Modeling the electron transport chain of purple non-sulfur bacteria

Purple non-sulfur bacteria (Rhodospirillaceae) have been extensively employed for studying principles of photosynthetic and respiratory electron transport phosphorylation and for investigating the regulation of gene expression in response to redox signals. Here, we use mathematical modeling to evaluate the steady-state behavior of the electron transport chain (ETC) in these bacteria under different environmental conditions. Elementary-modes analysis of a stoichiometric ETC model reveals nine operational modes. Most of them represent well-known functional states, however, two modes constitute reverse electron flow under respiratory conditions, which has been barely considered so far. We further present and analyze a kinetic model of the ETC in which rate laws of electron transfer steps are based on redox potential differences. Our model reproduces well-known phenomena of respiratory and photosynthetic operation of the ETC and also provides non-intuitive predictions. As one key result, model simulations demonstrate a stronger reduction of ubiquinone when switching from high-light to low-light conditions. This result is parameter insensitive and supports the hypothesis that the redox state of ubiquinone is a suitable signal for controlling photosynthetic gene expression

PIKES Analysis Reveals Response to Degraders and Key Regulatory Mechanisms of the CRL4 Network

Co-opting Cullin4 RING ubiquitin ligases (CRL4s) to inducibly degrade pathogenic proteins is emerging as a promising therapeutic strategy. Despite intense efforts to rationally design degrader molecules that co-opt CRL4s, much about the organization and regulation of these ligases remains elusive. Here, we establish protein interaction kinetics and estimation of stoichiometries (PIKES) analysis, a systematic proteomic profiling platform that integrates cellular engineering, affinity purification, chemical stabilization, and quantitative mass spectrometry to investigate the dynamics of interchangeable multiprotein complexes. Using PIKES, we show that ligase assemblies of Cullin4 with individual substrate receptors differ in abundance by up to 200-fold and that Cand1/2 act as substrate receptor exchange factors. Furthermore, degrader molecules can induce the assembly of their cognate CRL4, and higher expression of the associated substrate receptor enhances degrader potency. Beyond the CRL4 network, we show how PIKES can reveal systems level biochemistry for cellular protein networks important to drug development

Diffusive coupling can discriminate between similar reaction mechanisms in an allosteric enzyme system

<p>Abstract</p> <p>Background</p> <p>A central question for the understanding of biological reaction networks is how a particular dynamic behavior, such as bistability or oscillations, is realized at the molecular level. So far this question has been mainly addressed in well-mixed reaction systems which are conveniently described by ordinary differential equations. However, much less is known about how molecular details of a reaction mechanism can affect the dynamics in diffusively coupled systems because the resulting partial differential equations are much more difficult to analyze.</p> <p>Results</p> <p>Motivated by recent experiments we compare two closely related mechanisms for the product activation of allosteric enzymes with respect to their ability to induce different types of reaction-diffusion waves and stationary Turing patterns. The analysis is facilitated by mapping each model to an associated complex Ginzburg-Landau equation. We show that a sequential activation mechanism, as implemented in the model of Monod, Wyman and Changeux (MWC), can generate inward rotating spiral waves which were recently observed as glycolytic activity waves in yeast extracts. In contrast, in the limiting case of a simple Hill activation, the formation of inward propagating waves is suppressed by a Turing instability. The occurrence of this unusual wave dynamics is not related to the magnitude of the enzyme cooperativity (as it is true for the occurrence of oscillations), but to the sensitivity with respect to changes of the activator concentration. Also, the MWC mechanism generates wave patterns that are more stable against long wave length perturbations.</p> <p>Conclusions</p> <p>This analysis demonstrates that amplitude equations, which describe the spatio-temporal dynamics near an instability, represent a valuable tool to investigate the molecular effects of reaction mechanisms on pattern formation in spatially extended systems. Using this approach we have shown that the occurrence of inward rotating spiral waves in glycolysis can be explained in terms of an MWC, but not with a Hill mechanism for the activation of the allosteric enzyme phosphofructokinase. Our results also highlight the importance of enzyme oligomerization for a possible experimental generation of Turing patterns in biological systems.</p

Reciprocal Regulation as a Source of Ultrasensitivity in Two-Component Systems with a Bifunctional Sensor Kinase

<div><p>Two-component signal transduction systems, where the phosphorylation state of a regulator protein is modulated by a sensor kinase, are common in bacteria and other microbes. In many of these systems, the sensor kinase is bifunctional catalyzing both, the phosphorylation and the dephosphorylation of the regulator protein in response to input signals. Previous studies have shown that systems with a bifunctional enzyme can adjust the phosphorylation level of the regulator protein independently of the total protein concentrations – a property known as concentration robustness. Here, I argue that two-component systems with a bifunctional enzyme may also exhibit ultrasensitivity if the input signal reciprocally affects multiple activities of the sensor kinase. To this end, I consider the case where an allosteric effector inhibits autophosphorylation and, concomitantly, activates the enzyme's phosphatase activity, as observed experimentally in the PhoQ/PhoP and NRII/NRI systems. A theoretical analysis reveals two operating regimes under steady state conditions depending on the effector affinity: If the affinity is low the system produces a graded response with respect to input signals and exhibits stimulus-dependent concentration robustness – consistent with previous experiments. In contrast, a high-affinity effector may generate ultrasensitivity by a similar mechanism as phosphorylation-dephosphorylation cycles with distinct converter enzymes. The occurrence of ultrasensitivity requires saturation of the sensor kinase's phosphatase activity, but is restricted to low effector concentrations, which suggests that this mode of operation might be employed for the detection and amplification of low abundant input signals. Interestingly, the same mechanism also applies to covalent modification cycles with a bifunctional converter enzyme, which suggests that reciprocal regulation, as a mechanism to generate ultrasensitivity, is not restricted to two-component systems, but may apply more generally to bifunctional enzyme systems.</p></div

