Coherent feedback leads to robust background compensation in oscillatory and non-oscillatory homeostats.

When in a reaction kinetic integral controller a step perturbation is applied besides a constant background, the concentration of a controlled variable (described as A) will generally respond with decreased response amplitudes ΔA as backgrounds increase. The controller variable E will at the same time provide the necessary compensatory flux to move A back to its set-point. A typical example of decreased response amplitudes at increased backgrounds is found in retinal light adaptation. Due to remarks in the literature that retinal light adaptation would also involve a compensation of backgrounds we became interested in conditions how background compensation could occur. In this paper we describe novel findings how background influences can be robustly eliminated. When such a background compensation is active, oscillatory controllers will respond to a defined perturbation with always the same (damped or undamped) frequency profile, or in the non-oscillatory case, with the same response amplitude ΔA, irrespective of the background level. To achieve background compensation we found that two conditions need to apply: (i) an additional set of integral controllers (here described as I1 and I2) have to be employed to keep the manipulated variable E at a defined set-point, and (ii), I1 and I2 need to feed back to the A-E signaling axis directly through the controlled variable A. In analogy to a similar feedback applied in quantum control theory, we term these feedback conditions as 'coherent feedback'. When analyzing retinal light adaptations in more detail, we find no evidence of the presence of background compensation mechanisms. Although robust background compensation, as described theoretically here, appears to be an interesting regulatory property, relevant biological or biochemical examples still need to be identified.

Homeostasis at different backgrounds: The roles of overlayed feedback structures in vertebrate photoadaptation.

We have studied the resetting behavior of eight basic integral controller motifs with respect to different but constant backgrounds. We found that the controllers split symmetrically into two classes: one class, based on derepression of the compensatory flux, leads to more rapid resetting kinetics as backgrounds increase. The other class, which directly activates the compensatory flux, shows a slowing down in the resetting at increased backgrounds. We found a striking analogy between the resetting kinetics of vertebrate photoreceptors and controllers based on derepression, i.e. vertebrate rod or cone cells show decreased sensitivities and accelerated response kinetics as background illuminations increase. The central molecular model of vertebrate photoadaptation consists of an overlay of three negative feedback loops with cytosolic calcium ([Formula: see text]), cyclic guanosine monophosphate (cGMP) and cyclic nucleotide-gated (CNG) channels as components. While in one of the feedback loops the extrusion of [Formula: see text] by potassium-dependent sodium-calcium exchangers (NCKX) can lead to integral control with cGMP as the controlled variable, the expected robust perfect adaptation of cGMP is lost, because of the two other feedback loops. They avoid that [Formula: see text] levels become too high and toxic. Looking at psychophysical laws, we found that in all of the above mentioned basic controllers Weber's law is followed when a "just noticeable difference" (threshold) of 1% of the controlled variable's set-point was considered. Applying comparable threshold pulses or steps to the photoadaptation model we find, in agreement with experimental results, that Weber's law is followed for relatively high backgrounds, while Stephens' power law gives a better description when backgrounds are low. Limitations of our photoadaption model, in particular with respect to potassium/sodium homeostasis, are discussed. Finally, we discuss possible implication of background perturbations in biological controllers when compensatory fluxes are based on activation.

Modeling the interaction between donor-derived regulatory T cells and effector T cells early after allogeneic hematopoietic stem cell transplantation.

