Positive feedback in the Akt/mTOR pathway and its implications for growth signal progression in skeletal muscle cells: An analytical study

Abstract

The IGF-1 mediated Akt/mTOR pathway has been recently proposed as mediator of skeletal muscle growth and a positive feedback between Akt and mTOR was suggested to induce homogeneous growth signals along the whole spatial extension of such long cells. Here we develop two biologically justified approximations which we study under the presence of four different initial conditions that describe different paradigms of IGF-1 receptor-induced Akt/mTOR activation. In first scenario the activation of the feedback cascade was assumed to be mild or protein turnover considered to be high. In turn, in the second scenario the transcriptional regulation was assumed to maintain defined levels of inactive pro-enzymes. For both scenarios, we were able to obtain closed-form formulas for growth signal progression in time and space and found that a localised initial signal maintains its Gaussian shape, but gets delocalised and exponentially degraded. Importantly, mathematical treatment of the reaction diffusion system revealed that diffusion filtered out high frequencies of spatially periodic initiator signals suggesting that the muscle cell is robust against fluctuations in spatial receptor expression or activation. However, neither scenario was consistent with the presence of stably travelling signal waves. Our study highlights the role of feedback loops in spatiotemporal signal progression and results can be applied to studies in cell proliferation, cell differentiation and cell death in other spatially extended cells.

Introduction

The insulin-like growth factor (IGF-1) receptor pathway is a canonical pathway that mediates cell growth and survival. Upon growth factor binding to the receptor, the lipid kinase phosphoinositide-3-OH kinase (PI3K) gets phosphorylated and activated. This activation leads to phosphorylation and activation of the pro-survival kinase Akt. Through a double inhibitory step, active Akt leads to the activation of the mammalian target of rapamycin (mTOR) which switches on anabolic processes such as protein or nucleotide production. In turn, evidence has been provided that mTOR can phosphorylate and activate Akt (Granville et al., 2006, Sarbassov et al., 2005), thereby establishing a positive feedback loop.

Recent reports suggested the IGF-1 mediated PI3K-/Akt-/mTOR pathway to be a regulator of muscle cell growth. Indeed, studies that overexpressed active Akt by genetic mutations or pharmacological activation reported an increase in muscle fibre diameter (muscular hypertrophy) while muscle fibre diameter decreased upon inhibition of Akt or mTOR (muscular atrophy) (Pallafacchina et al., 2002, Bodine et al., 2001, Rommel et al., 2001). Trophic factor receptors such as IGF-1 can be randomly and anisotropically distributed along the cell surface (Grant et al., 1996, Kaiser et al., 1993, Wilkins et al., 2001) and activation of Akt by PI3K has been determined to be localised at the receptors. Therefore it remains to be understood how a signal that is associated with certain locations on the surface of a muscle cell can proceed through the entire spatial extension of this cell in a homogeneous fashion. Diffusion alone cannot be responsible for eliminating spatial gradients in larger cells as protein motility is limited by ubiquitenation and degradation of activated proteins (Huber et al., 2010). It is therefore assumed that the Akt/mTOR positive feedback loop acts as a signal regenerator (Ferrell, 2002, Kuroda et al., 2001, Tanaka and Augustine, 2008) in larger cells.

In this study, we will investigate a mathematical model that studies Akt/mTOR signal progression in skeletal muscle cells with an anisotropic distribution of IGF-1 receptors on the muscle cell surface. We will focus on an analytical treatment to study whether general principles of the resulting reaction diffusion equation can be derived. We will first discuss the time dependent, spatially invariant reaction system of a simple auto-activation network of Akt/mTOR and obtain criteria for stable enzyme activation. Subsequently, we will include one spatial dimension, so as to idealize the muscle cell as a linearly extended compartment and focus on two biologically reasonable scenarios that we solve in the presence of four different initiator signals. While no travelling waves are present under these assumptions, we will observe that the feedback loop together with diffusion can filter out spatial anisotropies. This filtering allows the translation of anisotropies arising from an inhomogeneous distribution of IGF-receptor or from fluctuations in the initiator signals into a homogeneous Akt/mTOR activation along the cell. We will further discuss the implications of our findings on receptor mediated activation in other large cells such as nerve cells.