Large-scale closed and generalized networks of ribosome flow model with different site sizes

Abstract

Dynamical systems play a key role in understanding the different biophysical aspects of many complex transport phenomena. The ribosome flow model with different site sizes (RFMD) is a dynamical system relevant to model various biological and physical processes such as phosphorelay, motion of vehicles along an isolated road, and more. However, many transport processes take place concurrently which give rise to networks comprising multiple tracks e.g., vehicular motion, cargo transport along the cytoskeletal highway, etc. Here, we present two large-scale network models: RFMDs network with a pool (RFMDNP), and the generalized network of RFMDs (RFMDN). The RFMDNP is a closed system that can model the simultaneous movement of particles along tracks having sites of different capacities in a resource-limited environment. We prove that the RFMDNP admits a continuum of linearly ordered steady-state points and it always phase-locks with the periodic excitations in the parameters. Furthermore, we also show that increasing any of the parameters in an RFMD leads to an increase in the output rate of this RFMD, and the output rate of other RFMDs all increase or decrease. Next, we analyze a generalized network of RFMDs that models static connections between the RFMDs and prove the important mathematical properties: (a) the network admits a unique steady-state, and (b) the problem of determining the connecting weights to maximize the steady-state network output rate is a convex optimization problem. We believe that these networks can have wide applicability to model various non-linear phenomena since their behavior is predictable and ordered.