Pseudo-nullclines enable the analysis and prediction of signaling model dynamics.

A powerful method to qualitatively analyze a 2D system is the use of nullclines, curves which separate regions of the plane where the sign of the time derivatives is constant, with their intersections corresponding to steady states. As a quick way to sketch the phase portrait of the system, they can be sufficient to understand the qualitative dynamics at play without integrating the differential equations. While it cannot be extended straightforwardly for dimensions higher than 2, sometimes the phase portrait can still be projected onto a 2-dimensional subspace, with some curves becoming pseudo-nullclines. In this work, we study cell signaling models of dimension higher than 2 with behaviors such as oscillations and bistability. Pseudo-nullclines are defined and used to qualitatively analyze the dynamics involved. Our method applies when a system can be decomposed into 2 modules, mutually coupled through 2 scalar variables. At the same time, it helps track bifurcations in a quick and efficient manner, key for understanding the different behaviors. Our results are both consistent with the expected dynamics, and also lead to new responses like excitability. Further work could test the method for other regions of parameter space and determine how to extend it to three-module systems.

A nested bistable module within a negative feedback loop ensures different types of oscillations in signaling systems.

In this article, we consider a double phosphorylation cycle, a ubiquitous signaling component, having the ability to display bistability, a behavior strongly related to the existence of positive feedback loops. If this component is connected to other signaling elements, it very likely undergoes some sort of protein-protein interaction. In several cases, these interactions result in a non-explicit negative feedback effect, leading to interlinked positive and negative feedbacks. This combination was studied in the literature as a way to generate relaxation-type oscillations. Here, we show that the two feedbacks together ensure two types of oscillations, the relaxation-type ones and a smoother type of oscillations functioning in a very narrow range of frequencies, in such a way that outside that range, the amplitude of the oscillations is severely compromised. Even more, we show that the two feedbacks are essential for both oscillatory types to emerge, and it is their hierarchy what determines the type of oscillation at work. We used bifurcation analyses and amplitude vs. frequency curves to characterize and classify the oscillations. We also applied the same ideas to another simple model, with the goal of generalizing what we learned from signaling models. The results obtained display the wealth of oscillatory dynamics that exists in a system with a bistable module nested within a negative feedback loop, showing how to transition between different types of oscillations and other dynamical behaviors such as excitability. Our work provides a framework for the study of other oscillatory systems based on bistable modules, from simple two-component models to more complex examples like the MAPK cascade and experimental cases like cell cycle oscillators.

Changes in the lipid profile of hamster liver after Schistosoma mansoni infection, characterized by mass spectrometry imaging and LC-MS/MS analysis.

Schistosomiasis, caused by the human parasite Schistosoma mansoni, is one of the WHO-listed neglected tropical diseases (NTDs), and it has severe impact on morbidity and mortality, especially in Africa. Not only the adult worms but also their eggs are responsible for health problems. Up to 50% of the eggs produced by the female worms are not excreted with the feces but are trapped in the host tissue, such as the liver, where they provoke immune responses and a change in the lipid profile. We built up a database with 372 infection markers found in livers of S. mansoni-infected hamsters, using LC-MS/MS for identification, followed by statistical analysis. Most of them belong to the lipid classes of phosphatidylcholines (PCs), phosphatidylethanolamines (PEs), and triglycerides (TGs). We assigned some of these markers to specific anatomical structures by applying high-resolution MALDI MSI to cryosections of hamster liver and generating ion images based on the marker list from the LC-MS/MS experiments. Furthermore, enrichment and depletion of several markers were visualized.

Spatial visualization of drug uptake and distribution in Fasciola hepatica using high-resolution AP-SMALDI mass spectrometry imaging.

