Computational Biology Research Center, National Institute of Advanced Industrial Science and Technology, Tokyo, Japan.
IET Syst Biol. 2011 Sep;5(5):281-92. doi: 10.1049/iet-syb.2010.0051.
Recent remarkable advances in computer performance have enabled us to estimate parameter values by the huge power of numerical computation, the so-called 'Brute force', resulting in the high-speed simultaneous estimation of a large number of parameter values. However, these advancements have not been fully utilised to improve the accuracy of parameter estimation. Here the authors review a novel method for parameter estimation using symbolic computation power, 'Bruno force', named after Bruno Buchberger, who found the Gröbner base. In the method, the objective functions combining the symbolic computation techniques are formulated. First, the authors utilise a symbolic computation technique, differential elimination, which symbolically reduces an equivalent system of differential equations to a system in a given model. Second, since its equivalent system is frequently composed of large equations, the system is further simplified by another symbolic computation. The performance of the authors' method for parameter accuracy improvement is illustrated by two representative models in biology, a simple cascade model and a negative feedback model in comparison with the previous numerical methods. Finally, the limits and extensions of the authors' method are discussed, in terms of the possible power of 'Bruno force' for the development of a new horizon in parameter estimation.
最近计算机性能的显著进步使我们能够通过数值计算的巨大力量来估计参数值，即所谓的“暴力破解”，从而实现大量参数值的高速同时估计。然而，这些进步并没有被充分利用来提高参数估计的准确性。在这里，作者回顾了一种使用符号计算能力进行参数估计的新方法，即“Bruno 力”，以 Bruno Buchberger 的名字命名，他发现了 Gröbner 基。在该方法中，将结合符号计算技术的目标函数进行公式化。首先，作者利用一种符号计算技术，即微分消元法，将等价的微分方程组符号地简化为给定模型中的系统。其次，由于其等价系统通常由大量方程组成，因此通过另一种符号计算进一步简化了系统。作者的方法在提高参数准确性方面的性能通过生物学中的两个代表性模型进行了说明，与之前的数值方法相比，作者的方法在一个简单的级联模型和一个负反馈模型中得到了展示。最后，作者讨论了他们的方法的局限性和扩展，以及“Bruno 力”在参数估计新领域发展中的可能力量。