While allogeneic hematopoietic stem cell transplantation (allo-HSCT) is a potential curative therapy against hematological malignancies, modulation of donor T cell alloreactivity is required to enhance the graft-versus-leukemia (GVL) effect and control graft-versus-host-disease (GVHD) after allo-HSCT. Donor-derived regulatory CD4+CD25+Foxp3+ T cells (Tregs) play a central role in establishing of immune tolerance after allo-HSCT. They could be a key target to be modulated for increasing the GVL effect and control of GVHD. We constructed an ordinary differential equation model incorporating bidirectional interactions between Tregs and effector CD4+ T cells (Teffs) as a mechanism for control of Treg cell concentration. The goal is to elucidate how the interaction between Tregs and Teffs is modulated in order to get insights into fine tuning of alloreactivity after allo-HSCT. The model was calibrated with respect to published Treg and Teff recovery data after allo-HSCT. The calibrated model exhibits perfect or near-perfect adaptation to stepwise perturbations between Treg and Teff interactions, as seen in Treg cell populations when patients with relapsed malignancy were treated with anti-CTLA-4 (cytotoxic T lymphocyte-associated antigen 4). In addition, the model predicts observed shifts of Tregs and Teffs concentrations after co-stimulatory receptor IL-2R or TNFR2 blockade with allo-HSCT. The present results suggest simultaneous blockades of co-stimulatory and co-inhibitory receptors as a potential treatment for enhancing the GVL effect after allo-HSCT without developing GVHD.

Kinetics and mechanisms of catalyzed dual-E (antithetic) controllers.

Homeostasis plays a central role in our understanding how cells and organisms are able to oppose environmental disturbances and thereby maintain an internal stability. During the last two decades there has been an increased interest in using control engineering methods, especially integral control, in the analysis and design of homeostatic networks. Several reaction kinetic mechanisms have been discovered which lead to integral control. In two of them integral control is achieved, either by the removal of a single control species E by zero-order kinetics ("single-E controllers"), or by the removal of two control species by second-order kinetics ("antithetic or dual-E control"). In this paper we show results when the control species E1 and E2 in antithetic control are removed enzymatically by ping-pong or ternary-complex mechanisms. Our findings show that enzyme-catalyzed dual-E controllers can work in two control modes. In one mode, one of the two control species is active, but requires zero-order kinetics in its removal. In the other mode, both controller species are active and both are removed enzymatically. Conditions for the two control modes are put forward and biochemical examples with the structure of enzyme-catalyzed dual-E controllers are discussed.

DOPA Homeostasis by Dopamine: A Control-Theoretic View.

Dopamine (DA) is an important signal mediator in the brain as well as in the periphery. The term "dopamine homeostasis" occasionally found in the literature refers to the fact that abnormal DA levels can be associated with a variety of neuropsychiatric disorders. An analysis of the negative feedback inhibition of tyrosine hydroxylase (TH) by DA indicates, with support from the experimental data, that the TH-DA negative feedback loop has developed to exhibit 3,4-dihydroxyphenylalanine (DOPA) homeostasis by using DA as a derepression regulator. DA levels generally decline when DOPA is removed, for example, by increased oxidative stress. Robust DOPA regulation by DA further implies that maximum vesicular DA levels are established, which appear necessary for a reliable translation of neural activity into a corresponding chemical transmitter signal. An uncontrolled continuous rise (windup) in DA occurs when Levodopa treatment exceeds a critical dose. Increased oxidative stress leads to the successive breakdown of DOPA homeostasis and to a corresponding reduction in DA levels. To keep DOPA regulation robust, the vesicular DA loading requires close to zero-order kinetics combined with a sufficiently high compensatory flux provided by TH. The protection of DOPA and DA due to a channeling complex is discussed.

Personalized Medicine to Improve Treatment of Dopa-Responsive Dystonia-A Focus on Tyrosine Hydroxylase Deficiency.

Dopa-responsive dystonia (DRD) is a rare movement disorder associated with defective dopamine synthesis. This impairment may be due to the fact of a deficiency in GTP cyclohydrolase I (GTPCHI, GCH1 gene), sepiapterin reductase (SR), tyrosine hydroxylase (TH), or 6-pyruvoyl tetrahydrobiopterin synthase (PTPS) enzyme functions. Mutations in GCH1 are most frequent, whereas fewer cases have been reported for individual SR-, PTP synthase-, and TH deficiencies. Although termed DRD, a subset of patients responds poorly to L-DOPA. As this is regularly observed in severe cases of TH deficiency (THD), there is an urgent demand for more adequate or personalized treatment options. TH is a key enzyme that catalyzes the rate-limiting step in catecholamine biosynthesis, and THD patients often present with complex and variable phenotypes, which results in frequent misdiagnosis and lack of appropriate treatment. In this expert opinion review, we focus on THD pathophysiology and ongoing efforts to develop novel therapeutics for this rare disorder. We also describe how different modeling approaches can be used to improve genotype to phenotype predictions and to develop in silico testing of treatment strategies. We further discuss the current status of mathematical modeling of catecholamine synthesis and how such models can be used together with biochemical data to improve treatment of DRD patients.

