Attenuation of noise in ultrasensitive signaling cascades

Ultrasensitive cascades often implement thresholding operations in cell signaling and gene regulatory networks, converting graded input signals into discrete all-or-none outputs. However, the biochemical and genetic reactions involved in such cascades are subject to random fluctuations, leading to noise in output signal levels. Here we prove that cascades operating near saturation have output signal fluctuations that are bounded in magnitude, even as the number of noisy cascade stages becomes large. We show that these fluctuation-bounded cascades can be used to attenuate the noise in an input signal, and we find the optimal cascade length required to achieve the best possible noise reduction. Cascades with ultrasensitive transfer functions naturally operate near saturation, and can be made to simultaneously implement thresholding and noise reduction. They are therefore ideally suited to mediate signal transfer in both natural and artificial biological networks.     

Tunable signal processing in synthetic MAP kinase cascades

The flexibility of MAPK cascade responses enables regulation of a vast array of cell fate decisions, but elucidating the mechanisms underlying this plasticity is difficult in endogenous signaling networks. We constructed insulated mammalian MAPK cascades in yeast to explore how intrinsic and extrinsic perturbations affect the flexibility of these synthetic signaling modules. Contrary to biphasic dependence on scaffold concentration, we observe monotonic decreases in signal strength as scaffold concentration increases. We find that augmenting the concentration of sequential kinases can enhance ultrasensitivity and lower the activation threshold. Further, integrating negative regulation and concentration variation can decouple ultrasensitivity and threshold from the strength of the response. Computational analyses show that cascading can generate ultrasensitivity and that natural cascades with different kinase concentrations are innately biased toward their distinct activation profiles. This work demonstrates that tunable signal processing is inherent to minimal MAPK modules and elucidates principles for rational design of synthetic signaling systems.     

Stochastic signal processing and transduction in chemotactic response of eukaryotic cells

Single-molecule imaging analysis of chemotactic response in eukaryotic cells has revealed a stochastic nature in the input signals and the signal transduction processes. This leads to a fundamental question about the signaling processes: how does the signaling system operate under stochastic fluctuations or noise? Here, we report a stochastic model of chemotactic signaling in which noise and signal propagation along the transmembrane signaling pathway by chemoattractant receptors can be analyzed quantitatively. The results obtained from this analysis reveal that the second-messenger-production reactions by the receptors generate noisy signals that contain intrinsic noise inherently generated at this reaction and extrinsic noise propagated from the ligand-receptor binding. Such intrinsic and extrinsic noise limits the directional sensing ability of chemotactic cells, which may explain the dependence of chemotactic accuracy on chemical gradients that has been observed experimentally. Our analysis also reveals regulatory mechanisms for signal improvement in the stochastically operating signaling system by analyzing how the SNR of chemotactic signals can be improved on or deteriorated by the stochastic properties of receptors and second-messenger molecules. Theoretical consideration of noisy signal transduction by chemotactic signaling systems can further be applied to signaling systems in general.     

Noise Management by Molecular Networks

Fluctuations in the copy number of key regulatory macromolecules (“noise”) may cause physiological heterogeneity in populations of (isogenic) cells. The kinetics of processes and their wiring in molecular networks can modulate this molecular noise. Here we present a theoretical framework to study the principles of noise management by the molecular networks in living cells. The theory makes use of the natural, hierarchical organization of those networks and makes their noise management more understandable in terms of network structure. Principles governing noise management by ultrasensitive systems, signaling cascades, gene networks and feedback circuitry are discovered using this approach. For a few frequently occurring network motifs we show how they manage noise. We derive simple and intuitive equations for noise in molecule copy numbers as a determinant of physiological heterogeneity. We show how noise levels and signal sensitivity can be set independently in molecular networks, but often changes in signal sensitivity affect noise propagation. Using theory and simulations, we show that negative feedback can both enhance and reduce noise. We identify a trade-off; noise reduction in one molecular intermediate by negative feedback is at the expense of increased noise in the levels of other molecules along the feedback loop. The reactants of the processes that are strongly (cooperatively) regulated, so as to allow for negative feedback with a high strength, will display enhanced noise.     

