Motile cells depend on an intricate network of feedback loops that are essential in driving cell movement. Integrin-based focal adhesions (FAs) along with actin are the two key factors that mediate such motile behaviour. Together, they generate excitable dynamics that are essential in forming protrusions at the leading edge of the cell and, in certain cases, traveling waves along the membrane. A partial differential equation (PDE) model of a self-organizing lamellipodium in crawling keratocytes has been previously developed to understand how the three spatiotemporal patterns of activity observed in such cells, namely, stalling, waving and smooth motility are produced. The model consisted of three key variables: the density of barbed actin filaments, newly formed FAs called nascent adhesions (NAs) and VASP, an anti-capping protein that gets sequestered by NAs during maturation. Using parameter sweeping techniques, the distinct regimes of behaviour associated with the three activity patterns were identified. In this study, we convert the PDE model into an ordinary differential equation (ODE) model to examine its excitability properties and determine all the patterns of activity exhibited by this system. Our results reveal that there are two additional regimes not previously identified, including bistability and oscillatory-like type IV excitability (generated by three steady states and their manifolds, rather than limit cycles). These regimes are also present in the PDE model. Applying slow-fast analysis on the ODE model shows that it exhibits a canard explosion through a folded-saddle and that rough motility seen in keratocytes is likely due to noise-dependent motility governed by dynamics near the interface of bistability and type IV excitability. The two parameter bifurcation suggests that the increase in the proportion of rough motion is due to a shift in activity towards the bistable and type IV excitable regimes induced by a decrease in NA maturation rate. Our results thus provide important insight into how microscopic mechanical effects are integrated to produce the observed modes of motility.

运动细胞依赖于复杂的反馈回路网络，这对于驱动细胞运动至关重要。基于整联蛋白的粘着斑（FAs）以及肌动蛋白是介导这种运动行为的两个关键因素。它们共同产生兴奋的动力学，这对于在细胞前缘形成突起以及在某些情况下沿着膜传播的波至关重要。先前已经开发了爬行的角膜细胞中自组织lamellipodium的偏微分方程（PDE）模型，以了解如何在这种细胞中观察到三种活动的时空模式，即失速，波动和平稳运动。该模型包含三个关键变量：带刺的肌动蛋白丝的密度，新生的FA（称为新生粘连（NAs）和VASP），在成熟过程中被NA隔离的一种抗加帽蛋白质。使用参数扫描技术，确定了与三种活动模式相关的不同行为方式。在这项研究中，我们将PDE模型转换为一个常微分方程（ODE）模型，以检查其兴奋性，并确定该系统表现出的所有活动模式。我们的结果表明，还有另外两个以前未发现的机制，包括双稳态和振荡型IV型兴奋性（由三个稳态及其流形而不是极限循环产生）。这些机制也存在于PDE模型中。在ODE模型上应用慢速分析表明，它通过折叠的鞍座表现出鸭式爆炸，并且在角膜细胞中看到的粗糙运动很可能是由于噪声依赖性运动引起的，该运动取决于双稳态和IV型兴奋性界面附近的动力学。两个参数分叉表明，粗略运动比例的增加是由于NA成熟速率降低引起的活动向双稳态和IV型可激发机制的转移。因此，我们的结果提供了关于如何整合微观机械效应以产生观察到的运动模式的重要见解。两个参数分叉表明，粗略运动比例的增加是由于NA成熟速率降低引起的活动向双稳态和IV型可激发机制的转移。因此，我们的结果提供了关于如何整合微观机械效应以产生观察到的运动模式的重要见解。两个参数分叉表明，粗略运动比例的增加是由于NA成熟速率降低引起的活动向双稳态和IV型可激发机制的转移。因此，我们的结果提供了关于如何整合微观机械效应以产生观察到的运动模式的重要见解。