Alleviation of C⋠C Mismatches in DNA by the Escherichia coli Fpg Protein.

DNA polymerase III mis-insertion may, where not corrected by its 3'→ 5' exonuclease or the mismatch repair (MMR) function, result in all possible non-cognate base pairs in DNA generating base substitutions. The most thermodynamically unstable base pair, the cytosine (C)⋅C mismatch, destabilizes adjacent base pairs, is resistant to correction by MMR in Escherichia coli, and its repair mechanism remains elusive. We present here in vitro evidence that C⋅C mismatch can be processed by base excision repair initiated by the E. coli formamidopyrimidine-DNA glycosylase (Fpg) protein. The k cat for C⋅C is, however, 2.5 to 10 times lower than for its primary substrate 8-oxoguanine (oxo8G)⋅C, but approaches those for 5,6-dihydrothymine (dHT)⋅C and thymine glycol (Tg)⋅C. The K M values are all in the same range, which indicates efficient recognition of C⋅C mismatches in DNA. Fpg activity was also exhibited for the thymine (T)⋅T mismatch and for N 4- and/or 5-methylated C opposite C or T, Fpg activity being enabled on a broad spectrum of DNA lesions and mismatches by the flexibility of the active site loop. We hypothesize that Fpg plays a role in resolving C⋅C in particular, but also other pyrimidine⋅pyrimidine mismatches, which increases survival at the cost of some mutagenesis.

An amplified derepression controller with multisite inhibition and positive feedback.

How organisms are able to maintain robust homeostasis has in recent years received increased attention by the use of combined control engineering and kinetic concepts, which led to the discovery of robust controller motifs. While these motifs employ kinetic conditions showing integral feedback and homeostasis for step-wise perturbations, the motifs' performance differ significantly when exposing them to time dependent perturbations. One type of controller motifs which are able to handle exponentially and even hyperbolically growing perturbations are based on derepression. In these controllers the compensatory reaction, which neutralizes the perturbation, is derepressed, i.e. its reaction rate is increased by the decrease of an inhibitor acting on the compensatory flux. While controllers in this category can deal well with different time-dependent perturbations they have the disadvantage that they break down once the concentration of the regulatory inhibitor becomes too low and the compensatory flux has gained its maximum value. We wondered whether it would be possible to bypass this restriction, while still keeping the advantages of derepression kinetics. In this paper we show how the inclusion of multisite inhibition and the presence of positive feedback loops lead to an amplified controller which is still based on derepression kinetics but without showing the breakdown due to low inhibitor concentrations. By searching for the amplified feedback motif in natural systems, we found it as a part of the plant circadian clock where it is highly interlocked with other feedback loops.

The Goodwin Oscillator and its Legacy.

In the 1960's Brian Goodwin published a couple of mathematical models showing how feedback inhibition can lead to oscillations and discussed possible implications of this behaviour for the physiology of the cell. He also presented key ideas about the rich dynamics that may result from the coupling between such biochemical oscillators. Goodwin's work motivated a series of theoretical investigations aiming at identifying minimal mechanisms to generate limit cycle oscillations and deciphering design principles of biological oscillators. The three-variable Goodwin model (adapted by Griffith) can be seen as a core model for a large class of biological systems, ranging from ultradian to circadian clocks. We summarize here main ideas and results brought by Goodwin and review a couple of modeling works directly or indirectly inspired by Goodwin's findings.

Frequency switching between oscillatory homeostats and the regulation of p53.