The neuronal MAP kinase cascade: a biochemical signal integration system subserving synaptic plasticity and memory

The mitogen-activated protein kinase (MAP kinase, MAPK) cascade, as the name implies, was originally discovered as a critical regulator of cell division and differentiation. As further details of this signaling cascade were worked out, it became clear that the MAPK cascade is in fact a prototype for a family of signaling cascades that share the motif of three serially linked kinases regulating each other by sequential phosphorylation. Thus, a revised nomenclature arose that uses the term MAPK to refer to the entire superfamily of signaling cascades (comprising the erks, the JNKs and the p38 stress activated protein kinases), and specifies the prototype MAPK as the extracellular signal-regulated kinase (erk). The two erk MAPK isoforms, p44 MAPK and p42 MAPK, are referred to as erk1 and erk2, respectively.The erks are abundantly expressed in neurons in the mature central nervous system, raising the question of why the prototype molecular regulators of cell division and differentiation are present in these non-dividing, terminally differentiated neurons. This review will describe the beginnings of an answer to this question. Interestingly, the general model has begun to emerge that the erk signaling system has been co-opted in mature neurons to function in synaptic plasticity and memory. Moreover, recent insights have led to the intriguing prospect that these molecules serve as biochemical signal integrators and molecular coincidence detectors for coordinating responses to extracellular signals in neurons. In this review I will first outline the essential components of this signal transduction cascade, and briefly describe recent results implicating the erks in mammalian synaptic plasticity and learning. I will then proceed to outline recent results implicating the erks as molecular signal integrators and, potentially, coincidence detectors. Finally, I will speculate on what the critical downstream effectors of the erks are in neurons, and how they might provide a readout of the integrated signal.     

The rice MAPKK–MAPK interactome: the biological significance of MAPK components in hormone signal transduction

Mitogen-activated protein kinase (MAPK) signaling cascades are evolutionarily conserved fundamental signal transduction pathways. A MAPK cascade consists of many distinct MAPKKK–MAPKK–MAPK modules linked to various upstream receptors and downstream targets through sequential phosphorylation and activation of the cascade components. These cascades collaborate in transmitting a variety of extracellular signals and in controlling cellular responses and processes such as growth, differentiation, cell death, hormonal signaling, and stress responses. Although MAPK proteins play central roles in signal transduction pathways, our knowledge of MAPK signaling in hormonal responses in rice has been limited to a small subset of specific upstream and downstream interacting targets. However, recent studies revealing direct MAPK and MAPKK interactions have provided the basis for elucidating interaction specificities, functional divergence, and functional modulation during hormonal responses. In this review, we highlight current insights into MAPKK–MAPK interaction patterns in rice, with emphasis on the biological significance of these interacting pairs in SA (salicylic acid), JA (jasmonic acid), ET (ethylene), and ABA (abscisic acid) responses, and discuss the challenges in understanding functional signal transduction networks mediated by these hormones.     

Effect of the MAPK cascade structure, nuclear translocation and regulation of transcription factors on gene expression

The mitogen activated protein kinase (MAP kinase) cascade system represents a highly conserved prototype of signal transduction by enzyme cascades. One of the best-studied properties of the MAPK system is its ability to convert graded input stimulus to switch-like all-or-none responses. Previous theoretical studies have centered on quantifying dual phosphorylated MAPK as a final output response and have not incorporated its influence on the regulation of gene expression. The main objective of the current work is to understand the regulatory effect of positive feedback loop embedded in the MAPK cascade, nuclear translocation of active MAPK, phosphorylation and activation of nuclear target proteins on the regulation of specific gene expression. To achieve this objective, we have simulated the MAPK cascade system, which resembles Hog1p activation pathway in yeast, at steady state. Thus, the input signal to the MAPK system is correlated with gene expression as a final system-level output response. The steady state simulation results suggest that other than regulating the signal propagation through cascades, the nuclear translocation of activated MAPK and subsequent regulation of gene expression represent one of the key modes to control the threshold level of response. This work proposes that, it is essential to consider the compartmental distributions of signaling species and the corresponding regulatory mechanisms of gene expression to study the system-level performance of signaling modules such as the MAPK cascade. Such an analysis will relate the extracellular cues to the final phenotypic response by capturing the mechanistic details of the signaling pathway.     

Operating regimes of signaling cycles: statics, dynamics, and noise filtering

A ubiquitous building block of signaling pathways is a cycle of covalent modification (e.g., phosphorylation and dephosphorylation in MAPK cascades). Our paper explores the kind of information processing and filtering that can be accomplished by this simple biochemical circuit. Signaling cycles are particularly known for exhibiting a highly sigmoidal (ultrasensitive) input–output characteristic in a certain steady-state regime. Here, we systematically study the cycle's steady-state behavior and its response to time-varying stimuli. We demonstrate that the cycle can actually operate in four different regimes, each with its specific input–output characteristics. These results are obtained using the total quasi–steady-state approximation, which is more generally valid than the typically used Michaelis-Menten approximation for enzymatic reactions. We invoke experimental data that suggest the possibility of signaling cycles operating in one of the new regimes. We then consider the cycle's dynamic behavior, which has so far been relatively neglected. We demonstrate that the intrinsic architecture of the cycles makes them act—in all four regimes—as tunable low-pass filters, filtering out high-frequency fluctuations or noise in signals and environmental cues. Moreover, the cutoff frequency can be adjusted by the cell. Numerical simulations show that our analytical results hold well even for noise of large amplitude. We suggest that noise filtering and tunability make signaling cycles versatile components of more elaborate cell-signaling pathways.     

