Mechanisms and constraints on yeast MAPK signaling specificity

Multiplexing oscillatory biochemical signals

In recent years it has been increasingly recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that the protein signaling network of living cells has a bow-tie structure and that components are often shared between different signaling pathways. Here we show by mathematical modeling that living cells can multiplex a constant and an oscillatory signal: they can transmit these two signals simultaneously through a common signaling pathway, and yet respond to them specifically and reliably. We find that information transmission is reduced not only by noise arising from the intrinsic stochasticity of biochemical reactions, but also by crosstalk between the different channels. Yet, under biologically relevant conditions more than 2 bits of information can be transmitted per channel, even when the two signals are transmitted simultaneously. These observations suggest that oscillatory signals are ideal for multiplexing signals.

Insulin signaling - mathematical modeling comes of age

Signaling pathways that only a few years ago appeared simple and understandable, albeit far from complete, have evolved into very complex multi-layered networks of cellular control mechanisms, which in turn are integrated in a similarly complex whole-body level of control mechanisms. This complexity sets limits for classical biochemical reasoning, such that a correct and complete analysis of experimental data while taking the full complexity into account is not possible. In this Opinion we propose that mathematical modeling can be used as a tool in insulin signaling research, and we demonstrate how recent developments in modeling - and the integration of modeling in the experimental process - provide new possibilities to approach and decipher complex biological systems more efficiently.

Integral control of plant gravitropism through the interplay of hormone signaling and gene regulation

The interplay between hormone signaling and gene regulatory networks is instrumental in promoting the development of living organisms. In particular, plants have evolved mechanisms to sense gravity and orient themselves accordingly. Here, we present a mathematical model that reproduces plant gravitropic responses based on known molecular genetic interactions for auxin signaling coupled with a physical description of plant reorientation. The model allows one to analyze the spatiotemporal dynamics of the system, triggered by an auxin gradient that induces differential growth of the plant with respect to the gravity vector. Our model predicts two important features with strong biological implications: 1), robustness of the regulatory circuit as a consequence of integral control; and 2), a higher degree of plasticity generated by the molecular interplay between two classes of hormones. Our model also predicts the ability of gibberellins to modulate the tropic response and supports the integration of the hormonal role at the level of gene regulation.

Multiplexing biochemical signals

In this Letter we show that living cells can multiplex biochemical signals, i.e., transmit multiple signals through the same signaling pathway simultaneously, and yet respond to them very specifically. We demonstrate how two binary input signals can be encoded in the concentration of a common signaling protein, which is then decoded such that each of the two output signals provides reliable information about one corresponding input. Under biologically relevant conditions the network can reach the maximum amount of information that can be transmitted, which is 2 bits.

Design principles and specificity in biological networks with cross activation

Cells sense and respond to diverse environmental stimuli using a set of intracellular signaling components. Often, the signal transduction pathways contain shared components which lead to cross activation at different levels of the pathway. To discover the design principles that ensure signaling specificity is a challenging task, especially for pathways that contain numerous components. Here, we present an analysis of cross-activating pathways and show that a general inhibitory scheme, asymmetric hierarchical inhibition, is sufficient to ensure signaling specificity. Based on this inhibitory scheme, we are able to enumerate all possible network topologies containing two inhibitory links that guarantee specificity. Furthermore, we apply our methodology to the mating and filamentous growth pathways of the yeast model system Saccharomyces cerevisiae. We enumerate the possible ways to wire this model system and determine which topology is consistent with experimental data.

Ultrasensitive responses and specificity in cell signaling

Background

Interconnected cell signaling pathways are able to efficiently and accurately transmit a multitude of different signals, despite an inherent potential for undesirable levels of cross-talk. To ensure that an appropriate response is produced, biological systems have evolved network-level mechanisms that insulate pathways from crosstalk and prevent 'leaking' or 'spillover' between pathways. Many signaling pathways have been shown to respond in an ultrasensitive (switch-like) fashion to graded input, and this behavior may influence specificity. The relationship of ultrasensitivity to signaling specificity has not been extensively explored.

Results

We studied the behavior of simple mathematical models of signaling networks composed of two interconnected pathways that share an intermediate component, asking if the two pathways in the network could exhibit both output specificity (preferentially activate their own output) and input fidelity (preferentially respond to their own input). Previous results with weakly-activated pathways indicated that neither mutual specificity nor mutual fidelity were obtainable in the absence of an insulating mechanism, such as cross-pathway inhibition, combinatorial signaling or scaffolding/compartmentalization. Here we found that mutual specificity is obtainable for hyperbolic or ultrasensitive pathways, even in the absence of an insulating mechanism. However, mutual fidelity is impossible at steady-state, even if pathways are hyperbolic or ultrasensitive. Nevertheless, ultrasensitivity does provide advantages in attaining specificity and fidelity to networks that contain an insulating mechanism. For networks featuring cross-pathway inhibition or combinatorial signaling, ultrasensitive activation can increase specificity in a limited way, and can only be utilized by one of the two pathways. In contrast, for networks featuring scaffolding/compartmentalization, ultrasensitive activation of both pathways can dramatically improve network specificity.

Conclusions

There are constraints to obtaining performance objectives associated with signaling specificity; such constraints may have influenced the evolution of signal transduction networks. Notably, input fidelity (preferential response to an authentic input) is a more difficult objective to achieve than output specificity (preferential targeting to an authentic output). Indeed, mutual fidelity is impossible in the absence of an insulating mechanism, even if pathways are ultrasensitive. Ultrasensitivity does, however, significantly enhance the performance of several insulating mechanisms. In particular, the ultrasensitive activation of both pathways can provide substantial improvement to networks containing scaffolding/compartmentalization.