Understanding drug penetration, distribution, and metabolization is fundamental for understanding drug efficacy. This also accounts for parasites during antiparasitic treatment. Recently, we established matrix-assisted laser desorption/ionization (MALDI) mass spectrometry imaging (MSI) in blood flukes and liver flukes. This label-free technique is capable of visualizing the molecular distribution of endogenous and exogenous molecules, such as drug compounds. Here, we conducted atmospheric-pressure scanning microprobe MALDI MSI (AP-SMALDI MSI) of tissue sections of adult Fasciola hepatica that have been treated in vitro with 100 µM of triclabendazole (TCBZ), the drug of choice for treatment of fasciolosis, and its main metabolite triclabendazole sulfoxide (TCBZ-SO). Measurements covered an m/z mass range of 250-1,000 and provided a high spatial resolution using a pixel size of 10 µm. To support the interpretation of drug distribution, we first identified endogenous lipids that mark characteristic tissues such as the gastrodermis, the tegument, and the parenchyma. The obtained results suggested an early tegumental route of TCBZ uptake within 20 min, followed by spreading throughout the parasite after 4 h, and an even distribution in most tissues after 12 h. This coincided with a strong reduction of parasite vitality. TCBZ-SO treatment demonstrated the accumulation of this metabolite in the same tissues as the parent drug compound. These data demonstrate the auspicious potential of MALDI MSI to visualize uptake and distribution patterns of drugs or drug-candidate compounds in parasites, which might contribute to preclinical drug discovery in liver fluke research and beyond.

Atmospheric-pressure scanning microprobe matrix-assisted laser desorption/ionization mass spectrometry imaging of Neospora caninum-infected cell monolayers.

Neospora caninum is an obligate intracellular protozoan parasite of the phylum Alveolata (subphylum Apicomplexa) which has not been studied extensively in a biochemical context. N. caninum is a primary cause of reproductive disorders causing mummification and abortion not only in cattle but also in other small ruminant species resulting in a substantial economic impact on the livestock industry. In canids, which are the final hosts of N. caninum, clinical disease includes neuromuscular symptoms, ataxia, and ascending paralysis. Fatal outcomes of neosporosis have also been reported depending on the host species, age and immune status, however, its zoonotic potential is still uncertain. Therefore, N. caninum should be thoroughly investigated. Matrix-assisted laser desorption/ionisation (MALDI) mass spectrometry (MS) and MS imaging (MSI) were used, combined with high-performance liquid chromatography (HPLC) to investigate these intracellular parasites. The aim of this study was to identify molecular biomarkers for N. caninum tachyzoite-infected host cells and to further clarify their functions. By atmospheric-pressure scanning microprobe MALDI MS(I), sections of N. caninum-infected and non-infected host cell pellets were examined in order to determine potential markers. In vivo, N. caninum infects different types of nucleated cells, such as endothelial cells which represent a highly immunoreactive cell type. Therefore, primary bovine umbilical vein endothelial cells were here used as a suitable infection system. For comparison, the permanent MARC-145 cell line was used as an additional, simplified in vitro cell culture model. HPLC-tandem MS (HPLC-MS/MS) experiments combined with database search were employed for structural verification of markers. The statistically relevant biomarkers found by MS and identified by HPLC-MS/MS measurements were partly also found in infected monolayers. Marker signals were imaged in cell layers of N. caninum-infected and non-infected host cells at 5 µm lateral resolution.

Synthesis and antischistosomal activity of linker- and thiophene-modified biaryl alkyl carboxylic acid derivatives.

Schistosomiasis is a neglected tropical disease caused by blood flukes of the genus Schistosoma and causes severe morbidity in infected patients. In 2018, 290.8 million people required treatment, and 200,000 deaths are reported per year. Treatment of this disease depends on a single drug, praziquantel (PZQ). However, in the past few years, reduced sensitivity of the parasites toward PZQ has been reported. Therefore, there is an urgent need for new drugs against this disease. In the past few years, we have focused on a new substance class called biaryl alkyl carboxylic acid derivatives, which showed promising antischistosomal activity in vitro. Structure-activity relationship (SAR) studies of the carboxylic acid moiety led to three promising carboxylic amides (morpholine, thiomorpholine, and methyl sulfonyl piperazine) with an antischistosomal activity down to 10 µM (morpholine derivative) and no cytotoxicity up to 100 µM. Here, we show our continued work on this substance class. We investigated, in extended SAR studies, whether modification of the linker and the thiophene ring could improve the antischistosomal activity. We found that the exchange of the alkyl linker by a pentadienyl or benzyl linker was tolerated and led to similar antischistosomal effects, whereas the exchange of the thiophene ring was not tolerated. Our data suggest that the thiophene ring is important for the antischistosomal activity of this compound class.

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.

Discriminating between negative cooperativity and ligand binding to independent sites using pre-equilibrium properties of binding curves.