Homeostasis is an essential concept to understand the stability of organisms and their adaptive behaviors when coping with external and internal assaults. Many hormones that take part in homeostatic control come in antagonistic pairs, such as glucagon and insulin reflecting the inflow and outflow compensatory mechanisms to control a certain internal variable, such as blood sugar levels. By including negative feedback loops homeostatic controllers can exhibit oscillations with characteristic frequencies. In this paper we demonstrate the associated frequency changes in homeostatic systems when individual controllers -in a set of interlocked feedback loops- gain control in response to environmental changes. Taking p53 as an example, we show how Per2, ATM and Mdm2 feedback loops -interlocked with p53- gain individual control in dependence to the level of DNA damage, and how each of these controllers provide certain functionalities in their regulation of p53. In unstressed cells, the circadian regulator Per2 ensures a basic p53 level to allow its rapid up-regulation in case of DNA damage. When DNA damage occurs the ATM controller increases the level of p53 and defends it towards uncontrolled degradation, which despite DNA damage, would drive p53 to lower values and p53 dysfunction. Mdm2 on its side keeps p53 at a high but sub-apoptotic level to avoid premature apoptosis. However, with on-going DNA damage the Mdm2 set-point is increased by HSP90 and other p53 stabilizers leading finally to apoptosis. An emergent aspect of p53 upregulation during cell stress is the coordinated inhibition of ubiquitin-independent and ubiquitin-dependent degradation reactions. Whether oscillations serve a function or are merely a by-product of the controllers are discussed in view of the finding that homeostatic control of p53, as indicated above, does in principle not require oscillatory homeostats.

The Escherichia coli alkA Gene Is Activated to Alleviate Mutagenesis by an Oxidized Deoxynucleoside.

The cellular methyl donor S-adenosylmethionine (SAM) and other endo/exogenous agents methylate DNA bases non-enzymatically into products interfering with replication and transcription. An important product is 3-methyladenine (m3A), which in Escherichia coli is removed by m3A-DNA glycosylase I (Tag) and II (AlkA). The tag gene is constitutively expressed, while alkA is induced by sub-lethal concentrations of methylating agents. We previously found that AlkA exhibits activity for the reactive oxygen-induced thymine (T) lesion 5-formyluracil (fU) in vitro. Here, we provide evidence for AlkA involvement in the repair of oxidized bases by showing that the adenine (A) ⋅ T → guanine (G) ⋅ cytosine (C) mutation rate increased 10-fold in E. coli wild-type and alkA - cells exposed to 0.1 mM 5-formyl-2'-deoxyuridine (fdU) compared to a wild-type specific reduction of the mutation rate at 0.2 mM fdU, which correlated with alkA gene induction. G⋅C → A⋅T alleviation occurred without alkA induction (at 0.1 mM fdU), correlating with a much higher AlkA efficiency for fU opposite to G than for that to A. The common keto form of fU is the AlkA substrate. Mispairing with G by ionized fU is favored by its exclusion from the AlkA active site.

Homeostatic controllers compensating for growth and perturbations.

Cells and organisms have developed homeostatic mechanisms which protect them against a changing environment. How growth and homeostasis interact is still not well understood, but of increasing interest to the molecular and synthetic biology community to recognize and design control circuits which can oppose the diluting effects of cell growth. In this paper we describe the performance of selected negative feedback controllers in response to different applied growth laws and time dependent outflow perturbations of a controlled variable. The approach taken here is based on deterministic mass action kinetics assuming that cell content is instantaneously mixed. All controllers behave ideal in the sense that they for step-wise perturbations in volume and a controlled compound A are able to drive A precisely back to the controllers' theoretical set-points. The applied growth kinetics reflect experimentally observed growth laws, which range from surface to volume ratio growth to linear and exponential growth. Our results show that the kinetic implementation of integral control and the structure of the negative feedback loop are two properties which affect controller performance. Best performance is observed for controllers based on derepression kinetics and controllers with an autocatalytic implementation of integral control. Both are able to defend exponential growth and perturbations, although the autocatalytic controller shows an offset from its theoretical set-point. Controllers with activating signaling using zero-order or bimolecular (antithetic) kinetics for integral control behave very similar but less well. Their performance can be improved by implementing negative feedback structures having repression/derepression steps or by increasing controller aggressiveness. Our results provide a guide what type of feedback structures and integral control kinetics are suitable to oppose the dilution effects by different growth laws and time dependent perturbations on a deterministic level.

