arXiv subjects

Ram Massas

Publications and source records attributed to Ram Massas.

4 recordsLinked to original sources

arXiv2026

Gain of Entrainment in Nonlinear Cascades

We consider the gain of entrainment (GOE)--the difference between the average steady-state output under a periodic input and the steady-state output under a constant input with the same mean--for an $n$-stage feedforward cascade of stable first-order filters interleaved with static nonlinearities. The main result is an exact decomposition of GOE as a weighted sum of local Jensen gaps, where each gap quantifies the mean shift generated by a nonlinearity, and each weight is a product of downstream incremental gains divided by linear time constants. We provide a Bregman-divergence interpretation of the decomposition, and a second-order small-amplitude of GOE separating local curvature, fluctuation energy, and differential gains. We demonstrate the theoretical results using a Michaelis-Menten cascade showing that any nonconstant periodic feeding strictly reduces the average terminal product relative to constant feeding with the same mean.

math.OC↗

arXiv2026

On the Cost of Entrainment in Protein Translation

Biological systems often synchronize their dynamics with periodic environmental and intracellular signals. Whether such periodic coordination can also improve performance, however, remains unclear. Here, we study this question in the ribosome flow model, a nonlinear dynamical model of ribosome movement along an mRNA transcript during translation. We compare the average protein production rate under positive periodic transition rates with that of a constant-rate system obtained by replacing each rate by its temporal average. We prove that periodic modulation can never increase average protein production: the gain of entrainment is always nonpositive. Moreover, the gain is zero if and only if all transition rates share a common positive periodic modulation of their mean values. This exceptional modulation merely reparametrizes time and leaves the trajectory through state space unchanged. Thus, any genuinely nonuniform temporal modulation strictly reduces average protein production. Our results establish a fundamental tradeoff between temporal coordination and translational efficiency: entrainment can synchronize translation with periodic cellular programs, but this synchronization comes at a quantifiable production cost.

q-bio.MN↗

arXiv2026

A universal multi-turnpike principle for optimal allocation of translational resources

mRNA translation in the cell requires efficient allocation of shared and limited resources including free ribosomes, tRNA molecules, and initiation factors across multiple transcripts. Using a network of dynamic mathematical models for ribosome flow along the mRNA, we pose the problem of maximizing the total steady-state protein production rate in the cell under a shared and limited total budget for all translation rates in all the transcripts. We prove that the optimal solution of this resource allocation problem admits a multi-turnpike structure: in each mRNA, the transition rates are high and nearly uniform along the bulk of the coding region, with lower and varying rates near the boundaries of the~mRNA. Our results are based on the emergence of hierarchical optimality: regardless of how resources are allocated among genes, every transcript should internally organize itself in essentially the same way. This suggests that to optimize the overall production rate it is sufficient to regulate the initiation and termination regions in each transcript. Remarkably, this universal turnpike structure holds for any number of transcripts, arbitrary transcript lengths, and various optimization criteria.This agrees with observed conserved translational phenomena, such as codon ramps and initiation-dominated regulation. Our findings may also provide guidelines for the rational design of intracellular circuits operating under translational control.

q-bio.MN↗

arXiv2026

On the gain of entrainment in stable linear control systems with a nonlinear output

A control system admits a positive gain of entrainment (GOE) if entrainment to a periodic input yields a larger output, on average, than the output generated by the corresponding constant input with the same mean value. We analyze GOE in continuous-time stable linear control systems with a static nonlinear output map. Although linear systems with linear outputs have zero GOE, we show that a nonlinear output may generate a nontrivial GOE through the mismatch between the average output along the entrained periodic orbit and the output evaluated at the corresponding averaged equilibrium. We derive a second-order characterization of GOE for smooth output maps revealing that the leading-order contribution is determined by the curvature of the output map. We then show that if the output is convex (concave) on the controllable subspace, then GOE is nonnegative (nonpositive) for every periodic input. Furthermore, GOE admits a natural geometric interpretation as the average Bregman divergence between the entrained periodic orbit and the equilibrium associated with the averaged input. For the special case of quadratic output functions, we derive explicit frequency-domain formulas for GOE. These yield necessary and sufficient conditions guaranteeing the sign of GOE, characterize the contribution of individual input harmonics, and lead to an optimal periodic excitation that maximizes GOE under an energy constraint. The theoretical results are illustrated using an electrical RLC circuit and a compartmental pharmacodynamic model with a nonlinear drug-effect map.

math.OC↗