Negative cooperativity is a phenomenon in which the binding of a first ligand or substrate molecule decreases the rate of subsequent binding. This definition is not exclusive to ligand-receptor binding, it holds whenever two or more molecules undergo two successive binding events. Negative cooperativity turns the binding curve more graded and cannot be distinguished from two independent and different binding events based on equilibrium measurements only. The need of kinetic data for this purpose was already reported. Here, we study the binding response as a function of the amount of ligand, at different times, from very early times since ligand is added and until equilibrium is reached. Over those binding curves measured at different times, we compute the dynamic range: the fold change required in input to elicit a change from 10 to 90% of maximum output, finding that it evolves in time differently and controlled by different parameters in the two situations that are identical in equilibrium. Deciphering which is the microscopic model that leads to a given binding curve adds understanding on the molecular mechanisms at play, and thus, is a valuable tool. The methods developed in this article were tested both with simulated and experimental data, showing to be robust to noise and experimental constraints.

Robustness in spatially driven bistability in signaling systems.

Biological systems are spatially organized. This microscopic heterogeneity has been shown to produce emergent complex behaviors such as bistability. Even though the connection between spatiality and dynamic response is essential to understand biological output, its robustness and extent has not been sufficiently explored. This work focuses on a previously described system which is composed of two monostable modules acting on different cellular compartments and sharing species through linear shuttling reactions. One of the two main purposes of this paper is to quantify the frequency of occurrence of bistability throughout the parameter space and to identify which parameters and in which value ranges control the emergence and the properties of bistability. We found that a very small fraction of the sampled parameter space produced a bistable response. Most importantly, shuttling parameters were among the most influential ones to control this property. The other goal of this paper is to simplify the same system as much as possible without losing compartment-induced bistability. This procedure provided a simplified model that still connects two monostable systems by a reduced set of linear shuttling reactions that circulates all the species around the two compartments. Bistable systems are one of the main building blocks of more complex behaviors such as oscillations, memory, and digitalization. Therefore, we expect that the proposed minimal system provides insight into how these behaviors can arise from compartmentalization.

Development of Biarylalkyl Carboxylic Acid Amides with Improved Anti-schistosomal Activity.

The parasitic disease schistosomiasis is the cause of more than 200 000 human deaths per year. Although the disease is treatable, there is one major shortcoming: praziquantel has been the only drug used to combat these parasites since 1977. The risk of the emergence of resistant schistosomes is known to be increasing, as a reduced sensitivity of these parasites toward praziquantel has been observed. We developed a new class of substances, which are derived from inhibitors of human aldose reductase, and which showed promising activity against Schistosoma mansoni couples in vitro. Further optimisation of the compounds led to an increase in anti-schistosomal activity with observed phenotypes such as reduced egg production, vitality, and motility as well as tegumental damage and gut dilatation. Here, we performed structure-activity relationship studies on the carboxylic acid moiety of biarylalkyl carboxylic acids. Out of 82 carboxylic acid amides, we identified 10 compounds that are active against S. mansoni at 25 µm. The best five compounds showed an anti-schistosomal activity up to 10 µm and induced severe phenotypes. Cytotoxicity tests in human cell lines showed that two derivatives had no cytotoxicity at 50 or 100 µm. These compounds are promising candidates for further optimisation toward the new anti-schistosomal agents.

Cell cycle dynamics of mouse embryonic stem cells in the ground state and during transition to formative pluripotency.

Mouse embryonic stem cells (mESCs) can be maintained as homogeneous populations in the ground state of pluripotency. Release from this state in minimal conditions allows to obtain cells that resemble those of the early post-implantation epiblast, providing an important developmental model to study cell identity transitions. However, the cell cycle dynamics of mESCs in the ground state and during its dissolution have not been extensively studied. By performing live imaging experiments of mESCs bearing cell cycle reporters, we show here that cells in the pluripotent ground state display a cell cycle structure comparable to the reported for mESCs in serum-based media. Upon release from self-renewal, the cell cycle is rapidly accelerated by a reduction in the length of the G1 phase and of the S/G2/M phases, causing an increased proliferation rate. Analysis of cell lineages indicates that cell cycle variables of sister cells are highly correlated, suggesting the existence of inherited cell cycle regulators from the parental cell. Together with a major morphological reconfiguration upon differentiation, our findings support a correlation between this in vitro model and early embryonic events.

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.

Chemotherapy for Fighting Schistosomiasis: Past, Present and Future.