Sensitivity analysis of a pathway with respect to fast and small temperature change.

Temperature affects all enzymes simultaneously in a metabolic system. The enzyme concentration in a biochemical system can be considered as invariant under fast and small temperature change. Therefore, the total sensitivity of a steady state flux through a pathway with respect to the temperature can be expressed as: the apparent activation energy of a steady state pathway flux equals the sum of weighted activation energies of the individual reactions contributing to the flux, where the weighting factors are the flux control coefficients of these reactions in the context of the network. Correspondingly, since the elasticity of any enzyme with respect to temperature is always nonzero, only the reactions with a nonzero flux control coefficient contribute accordingly to the temperature sensitivity of the pathway.

Considerably Lower Levels of Hypocretin-1 in Cerebrospinal Fluid Is Revealed by a Novel Mass Spectrometry Method Compared with Standard Radioimmunoassay.

Low levels of hypocretin-1 (Hcrt1) in cerebrospinal fluid (CSF) are associated with narcolepsy type 1 (NT1). Although immunoassays are prone to antibody batch differences, detection methods and variation between laboratories, the standard method for Hcrt1 measurement is a radioimmunoassay (RIA). Liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) is an antibody- and radioactive free alternative for precise measurement of Hcrt1. We developed an LC-MS/MS method for measurement of Hcrt1 in CSF with automated sample preparation by solid-phase extraction (SPE). The LC-MS/MS method was compared with the RIA method for Hcrt1 detection. CSF samples from healthy subjects and NT1 patients was obtained by lumbar puncture. NT1 patients were diagnosed according to the minimal criteria by the International Classification of Sleep Disorders (ICSD). The LC-MS/MS method showed linearity across the range of calibrators and had a limit of detection (LOD) of 2.5 pg/mL and a limit of quantitation (LOQ) of 3.6 pg/mL. Comparison of the LC-MS/MS method with RIA revealed a 19 times lower level in healthy controls and 22 times lower level in NT1 patients with the LC-MS/MS method than with RIA. Bland-Altman analysis demonstrated agreement between the methods. These results question what is detected by RIA and strongly suggest that the physiological concentrations of the peptide are much lower than previously believed. LC-MS/MS proves to be an alternative for detection of Hcrt1 for diagnosis of narcolepsy.

Fatigue in primary Sjögren's syndrome: A proteomic pilot study of cerebrospinal fluid.

OBJECTIVES: Fatigue is a frequent and often disabling phenomenon that occurs in patients with chronic inflammatory and immunological diseases, and the underlying biological mechanisms are largely unknown. Because fatigue is generated in the brain, we aimed to investigate cerebrospinal fluid and search for molecules that participate in the pathophysiology of fatigue processes. METHODS: A label-free shotgun proteomics approach was applied to analyze the cerebrospinal fluid proteome of 20 patients with primary Sjögren's syndrome. Fatigue was measured with the fatigue visual analog scale. RESULTS: A total of 828 proteins were identified and the 15 top discriminatory proteins between patients with high and low fatigue were selected. Among these were apolipoprotein A4, hemopexin, pigment epithelium-derived factor, secretogranin-1, secretogranin-3, selenium-binding protein 1, and complement factor B. CONCLUSION: Most of the discriminatory proteins have important roles in regulation of innate immunity, cellular stress defense, and/or functions in the central nervous system. These proteins and their interacting protein networks may therefore have central roles in the generation and regulation of fatigue, and the findings contribute with evidence to the concept of fatigue as a biological phenomenon signaled through specific molecular pathways.

Interleukin-1-related activity and hypocretin-1 in cerebrospinal fluid contribute to fatigue in primary Sjögren's syndrome.

