Miller Paul, Wang Xiao-Jing
Volen Center for Complex Systems, Brandeis University, Waltham, Massachusetts 02454, USA.
Chaos. 2006 Jun;16(2):026109. doi: 10.1063/1.2208923.
Noise can degrade memories by causing transitions from one memory state to another. For any biological memory system to be useful, the time scale of such noise-induced transitions must be much longer than the required duration for memory retention. Using biophysically-realistic modeling, we consider two types of memory in the brain: short-term memories maintained by reverberating neuronal activity for a few seconds, and long-term memories maintained by a molecular switch for years. Both systems require persistence of (neuronal or molecular) activity self-sustained by an autocatalytic process and, we argue, that both have limited memory lifetimes because of significant fluctuations. We will first discuss a strongly recurrent cortical network model endowed with feedback loops, for short-term memory. Fluctuations are due to highly irregular spike firing, a salient characteristic of cortical neurons. Then, we will analyze a model for long-term memory, based on an autophosphorylation mechanism of calcium/calmodulin-dependent protein kinase II (CaMKII) molecules. There, fluctuations arise from the fact that there are only a small number of CaMKII molecules at each postsynaptic density (putative synaptic memory unit). Our results are twofold. First, we demonstrate analytically and computationally the exponential dependence of stability on the number of neurons in a self-excitatory network, and on the number of CaMKII proteins in a molecular switch. Second, for each of the two systems, we implement graded memory consisting of a group of bistable switches. For the neuronal network we report interesting ramping temporal dynamics as a result of sequentially switching an increasing number of discrete, bistable, units. The general observation of an exponential increase in memory stability with the system size leads to a trade-off between the robustness of memories (which increases with the size of each bistable unit) and the total amount of information storage (which decreases with increasing unit size), which may be optimized in the brain through biological evolution.
噪声可通过导致记忆状态从一种转变为另一种来使记忆退化。对于任何有用的生物记忆系统而言，这种由噪声引起的转变的时间尺度必须比记忆保留所需的持续时间长得多。我们使用生物物理逼真的模型，考虑大脑中的两种记忆类型：通过神经元活动回响持续几秒维持的短期记忆，以及通过分子开关维持数年的长期记忆。这两种系统都需要由自催化过程自我维持的（神经元或分子）活动的持续性，并且我们认为，由于显著的波动，两者的记忆寿命都有限。我们将首先讨论一个具有反馈回路的强循环皮质网络模型，用于短期记忆。波动是由于高度不规则的脉冲发放，这是皮质神经元的一个显著特征。然后，我们将分析一个基于钙/钙调蛋白依赖性蛋白激酶II（CaMKII）分子自磷酸化机制的长期记忆模型。在那里，波动源于每个突触后密度（假定的突触记忆单元）处只有少量CaMKII分子这一事实。我们的结果有两方面。首先，我们通过分析和计算证明了稳定性对自兴奋性网络中神经元数量以及分子开关中CaMKII蛋白数量的指数依赖性。其次，对于这两个系统中的每一个，我们实现了由一组双稳开关组成的分级记忆。对于神经网络，我们报告了由于依次切换越来越多离散的双稳单元而产生的有趣的斜坡时间动态。随着系统大小记忆稳定性呈指数增加这一普遍观察结果导致了记忆稳健性（随每个双稳单元大小增加）与信息存储总量（随单元大小增加而减少）之间的权衡，这可能通过生物进化在大脑中得到优化。