Chemotherapy based on repeated doses of praziquantel remains the most effective control strategy against schistosomiasis, a neglected tropical disease caused by platyhelminths of the genus Schistosoma spp. Its long-term use, however, raises serious concerns about drug resistance against praziquantel. Therefore, it is generally acknowledged that alternative treatment options are urgently needed. This Review summarizes data on relinquished drugs as well as recent advances in the area of antischistosomal compounds from a medicinal chemistry point of view. Furthermore, insights into the structure-activity relationships of each class of compounds are presented including in vitro and in vivo data, if available. Although many compounds have demonstrated good antischistosomal activity in vitro, they offer little promise to replace praziquantel. Nevertheless, the race to develop novel antischistosomal agents is ongoing.

Ultrasensitivity in signaling cascades revisited: Linking local and global ultrasensitivity estimations.

Ultrasensitive response motifs, capable of converting graded stimuli into binary responses, are well-conserved in signal transduction networks. Although it has been shown that a cascade arrangement of multiple ultrasensitive modules can enhance the system's ultrasensitivity, how a given combination of layers affects a cascade's ultrasensitivity remains an open question for the general case. Here, we introduce a methodology that allows us to determine the presence of sequestration effects and to quantify the relative contribution of each module to the overall cascade's ultrasensitivity. The proposed analysis framework provides a natural link between global and local ultrasensitivity descriptors and it is particularly well-suited to characterize and understand mathematical models used to study real biological systems. As a case study, we have considered three mathematical models introduced by O'Shaughnessy et al. to study a tunable synthetic MAPK cascade, and we show how our methodology can help modelers better understand alternative models.

Signaling cascades transmit information downstream and upstream but unlikely simultaneously.

BACKGROUND: Signal transduction is the process through which cells communicate with the external environment, interpret stimuli and respond to them. This mechanism is controlled by signaling cascades, which play the role of intracellular transmitter, being able to transmit biochemical information between cell membrane and nucleus. In theory as well as in practice, it has been shown that a perturbation can propagate upstream (and not only downstream) a cascade, by a mechanism known as retroactivity. This study aims to compare the conditions on biochemical parameters which favor one or the other direction of signaling in such a cascade. RESULTS: From a mathematical point of view, we show that the steady states of a cascade of arbitrary length n are described by an iterative map of second order, meaning that the cascade tiers are actually coupled three-by-three. We study the influence of the biochemical parameters in the control of the direction of transmission - upstream and/or downstream - along a signaling cascade. A numerical and statistical approach, based on the random scan of parameters describing a 3-tier signaling cascade, provides complementary findings to the analytical study. In particular, computing the likelihood of parameters with respect to various signaling regimes, we identify conditions on biochemical parameters which enhance a specific direction of propagation corresponding to forward or retro-signaling regimes. A compact graphical representation is designed to relay the gist of these conditions. CONCLUSIONS: The values of biochemical parameters such as kinetic rates, Michaelis-Menten constants, total concentrations of kinases and of phosphatases, determine the propensity of a cascade to favor or impede downstream or upstream signal transmission. We found that generally there is an opposition between parameter sets favoring forward and retro-signaling regimes. Therefore, on one hand our study supports the idea that in most cases, retroactive effects can be neglected when a cascade which is efficient in forward signaling, is perturbed by an external ligand inhibiting the activation at some tier of the cascade. This result is relevant for therapeutic methodologies based on kinase inhibition. On the other hand, our study highlights a less-known part of the parameter space where, although the forward signaling is inefficient, the cascade can interestingly act as a retro-signaling device.

Impact of upstream and downstream constraints on a signaling module's ultrasensitivity.

Much work has been done on the study of the biochemical mechanisms that result in ultrasensitive behavior of simple biochemical modules. However, in a living cell, such modules are embedded in a bigger network that constrains the range of inputs that the module will receive as well as the range of the module's outputs that network will be able to detect. Here, we studied how the effective ultrasensitivity of a modular system is affected by these restrictions. We use a simple setup to explore to what extent the dynamic range spanned by upstream and downstream components of an ultrasensitive module impact on the effective sensitivity of the system. Interestingly, we found for some ultrasensitive motifs that dynamic range limitations imposed by downstream components can produce effective sensitivities much larger than that of the original module when considered in isolation.

Utilization of extracellular information before ligand-receptor binding reaches equilibrium expands and shifts the input dynamic range.