BACKGROUND: Fatigue is a common and sometimes debilitating phenomenon in primary Sjögren's syndrome (pSS) and other chronic inflammatory diseases. We aimed to investigate how IL-1 ß-related molecules and the neuropeptide hypocretin-1 (Hcrt1), a regulator of wakefulness, influence fatigue. METHODS: Hcrt1 was measured by radioimmunoassay (RIA) in cerebrospinal fluid (CSF) from 49 patients with pSS. Interleukin-1 receptor antagonist (IL-1Ra), IL-1 receptor type 2 (IL-1RII), IL-6, and S100B protein were measured by enzyme-linked immunosorbent assay (ELISA). Fatigue was rated by the fatigue visual analog scale (fVAS). RESULTS: Simple univariate regression and multiple regression analyses with fatigue as a dependent variable revealed that depression, pain, and the biochemical variable IL-1Ra had a significant association with fatigue. In PCA, two significant components were revealed. The first component (PC1) was dominated by variables related to IL-1ß activity (IL-1Ra, IL-1RII, and S100B). PC2 showed a negative association between IL-6 and Hcrt1. fVAS was then introduced as an additional variable. This new model demonstrated that fatigue had a higher association with the IL-1ß-related PC1 than to PC2. Additionally, a third component (PC3) became significant between low Hcrt1 concentrations and fVAS scores. CONCLUSIONS: The main findings of this study indicate a functional network in which several IL-1ß-related molecules in CSF influence fatigue in addition to the classical clinical factors of depression and pain. The neuropeptide Hcrt1 seems to participate in fatigue generation, but likely not through the IL-1 pathway.

Excision of uracil from DNA by hSMUG1 includes strand incision and processing.

Uracil arises in DNA by hydrolytic deamination of cytosine (C) and by erroneous incorporation of deoxyuridine monophosphate opposite adenine, where the former event is devastating by generation of C → thymine transitions. The base excision repair (BER) pathway replaces uracil by the correct base. In human cells two uracil-DNA glycosylases (UDGs) initiate BER by excising uracil from DNA; one is hSMUG1 (human single-strand-selective mono-functional UDG). We report that repair initiation by hSMUG1 involves strand incision at the uracil site resulting in a 3'-α,ß-unsaturated aldehyde designated uracil-DNA incision product (UIP), and a 5'-phosphate. UIP is removed from the 3'-end by human apurinic/apyrimidinic (AP) endonuclease 1 preparing for single-nucleotide insertion. hSMUG1 also incises DNA or processes UIP to a 3'-phosphate designated uracil-DNA processing product (UPP). UIP and UPP were indirectly identified and quantified by polyacrylamide gel electrophoresis and chemically characterised by matrix-assisted laser desorption/ionisation time-of-flight mass-spectrometric analysis of DNA from enzyme reactions using 18O- or 16O-water. The formation of UIP accords with an elimination (E2) reaction where deprotonation of C2' occurs via the formation of a C1' enolate intermediate. A three-phase kinetic model explains rapid uracil excision in phase 1, slow unspecific enzyme adsorption/desorption to DNA in phase 2 and enzyme-dependent AP site incision in phase 3.

Variable setpoint as a relaxing component in physiological control.

Setpoints in physiology have been a puzzle for decades, and especially the notion of fixed or variable setpoints have received much attention. In this paper, we show how previously presented homeostatic controller motifs, extended with saturable signaling kinetics, can be described as variable setpoint controllers. The benefit of a variable setpoint controller is that an observed change in the concentration of the regulated biochemical species (the controlled variable) is fully characterized, and is not considered a deviation from a fixed setpoint. The variation in this biochemical species originate from variation in the disturbances (the perturbation), and thereby in the biochemical species representing the controller (the manipulated variable). Thus, we define an operational space which is spanned out by the combined high and low levels of the variations in (1) the controlled variable, (2) the manipulated variable, and (3) the perturbation. From this operational space, we investigate whether and how it imposes constraints on the different motif parameters, in order for the motif to represent a mathematical model of the regulatory system. Further analysis of the controller's ability to compensate for disturbances reveals that a variable setpoint represents a relaxing component for the controller, in that the necessary control action is reduced compared to that of a fixed setpoint controller. Such a relaxing component might serve as an important property from an evolutionary point of view. Finally, we illustrate the principles using the renal sodium and aldosterone regulatory system, where we model the variation in plasma sodium as a function of salt intake. We show that the experimentally observed variations in plasma sodium can be interpreted as a variable setpoint regulatory system.

