Flexibility and sensitivity in gene regulation out of equilibrium

Abstract

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume biochemical energy. How does this dissipation enable cellular behaviors unobtainable in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different levels or achieve outputs with multiple concentration regions of locally-enhanced sensitivity. We systematically dissect how energetically-driving individual transitions within regulatory networks, or pairs of transitions, generates more adjustable and sensitive phenotypic responses. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors－feasibly accessed using biological energy budgets and rates－may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

The Hill function is the universal Hopfield barrier for sharpness of input-output responses

“…The use of graphs to study Markov processes has its roots in the pioneering work of Hill [20] and Schnakenberg [21]. It is rarely seen in the Markov process literature and has only occasionally appeared in the biophysics literature [22], until the development of the linear framework [23, 24, 25, 26]. The main distinction in the linear framework approach is to treat the graph as a mathematical object in its own right, in terms of which results can be formulated, which, as we will see here, can accommodate some of the molecular complexity found in biology.…”

Time will tell: comparing timescales to gain insight into transcriptional bursting

“…As more and more quantitative measurements will become available and the ability to capture interdependencies between regulatory factors increases, we expect that the complexity of the system will increasingly demand mathematical and physical modeling to provide a thorough and quantitative understanding of the regulatory processes [ 5 , 115 ]. In addition, the presence of energy expending mechanisms in transcription demands new kinetic models to investigate the nonequilibrium nature of eukaryotic gene regulation [ 67 , 71 , 72 , 120 ]. Last, the ability to specifically edit mammalian genomes has substantially increased in recent years, allowing for more mechanistic studies, but it nevertheless remains essential to continue to use diverse model organisms to exploit the natural variation in nuclear environments, 3D genome architecture, and regulatory complexity to reveal the scope of possible regulatory mechanisms at different scales.…”

“…The benefit of this energy expenditure is that it enables ‘kinetic proofreading’, which provides specificity while maintaining high responsiveness from dynamic TF–DNA interactions. Nonequilibrium energy-dependent steps can also make a system more sensitive and allow for more complex signal processing [ 71 , 72 ].…”

Governing principles of transcriptional logic out of equilibrium

“…In this model, the detailed balance condition was assumed to be broken during TF binding, leading to energy expenditure. Subsequent theoretical studies have shown that non-equilibrium allows for TF binding specificity [21][22][23], leads to accelerated information transmission during transcription [24], and enhanced sensitivity to TF concentration [25,26]. Intriguingly, another theoretical study showed that, when operating out of equilibrium, a single transcription factor can show a non-monotonic response curve [26].…”

“…Subsequent theoretical studies have shown that non-equilibrium allows for TF binding specificity [21][22][23], leads to accelerated information transmission during transcription [24], and enhanced sensitivity to TF concentration [25,26]. Intriguingly, another theoretical study showed that, when operating out of equilibrium, a single transcription factor can show a non-monotonic response curve [26]. Nonetheless, the governing principles of transcriptional logic out of equilibrium remain elusive.…”