Cell signaling systems sense and respond to ligands that bind cell surface receptors. These systems often respond to changes in the concentration of extracellular ligand more rapidly than the ligand equilibrates with its receptor. We demonstrate, by modeling and experiment, a general "systems level" mechanism cells use to take advantage of the information present in the early signal, before receptor binding reaches a new steady state. This mechanism, pre-equilibrium sensing and signaling (PRESS), operates in signaling systems in which the kinetics of ligand-receptor binding are slower than the downstream signaling steps, and it typically involves transient activation of a downstream step. In the systems where it operates, PRESS expands and shifts the input dynamic range, allowing cells to make different responses to ligand concentrations so high as to be otherwise indistinguishable. Specifically, we show that PRESS applies to the yeast directional polarization in response to pheromone gradients. Consideration of preexisting kinetic data for ligand-receptor interactions suggests that PRESS operates in many cell signaling systems throughout biology. The same mechanism may also operate at other levels in signaling systems in which a slow activation step couples to a faster downstream step.

Intrinsic feedbacks in MAPK signaling cascades lead to bistability and oscillations.

Previous studies have demonstrated that double phosphorylation of a protein can lead to bistability if some conditions are fulfilled. It was also shown that the signaling behavior of a covalent modification cycle can be quantitatively and, more importantly, qualitatively modified when this cycle is coupled to a signaling pathway as opposed to being isolated. This property was named retroactivity. These two results are studied together in this paper showing the existence of interesting phenomena--oscillations and bistability--in signaling cascades possessing at least one stage with a double-phosphorylation cycle as in MAPK cascades.

Characterization of the reconstituted UTase/UR-PII-NRII-NRI bicyclic signal transduction system that controls the transcription of nitrogen-regulated (Ntr) genes in Escherichia coli.

A reconstituted UTase/UR-PII-NRII-NRI bicyclic cascade regulated PII uridylylation and NRI phosphorylation in response to glutamine. We examined the sensitivity and robustness of the responses of the individual cycles and of the bicyclic system. The sensitivity of the glutamine response of the upstream UTase/UR-PII monocycle depended upon the PII concentration, and we show that PII exerted substrate inhibition of the UTase activity of UTase/UR, potentially contributing to this dependence of sensitivity on PII. In the downstream NRII-NRI monocycle, PII controlled NRI phosphorylation state, and the response to PII was hyperbolic at both saturating and unsaturating NRI concentration. As expected from theory, the level of NRI∼P produced by the NRII-NRI monocycle was robust to changes in the NRII or NRI concentrations when NRI was in excess over NRII, as long as the NRII concentration was above a threshold value, an example of absolute concentration robustness (ACR). Because of the parameters of the system, at physiological protein levels and ratios of NRI to NRII, the level of NRI∼P depended upon both protein concentrations. In bicyclic UTase/UR-PII-NRII-NRI systems, the NRI phosphorylation state response to glutamine was always hyperbolic, regardless of the PII concentration or sensitivity of the upstream UTase/UR-PII cycle. In these bicyclic systems, NRI phosphorylation state was only robust to variation in the PII/NRII ratio within a narrow range; when PII was in excess NRI∼P was low, and when NRII was in excess NRI phosphorylation was elevated, throughout the physiological range of glutamine concentrations. Our results show that the bicyclic system produced a graded response of NRI phosphorylation to glutamine under a range of conditions, and that under most conditions the response of NRI phosphorylation state to glutamine levels depended on the concentrations of NRI, NRII, and PII.

Retroactive signaling in short signaling pathways.

In biochemical signaling pathways without explicit feedback connections, the core signal transduction is usually described as a one-way communication, going from upstream to downstream in a feedforward chain or network of covalent modification cycles. In this paper we explore the possibility of a new type of signaling called retroactive signaling, offered by the recently demonstrated property of retroactivity in signaling cascades. The possibility of retroactive signaling is analysed in the simplest case of the stationary states of a bicyclic cascade of signaling cycles. In this case, we work out the conditions for which variables of the upstream cycle are affected by a change of the total amount of protein in the downstream cycle, or by a variation of the phosphatase deactivating the same protein. Particularly, we predict the characteristic ranges of the downstream protein, or of the downstream phosphatase, for which a retroactive effect can be observed on the upstream cycle variables. Next, we extend the possibility of retroactive signaling in short but nonlinear signaling pathways involving a few covalent modification cycles.