Simple biochemical pathways far from steady state can provide switchlike and integrated responses

Transient frequency preference responses in cell signaling systems

Ligand-receptor systems, covalent modification cycles, and transcriptional networks are the fundamental components of cell signaling and gene expression systems. While their behavior in reaching a steady-state regime under step-like stimulation is well understood, their response under repetitive stimulation, particularly at early time stages is poorly characterized. Yet, early-stage responses to external inputs are arguably as informative as late-stage ones. In simple systems, a periodic stimulation elicits an initial transient response, followed by periodic behavior. Transient responses are relevant when the stimulation has a limited time span, or when the stimulated component's timescale is slow as compared to the timescales of the downstream processes, in which case the latter processes may be capturing only those transients. In this study, we analyze the frequency response of simple motifs at different time stages. We use dose-conserved pulsatile input signals and consider different metrics versus frequency curves. We show that in ligand-receptor systems, there is a frequency preference response in some specific metrics during the transient stages, which is not present in the periodic regime. We suggest this is a general system-level mechanism that cells may use to filter input signals that have consequences for higher order circuits. In addition, we evaluate how the described behavior in isolated motifs is reflected in similar types of responses in cascades and pathways of which they are a part. Our studies suggest that transient frequency preferences are important dynamic features of cell signaling and gene expression systems, which have been overlooked.

Frequency-preference response in covalent modification cycles under substrate sequestration conditions

Covalent modification cycles (CMCs) are basic units of signaling systems and their properties are well understood. However, their behavior has been mostly characterized in situations where the substrate is in excess over the modifying enzymes. Experimental data on protein abundance suggest that the enzymes and their target proteins are present in comparable concentrations, leading to substrate sequestration by the enzymes. In this enzyme-in-excess regime, CMCs have been shown to exhibit signal termination, the ability of the product to return to a stationary value lower than its peak in response to constant stimulation, while this stimulation is still active, with possible implications for the ability of systems to adapt to environmental inputs. We characterize the conditions leading to signal termination in CMCs in the enzyme-in-excess regime. We also demonstrate that this behavior leads to a preferred frequency response (band-pass filters) when the cycle is subjected to periodic stimulation, whereas the literature reports that CMCs investigated so far behave as low-pass filters. We characterize the relationship between signal termination and the preferred frequency response to periodic inputs and we explore the dynamic mechanism underlying these phenomena. Finally, we describe how the behavior of CMCs is reflected in similar types of responses in the cascades of which they are part. Evidence of protein abundance in vivo shows that enzymes and substrates are present in comparable concentrations, thus suggesting that signal termination and frequency-preference response to periodic inputs are also important dynamic features of cell signaling systems, which have been overlooked.

Information Thermodynamics for Time Series of Signal-Response Models

The entropy production in stochastic dynamical systems is linked to the structure of their causal representation in terms of Bayesian networks. Such a connection was formalized for bipartite (or multipartite) systems with an integral fluctuation theorem in [Phys. Rev. Lett. 111, 180603 (2013)]. Here we introduce the information thermodynamics for time series, that are non-bipartite in general, and we show that the link between irreversibility and information can only result from an incomplete causal representation. In particular, we consider a backward transfer entropy lower bound to the conditional time series irreversibility that is induced by the absence of feedback in signal-response models. We study such a relation in a linear signal-response model providing analytical solutions, and in a nonlinear biological model of receptor-ligand systems where the time series irreversibility measures the signaling efficiency.

Properties of cell signaling pathways and gene expression systems operating far from steady-state

Ligand-receptor systems, covalent modification cycles, and transcriptional networks are basic units of signaling systems and their steady-state properties are well understood. However, the behavior of such systems before steady-state is poorly characterized. Here, we analyzed the properties of input-output curves for each of these systems as they approach steady-state. In ligand-receptor systems, the EC₅₀ (concentration of the ligand that occupies 50% of the receptors) is higher before the system reaches steady-state. Based on this behavior, we have previously defined PRESS (for pre-equilibrium sensing and signaling), a general “systems level” mechanism cells may use to overcome input saturation. Originally, we showed that, given a step stimulation, PRESS operates when the kinetics of ligand-receptor binding are slower than the downstream signaling steps. Now, we show that, provided the input increases slowly, it is not essential for the ligand binding reaction itself to be slow. In addition, we demonstrate that covalent modification cycles and gene expression systems may also operate in PRESS mode. Thus, nearly all biochemical processes may operate in PRESS mode, suggesting that this mechanism may be ubiquitous in cell signaling systems.

Measuring time during early embryonic development

In most metazoans, embryonic development is orchestrated by a precise series of cellular behaviors. Understanding how such events are regulated to achieve a stereotypical temporal progression is a fundamental problem in developmental biology. In this review, we argue that studying the regulation of the cell cycle in early embryonic development will reveal novel principles of how embryos accurately measure time. We will discuss the strategies that have emerged from studying early development of Drosophila embryos. By comparing the development of flies to that of other metazoans, we will highlight both conserved and alternative mechanisms to generate precision during embryonic development.