许多神经退行性疾病(ND)的特征是大脑中有毒蛋白质种类的缓慢空间传播。毒性蛋白可以诱导神经元应激,触发未折叠蛋白反应(UPR),减缓或停止蛋白质翻译,并可以间接减少毒性负荷。然而,UPR还可能触发导致凋亡性细胞死亡的过程,并且UPR与几种ND的进展有关.在本文中,我们开发了一个新的数学模型来描述pr病毒疾病的UPR机制的时空动态。我们的模型以一个神经元为中心,具有代表性的蛋白质P(健康)和S(有毒)与异二聚体动力学相互作用(S与P相互作用形成两个S\s)。该模型采用非线性反应扩散方程的耦合系统的形式,P的非线性通量(来自UPR的延迟)。通过延迟,我们发现在P蛋白和S蛋白水平上表现出振荡的参数机制。我们发现,与P-清除率和P-扩散系数相比,当S-清除率和S-扩散系数较小时,振荡更明显,分别。随着启动UPR的延迟增加,振荡变得更加明显。我们还考虑了准现实的临床参数,以了解可能的药物治疗如何改变朊病毒疾病的病程。我们发现减少P的产量,降低招聘率,增加S的扩散系数,提高UPRS阈值,增加S清除率似乎是降低平均UPR强度并可能减缓疾病进展的最有力的修改。
Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering the Unfolded Protein Response (UPR), which slows or stops protein translation and can indirectly reduce the toxic load. However, the UPR may also trigger processes leading to apoptotic cell death and the UPR is implicated in the progression of several NDs. In this paper, we develop a novel mathematical model to describe the spatiotemporal dynamics of the UPR mechanism for prion diseases. Our model is centered around a single neuron, with representative proteins P (healthy) and S (toxic) interacting with heterodimer dynamics (S interacts with P to form two S\'s). The model takes the form of a coupled system of nonlinear reaction-diffusion equations with a delayed, nonlinear flux for P (delay from the UPR). Through the delay, we find parameter regimes that exhibit oscillations in the P- and S-protein levels. We find that oscillations are more pronounced when the S-clearance rate and S-diffusivity are small in comparison to the P-clearance rate and P-diffusivity, respectively. The oscillations become more pronounced as delays in initiating the UPR increase. We also consider quasi-realistic clinical parameters to understand how possible drug therapies can alter the course of a prion disease. We find that decreasing the production of P, decreasing the recruitment rate, increasing the diffusivity of S, increasing the UPR S-threshold, and increasing the S clearance rate appear to be the most powerful modifications to reduce the mean UPR intensity and potentially moderate the disease progression.