Autophosphatase activity of NRI may compromise ultrasensitivity in the NRII/NRI/PII system.

<p>(A) Comparison of experimental data (filled boxes, data taken from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi-1003614-g004" target="_blank">Fig. 4A</a> of Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Jiang3" target="_blank">[27]</a>) with the steady state response curve calculated from the extended Batchelor-Goulian model in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e180" target="_blank">Eqs. (22)</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e187" target="_blank">(29)</a> with an extra term ‘’ added to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e180" target="_blank">Eq. (22)</a>, which accounts for autodephosphorylation of NRI-P. The blue dashed line represents the best fit obtained for , , and . The other parameters were kept fixed: , , , so that and corresponding to a half-life of 5 minutes <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Jiang3" target="_blank">[27]</a>. (B) As the autodephosphorylation rate constant of NRI-P is lowered (bottom to top: , , , ) the response curve becomes more and more ultrasensitive (solid lines). Note that ultrasensitivity is restricted to the region as predicted by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e293" target="_blank">Eq. (38)</a>. The dashed (blue) lines in (A) and (B) are identical.</p

Ultrasensitivity in covalent modification cycles with a bifunctional converter enzyme.

<p>(A) Reaction scheme: A substrate molecule () undergoes reversible phosphorylation by a bifunctional converter enzyme which can exist in two activity states. Binding of the allosteric effector inhibits the kinase activity () and, concomitantly, activates the phosphatase activity () of the enzyme. (B) As the value of the dissociation constant is lowered from to (from right to left) the steady state curve becomes ultrasensitive near the transition point , as defined in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e175" target="_blank">Eq. (21)</a>. The solid lines were computed from the full model using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e096" target="_blank">Eqs. (4)</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e105" target="_blank">(7)</a>. Dashed lines were computed from the reduced models using <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e142" target="_blank">Eq. (14)</a> (right curve) and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e159" target="_blank">Eq. (18)</a> (left curve). Parameters: , , so that , and (for ) or (for ).</p

Experimental observations of concentration robustness in TCSs.

<p>Comparison between predictions of the Batchelor-Goulian model and measurements in the PhoR/PhoB <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Gao1" target="_blank">[26]</a> and NRII/NRI systems <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Jiang3" target="_blank">[27]</a>. (A) Symbols denote measurements of PhoB-P as a function of total PhoB amounts in the wild-type system (open squares) and in a mutant strain (filled circles) (data were taken from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi-1003614-g004" target="_blank">Fig. 4C</a> in Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Gao1" target="_blank">[26]</a>). Solid lines were calculated from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e199" target="_blank">Eq. (31)</a> with pmol, pmol and pmol, pmol. Note that (dotted lines) determines both, the threshold amount of total PhoB beyond which PhoB-P becomes constant as well as the value of that constant, as expected from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e027" target="_blank">Eq. (2)</a>. (B) Symbols denote <i>in vitro</i> measurements of NRI-P as a function of total NRI (reproduced from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi-1003614-g004" target="_blank">Fig. 4A</a> in Ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Jiang3" target="_blank">[27]</a>). Solid line represents the best fit of the data to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614.e028" target="_blank">Eq. (3)</a> with and , which indicates that the NRII/NRI system operates in the regime .</p

Reciprocal regulation in two-component systems.

<p>(A) Schematic representation of reciprocal regulation in the PhoQ/PhoP <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Chamnongpol1" target="_blank">[20]</a> and NRII/NRI systems <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Jiang2" target="_blank">[21]</a>. In both cases, an allosteric effector ( or PII) inhibits autophosphorylation of the sensor kinase and increases the enzyme's phosphatase activity. (B) Batchelor-Goulian model <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi.1003614-Batchelor1" target="_blank">[11]</a> based on the three activities of the sensor kinase (cf. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003614#pcbi-1003614-g001" target="_blank">Fig. 1</a>): (1) Autophosphorylation of the sensor kinase (HK), (2) phosphotransfer to the response regulator (RR) and (3) dephosphorylation of the RR. Cofactors such as ATP are assumed to be constant. (C) Extension of the Batchelor-Goulian model to include reciprocal regulation of the HK's activities as schematized in (A). Binding of the allosteric effector (4) inhibits autophosphorylation (1) and activates the phosphatase activity (3) of the sensor kinase. For simplicity, the free form of the enzyme () is assumed to have no phosphatase activity whereas the effector-bound form () is assumed to have no autokinase activity.</p