Abstract
The nerve growth cone is bi-directionally attracted and repelled by the same cue molecules depending on the situations, while other non-neural chemotactic cells usually show uni-directional attraction or repulsion toward their specific cue molecules. However, how the growth cone differs from other non-neural cells remains unclear. Toward this question, we developed a theory for describing chemotactic response based on a mathematical model of intracellular signaling of activator and inhibitor. Our theory was first able to clarify the conditions of attraction and repulsion, which are determined by balance between activator and inhibitor, and the conditions of uni- and bi-directional responses, which are determined by dose-response profiles of activator and inhibitor to the guidance cue. With biologically realistic sigmoidal dose-responses, our model predicted tri-phasic turning response depending on intracellular Ca2+ level, which was then experimentally confirmed by growth cone turning assays and Ca2+ imaging. Furthermore, we took a reverse-engineering analysis to identify balanced regulation between CaMKII (activator) and PP1 (inhibitor) and then the model performance was validated by reproducing turning assays with inhibitions of CaMKII and PP1. Thus, our study implies that the balance between activator and inhibitor underlies the multi-phasic bi-directional turning response of the growth cone.
Highlights
Netrin-1 leads to the production of cAMP and cGMP, which activate cAMP-dependent protein kinase (PKA) and cGMP-dependent protein kinase (PKG), respectively, and, in turn, induces Ca2+ influx[13] (Fig. 1A,B)
We developed a mathematical model of chemotactic cells based on intracellular signaling
To identify how CaMKII (A; activator) and phosphatase 1 (PP1) (I; inhibitor) are up-regulated in a Ca2+ -dose-dependent manner, we developed a mathematical model; the activity of CaMKII was expressed as a Hill equation of the Ca2+ concentration (Equation (10)), while the activity of PP1 was expressed as double Hill equations (Equation (11)) with lower and higher Kd values, which correspond to two distinct pathways: the CaN- and Calpain-dependent pathways, respectively (Fig. 5A), because higher level of Ca2+ is necessary for up-regulating Calpain than that for CaN49
Summary
Netrin-1 leads to the production of cAMP and cGMP, which activate cAMP-dependent protein kinase (PKA) and cGMP-dependent protein kinase (PKG), respectively, and, in turn, induces Ca2+ influx[13] (Fig. 1A,B). Calmodulin (CaM)-dependent kinase II (CaMKII) and Protein phosphatase 1 (PP1) function in the growth cone as an activator-inhibitor system in the downstream of Ca2+, as PI3K and PTEN function in non-neural cells; CaMKII and PP1 act as an activator and inhibitor, respectively, of the effectors that regulate growth cone motility, e.g., Rac[1] and Cdc[42] (Fig. 1B)[19,20,21,22] These downstream molecules modulate the turning direction in response to an external cue: CaMKII triggers attraction, whereas PP1 triggers repulsion[18]. We reverse engineered the model parameters to fit the growth cone turning assays, so that its predictive performance was experimentally validated by pharmacological suppression of the activator (CaMKII) or inhibitor (PP1)
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