Stable IL-1-Activation in an Inflammasome Signalling Model Depends on Positive and Negative Feedbacks and Tight Regulation of Protein Production.

INTRODUCTION: NLRP3-dependent inflammasome signalling is a key pathway during inflammatory processes and its deregulation is implicated in several diseases. NLRP3-inflammasome pathway activation leads to the rapid, hosphorylation-driven NFB-pathway signalling, subsequently proceeds via lower transcription/translation process for producing pro-enzymes, and finally leads to the medium-speed enzymatic activation of the central inflammatory ediator IL-1 [1]. We here were interested how the timing of the rate-limiting step of transcription/translation and the presence of a positive and negative auto-regulation would pose conditions for meaningful and stable IL-1-activation.

METHODS: We extracted the essential topology of the inflammasome pathway network using a linear chain of first order reaction and a second order reaction for inhibitory feedback. We then performed an analytical treatment of the resulting ODE set to obtain closed-form formulae. We therefore looked for the steady states and characterised their stability by using a Jacobian-based, local analysis. We employed the Small Gain Theorem from Control Theory as recently applied by us [2] and the Gershgorin Circle Theorem to obtain mathematically exact conditions for a positive on state and stabilities for on and off steady states.

RESULTS: We identified an on- and one off- steady state whose properties we characterised in terms of the kinetic parameters by closed-form formulae. We found that under the assumption of a first-order information flow through the network the existence of a biologically reasonable ON steady state required the simultaneous presence of the positive and the negative feedback. Assuming non-competitivity between IL-1 entities binding to different receptors, we found that a minimum kinetics for protein production is required to sustain a steady state with IL-1 activation. Assuming competitivity between IL-1 entities introduced additional restrictions on the maximum protein production speed to guarantee a biologically reasonable ON steady state. Finally, for both models we ruled out bistability, suggesting that IL- 1 activation would undergo a smooth change upon alterations of its parameters.

CONCLUSION: Exemplified by the core pathway of NLRP3-inflammasome signalling, we here demonstrate that a mostly linear activation cascade containing an intermediate rate limiting step poses kinetic restrictions on this step and requires positive and negative autoregulation for obtaining a meaningful ON steady state. Due to the generality of our framework, our results are important for a wide class of receptor mediated-pathways, where a fast initial phosphorylation cascade is followed by a (slower) transcriptional response and subsequent autoregulation. Our results may further provide important design principles for synthetic biological networks involving biochemical activation and transcription/translation, by relating timing considerations and autoregulation to stable pathway activation.