方法基于多变量元建模(确定性模型输入 - 输出关系的统计近似)与通过迭代生成新的实验设计并在测量数据附近查找模拟结果,系统地深入参数空间的生物学可行区域的组合。参数拟合流程包括隐式灵敏度分析和参数可识别性分析,使其适用于测试模型简化的假设。使用这种方法,可以识别欠约束的模型参数以及模型内参数之间的耦合。通过结合同一系统另一个模型的测量数据和合成数据,重新拟合已发表的心脏细胞力学模型的参数,对该方法进行了验证。使用这种方法,通过识别在不影响对参数化数据拟合的情况下可以省略的模型组件,找到了具有简化的原肌球蛋白/横桥动力学表达式的简化模型。我们的分析表明,在后续参数集中,模型参数可以被约束到平均值标准差平均为 15%。
我们的结果表明,所提出的方法对于比较模型备选方案以及将模型简化到复制测量数据的最小复杂度是有效的。因此,我们认为这种方法在重新参数化现有框架、识别大型生物物理模型的冗余模型组件以及提高其预测能力方面具有巨大潜力。