Biophysically Inspired Rational Design of Structured Chimeric Substrates for DNAzyme Cascade Engineering

The development of large-scale molecular computational networks is a promising approach to implementing logical decision making at the nanoscale, analogous to cellular signaling and regulatory cascades. DNA strands with catalytic activity (DNAzymes) are one means of systematically constructing molecular computation networks with inherent signal amplification. Linking multiple DNAzymes into a computational circuit requires the design of substrate molecules that allow a signal to be passed from one DNAzyme to another through programmed biochemical interactions. In this paper, we chronicle an iterative design process guided by biophysical and kinetic constraints on the desired reaction pathways and use the resulting substrate design to implement heterogeneous DNAzyme signaling cascades. A key aspect of our design process is the use of secondary structure in the substrate molecule to sequester a downstream effector sequence prior to cleavage by an upstream DNAzyme. Our goal was to develop a concrete substrate molecule design to achieve efficient signal propagation with maximal activation and minimal leakage. We have previously employed the resulting design to develop high-performance DNAzyme-based signaling systems with applications in pathogen detection and autonomous theranostics.     

MAP Kinase Pathways in the Yeast Saccharomyces cerevisiae

A cascade of three protein kinases known as a mitogen-activated protein kinase (MAPK) cascade is commonly found as part of the signaling pathways in eukaryotic cells. Almost two decades of genetic and biochemical experimentation plus the recently completed DNA sequence of the Saccharomyces cerevisiae genome have revealed just five functionally distinct MAPK cascades in this yeast. Sexual conjugation, cell growth, and adaptation to stress, for example, all require MAPK-mediated cellular responses. A primary function of these cascades appears to be the regulation of gene expression in response to extracellular signals or as part of specific developmental processes. In addition, the MAPK cascades often appear to regulate the cell cycle and vice versa. Despite the success of the gene hunter era in revealing these pathways, there are still many significant gaps in our knowledge of the molecular mechanisms for activation of these cascades and how the cascades regulate cell function. For example, comparison of different yeast signaling pathways reveals a surprising variety of different types of upstream signaling proteins that function to activate a MAPK cascade, yet how the upstream proteins actually activate the cascade remains unclear. We also know that the yeast MAPK pathways regulate each other and interact with other signaling pathways to produce a coordinated pattern of gene expression, but the molecular mechanisms of this cross talk are poorly understood. This review is therefore an attempt to present the current knowledge of MAPK pathways in yeast and some directions for future research in this area.     

The Interplay of Intrinsic and Extrinsic Bounded Noises in Biomolecular Networks

After being considered as a nuisance to be filtered out, it became recently clear that biochemical noise plays a complex role, often fully functional, for a biomolecular network. The influence of intrinsic and extrinsic noises on biomolecular networks has intensively been investigated in last ten years, though contributions on the co-presence of both are sparse. Extrinsic noise is usually modeled as an unbounded white or colored gaussian stochastic process, even though realistic stochastic perturbations are clearly bounded. In this paper we consider Gillespie-like stochastic models of nonlinear networks, i.e. the intrinsic noise, where the model jump rates are affected by colored bounded extrinsic noises synthesized by a suitable biochemical state-dependent Langevin system. These systems are described by a master equation, and a simulation algorithm to analyze them is derived. This new modeling paradigm should enlarge the class of systems amenable at modeling. We investigated the influence of both amplitude and autocorrelation time of a extrinsic Sine-Wiener noise on: the Michaelis-Menten approximation of noisy enzymatic reactions, which we show to be applicable also in co-presence of both intrinsic and extrinsic noise, a model of enzymatic futile cycle and a genetic toggle switch. In and we show that the presence of a bounded extrinsic noise induces qualitative modifications in the probability densities of the involved chemicals, where new modes emerge, thus suggesting the possible functional role of bounded noises.     

