Biological sensors must often predict their input while operating under metabolic constraints. However, determining whether or not a particular sensor is evolved or designed to be accurate and efficient is challenging. This arises partly from the functional constraints being at cross purposes and partly since quantifying the prediction performance of even in silico sensors can require prohibitively long simulations, especially when highly complex environments drive sensors out of equilibrium. To circumvent these difficulties, we develop new expressions for the prediction accuracy and thermodynamic costs of the broad class of conditionally Markovian sensors subject to complex, correlated (unifilar hidden semi-Markov) environmental inputs in nonequilibrium steady state. Predictive metrics include the instantaneous memory and the total predictable information (the mutual information between present sensor state and input future), while dissipation metrics include power extracted from the environment and the nonpredictive information rate. Success in deriving these formulae relies on identifying the environment’s causal states, the input’s minimal sufficient statistics for prediction. Using these formulae, we study large random channels and the simplest nontrivial biological sensor model—that of a Hill molecule, characterized by the number of ligands that bind simultaneously—the sensor’s cooperativity. We find that the seemingly impoverished Hill molecule can capture an order of magnitude more predictable information than large random channels.

中文翻译：

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非平衡分子传感器的预测和耗散：由记忆环境驱动的条件马尔可夫通道

生物传感器必须经常在代谢限制下运行时预测它们的输入。然而，确定特定传感器是否经过改进或设计为准确和高效是具有挑战性的。这部分是由于功能限制的交叉目的，部分是因为量化甚至在 silico 传感器的预测性能可能需要非常长的模拟，特别是当高度复杂的环境使传感器失去平衡时。为了规避这些困难，我们为在非平衡稳态下受到复杂、相关（单线隐藏半马尔可夫）环境输入的广泛类别的条件马尔可夫传感器的预测精度和热力学成本开发了新的表达式。预测指标包括瞬时记忆和总可预测信息（当前传感器状态和输入未来之间的互信息），而耗散指标包括从环境中提取的功率和非预测信息率。推导出这些公式的成功依赖于识别环境的因果状态，输入的最小足够的预测统计数据。使用这些公式，我们研究了大的随机通道和最简单的非平凡生物传感器模型——希尔分子的模型，以同时结合的配体数量为特征——传感器的协同性。我们发现，看似贫乏的希尔分子可以比大型随机通道捕获更可预测的信息数量级。