BMC Med Genomics. 2013;6 Suppl 3(Suppl 3):S3. doi: 10.1186/1755-8794-6-S3-S3. Epub 2013 Nov 11.
The aim of this report is to provide a mathematical model of the mechanism for making binary fate decisions about cell death or survival, during and after Photodynamic Therapy (PDT) treatment, and to supply the logical design for this decision mechanism as an application of rate distortion theory to the biochemical processing of information by the physical system of a cell.
Based on system biology models of the molecular interactions involved in the PDT processes previously established, and regarding a cellular decision-making system as a noisy communication channel, we use rate distortion theory to design a time dependent Blahut-Arimoto algorithm where the input is a stimulus vector composed of the time dependent concentrations of three PDT related cell death signaling molecules and the output is a cell fate decision. The molecular concentrations are determined by a group of rate equations. The basic steps are: initialize the probability of the cell fate decision, compute the conditional probability distribution that minimizes the mutual information between input and output, compute the cell probability of cell fate decision that minimizes the mutual information and repeat the last two steps until the probabilities converge. Advance to the next discrete time point and repeat the process.
Based on the model from communication theory described in this work, and assuming that the activation of the death signal processing occurs when any of the molecular stimulants increases higher than a predefined threshold (50% of the maximum concentrations), for 1800s of treatment, the cell undergoes necrosis within the first 30 minutes with probability range 90.0%-99.99% and in the case of repair/survival, it goes through apoptosis within 3-4 hours with probability range 90.00%-99.00%. Although, there is no experimental validation of the model at this moment, it reproduces some patterns of survival ratios of predicted experimental data.
Analytical modeling based on cell death signaling molecules has been shown to be an independent and useful tool for prediction of cell surviving response to PDT. The model can be adjusted to provide important insights for cellular response to other treatments such as hyperthermia, and diseases such as neurodegeneration.
本报告的目的是提供一个关于细胞死亡或存活的二元命运决策机制的数学模型，该机制发生在光动力疗法（PDT）治疗期间和之后，并提供该决策机制的逻辑设计，作为率失真理论在细胞物理系统中对生化信息处理的应用。
基于先前建立的涉及 PDT 过程的分子相互作用的系统生物学模型，并将细胞决策系统视为噪声通信通道，我们使用率失真理论设计一个时变的 Blahut-Arimoto 算法，其中输入是由三个与 PDT 相关的细胞死亡信号分子的时变浓度组成的刺激向量，输出是细胞命运决策。分子浓度由一组速率方程确定。基本步骤是：初始化细胞命运决策的概率，计算最小化输入和输出之间互信息的条件概率分布，计算最小化互信息的细胞命运决策概率，并重复最后两个步骤，直到概率收敛。推进到下一个离散时间点并重复该过程。
基于本文所述的通信理论模型，并假设死亡信号处理的激活发生在任何分子刺激物的浓度增加超过预定义阈值（最大浓度的 50%）时，对于 1800s 的治疗，细胞在最初的 30 分钟内经历坏死的概率范围为 90.0%-99.99%，而在修复/存活的情况下，细胞在 3-4 小时内经历凋亡的概率范围为 90.00%-99.00%。虽然目前还没有对该模型进行实验验证，但它再现了一些预测实验数据的存活比例模式。
基于细胞死亡信号分子的分析模型已被证明是预测细胞对 PDT 存活反应的独立且有用的工具。该模型可以进行调整，为细胞对其他治疗方法（如热疗）和疾病（如神经退行性变）的反应提供重要见解。