Systems biology of the modified branched Entner-Doudoroff pathway in Sulfolobus solfataricus.

Sulfolobus solfataricus is a thermoacidophilic Archaeon that thrives in terrestrial hot springs (solfatares) with optimal growth at 80°C and pH 2-4. It catabolizes specific carbon sources, such as D-glucose, to pyruvate via the modified Entner-Doudoroff (ED) pathway. This pathway has two parallel branches, the semi-phosphorylative and the non-phosphorylative. However, the strategy of S.solfataricus to endure in such an extreme environment in terms of robustness and adaptation is not yet completely understood. Here, we present the first dynamic mathematical model of the ED pathway parameterized with quantitative experimental data. These data consist of enzyme activities of the branched pathway at 70°C and 80°C and of metabolomics data at the same temperatures for the wild type and for a metabolic engineered knockout of the semi-phosphorylative branch. We use the validated model to address two questions: 1. Is this system more robust to perturbations at its optimal growth temperature? 2. Is the ED robust to deletion and perturbations? We employed a systems biology approach to answer these questions and to gain further knowledge on the emergent properties of this biological system. Specifically, we applied deterministic and stochastic approaches to study the sensitivity and robustness of the system, respectively. The mathematical model we present here, shows that: 1. Steady state metabolite concentrations of the ED pathway are consistently more robust to stochastic internal perturbations at 80°C than at 70°C; 2. These metabolite concentrations are highly robust when faced with the knockout of either branch. Connected with this observation, these two branches show different properties at the level of metabolite production and flux control. These new results reveal how enzyme kinetics and metabolomics synergizes with mathematical modelling to unveil new systemic properties of the ED pathway in S.solfataricus in terms of its adaptation and robustness.

PLATINUM SENSITIVE 2 LIKE impacts growth, root morphology, seed set, and stress responses.

Eukaryotic protein phosphatase 4 (PP4) is a PP2A-type protein phosphatase that is part of a conserved complex with regulatory factors PSY2 and PP4R2. Various lines of Arabidopsis thaliana with mutated PP4 subunit genes were constructed to study the so far completely unknown functions of PP4 in plants. Mutants with knocked out putative functional homolog of the PSY2 LIKE (PSY2L) gene were dwarf and bushy, while plants with knocked out PP4R2 LIKE (PP4R2L) looked very similar to WT. The psy2l seedlings had short roots with disorganized morphology and impaired meristem. Seedling growth was sensitive to the genotoxin cisplatin. Global transcript analysis (RNA-seq) of seedlings and rosette leaves revealed several groups of genes, shared between both types of tissues, strongly influenced by knocked out PSY2L. Receptor kinases, CRINKLY3 and WAG1, important for growth and development, were down-regulated 3-7 times. EUKARYOTIC ELONGATION FACTOR5A1 was down-regulated 4-6 fold. Analysis of hormone sensitive genes indicated that abscisic acid levels were high, while auxin, cytokinin and gibberellic acid levels were low in psy2l. Expression of specific transcription factors involved in regulation of anthocyanin synthesis were strongly elevated, e.g. the master regulator PAP1, and intriguingly TT8, which is otherwise mainly expressed in seeds. The psy2l mutants accumulated anthocyanins under conditions where WT did not, pointing to PSY2L as a possible upstream negative regulator of PAP1 and TT8. Expression of the sugar-phosphate transporter GPT2, important for cellular sugar and phosphate homeostasis, was enhanced 7-8 times. Several DNA damage response genes, including the cell cycle inhibitor gene WEE1, were up-regulated in psy2l. The activation of DNA repair signaling genes, in combination with phenotypic traits showing aberrant root meristem and sensitivity to the genotoxic cisplatin, substantiate the involvement of Arabidopsis PSY2L in maintenance of genome integrity.