Signal propagation of the MAPK cascade in Xenopus oocytes: role of bistability and ultrasensitivity for a mixed problem

The MAPK signaling cascade is nowadays understood as a network module highly conserved across species. Its main function is to transfer a signal arriving at the plasma membrane to the cellular interior. Current understanding of ‘how’ this is achieved involves the notions of ultrasensitivity and bistability which relate to the nonlinear dynamics of the biochemical network, ignoring spatial aspects. Much less, indeed, is so far known about the propagation of the signal through the cytoplasm. In this work we formulate, starting from a Michaelis–Menten model for the MAPK cascade in Xenopus oocytes, a reaction-diffusion model of the cascade. We study this model in one space dimension. Basing ourselves on previous general results on reaction diffusion models, we particularly study for our model the conditions for signal propagation. We show that the existence of a propagating front depends sensitively on the initial and boundary conditions at the plasma membrane. Possible biological consequences of this finding are discussed.     

Noise generation, amplification and propagation in chemotactic signaling systems of living cells

Theoretical considerations of stochastic signal transduction in living cells have revealed the gain-fluctuation relation, which provides a theoretical framework to describe quantitatively how noise is generated, amplified and propagated along a signaling cascade in living cells. We chose the chemotactic signaling of bacteria and eukaryotic cells as a typical example of noisy signal transduction and applied the gain-fluctuation relation to these signaling systems in order to analyze the effects of noise on signal transduction. Comparing our theoretical analysis with the experimental results of chemotaxis in bacteria Escherichia coli and eukaryote Dictyostelium discoideum revealed that noise in signal transduction systems limits the cells' chemotactic ability and contributes to their behavioral variability. Based on the kinetic properties of signaling molecules in living cells, the gain-fluctuation relation can quantitatively explain stochastic cellular behaviors.     

Sharing of Phosphatases Promotes Response Plasticity in Phosphorylation Cascades

Sharing of positive or negative regulators between multiple targets is frequently observed in cellular signaling cascades. For instance, phosphatase sharing between multiple kinases is ubiquitous within the MAPK pathway. Here we investigate how such phosphatase sharing could shape robustness and evolvability of the phosphorylation cascade. Through modeling and evolutionary simulations, we demonstrate that 1) phosphatase sharing dramatically increases robustness of a bistable MAPK response, and 2) phosphatase-sharing cascades evolve faster than nonsharing cascades. This faster evolution is particularly pronounced when evolving from a monostable toward a bistable phenotype, whereas the transition speed of a population from a bistable to monostable response is not affected by phosphatase sharing. This property may enable the phosphatase-sharing design to adapt better in a changing environment. Analysis of the respective mutational landscapes reveal that phosphatase sharing reduces the number of limiting mutations required for transition from monostable to bistable responses, hence facilitating a faster transition to such response types. Taken together, using MAPK cascade as an example, our study offers a general theoretical framework to explore robustness and evolutionary plasticity of signal transduction cascades.     

Positional Information Generated by Spatially Distributed Signaling Cascades

The temporal and stationary behavior of protein modification cascades has been extensively studied, yet little is known about the spatial aspects of signal propagation. We have previously shown that the spatial separation of opposing enzymes, such as a kinase and a phosphatase, creates signaling activity gradients. Here we show under what conditions signals stall in the space or robustly propagate through spatially distributed signaling cascades. Robust signal propagation results in activity gradients with long plateaus, which abruptly decay at successive spatial locations. We derive an approximate analytical solution that relates the maximal amplitude and propagation length of each activation profile with the cascade level, protein diffusivity, and the ratio of the opposing enzyme activities. The control of the spatial signal propagation appears to be very different from the control of transient temporal responses for spatially homogenous cascades. For spatially distributed cascades where activating and deactivating enzymes operate far from saturation, the ratio of the opposing enzyme activities is shown to be a key parameter controlling signal propagation. The signaling gradients characteristic for robust signal propagation exemplify a pattern formation mechanism that generates precise spatial guidance for multiple cellular processes and conveys information about the cell size to the nucleus.     

MAPK级联途径参与ABA信号转导调节的植物生长发育过程

植物激素ABA参与调控植物生长发育和生理代谢以及多种胁迫应答过程,促分裂原活化蛋白激酶（MAPK）级联途径应答于多种生物和非生物胁迫,广泛参与调控植物的生长发育。MAPK级联途径与ABA信号转导协同作用参与调控植物种子萌发、气孔运动和生长发育,本文主要归纳了植物中受ABA调控激活的MAPK级联途径成员,阐述了它们参与ABA信号转导调控植物生理反应和生长发育的过程,并对MAPK级联途径与ABA信号转导的研究方向作出了展望,指出对MAPK下游底物的筛选是完善MAPK级联途径的重要组成部分。