In silico evolved lac operons exhibit bistability for artificial inducers, but not for lactose

Bistability in the lac operon of Escherichia coli has been widely studied, both experimentally and theoretically. Experimentally, bistability has been observed when E. coli is induced by an artificial, nonmetabolizable, inducer. However, if the lac operon is induced with lactose, the natural inducer, bistability has not been demonstrated. We derive an analytical expression that can predict the occurrence of bistability both for artificial inducers and lactose. We find very different conditions for bistability in the two cases. Indeed, for artificial inducers bistability is predicted, but for lactose the condition for bistability is much more difficult to satisfy. Moreover, we demonstrate that in silico evolution of the lac operon generates an operon that avoids bistability with respect to lactose, but does exhibit bistability with respect to artificial inducers. The activity of this evolved operon strikingly resembles the experimentally observed activity of the operon. Thus our computational experiments suggest that the wild-type lac operon, which regulates lactose metabolism, is not a bistable switch. Nevertheless, for engineering purposes, this operon can be used as a bistable switch with artificial inducers.     

The Delicate Bistability of CaMKII

Calcium/calmodulin-dependent protein kinase II (CaMKII) is a synaptic, autophosphorylating kinase that is essential for learning and memory. Previous models have suggested that CaMKII functions as a bistable switch that could be the molecular correlate of long-term memory, but experiments have failed to validate these predictions. These models involved significant approximations to overcome the combinatorial complexity inherent in a multisubunit, multistate system. Here, we develop a stochastic particle-based model of CaMKII activation and dynamics that overcomes combinatorial complexity without significant approximations. We report four major findings. First, the CaMKII model system is never bistable at resting calcium concentrations, which suggests that CaMKII activity does not function as the biochemical switch underlying long-term memory. Second, the steady-state activation curves are either laserlike or steplike. Both are characterized by a well-defined threshold for activation, which suggests that thresholding is a robust feature of this system. Third, transiently activated CaMKII can maintain its activity over the time course of many experiments, and such slow deactivation may account for the few reports of bistability in the literature. And fourth, under in vivo conditions, increases in phosphatase activity can increase CaMKII activity. This is a surprising and counterintuitive effect, as dephosphorylation is generally associated with CaMKII deactivation.     

The Delicate Bistability of CaMKII

Calcium/calmodulin-dependent protein kinase II (CaMKII) is a synaptic, autophosphorylating kinase that is essential for learning and memory. Previous models have suggested that CaMKII functions as a bistable switch that could be the molecular correlate of long-term memory, but experiments have failed to validate these predictions. These models involved significant approximations to overcome the combinatorial complexity inherent in a multisubunit, multistate system. Here, we develop a stochastic particle-based model of CaMKII activation and dynamics that overcomes combinatorial complexity without significant approximations. We report four major findings. First, the CaMKII model system is never bistable at resting calcium concentrations, which suggests that CaMKII activity does not function as the biochemical switch underlying long-term memory. Second, the steady-state activation curves are either laserlike or steplike. Both are characterized by a well-defined threshold for activation, which suggests that thresholding is a robust feature of this system. Third, transiently activated CaMKII can maintain its activity over the time course of many experiments, and such slow deactivation may account for the few reports of bistability in the literature. And fourth, under in vivo conditions, increases in phosphatase activity can increase CaMKII activity. This is a surprising and counterintuitive effect, as dephosphorylation is generally associated with CaMKII deactivation.     

Structural phylogenetic analysis of activation-induced deaminase function

In mammals, activation-induced deaminase (AID) initiates somatic hypermutation (SHM) and class switch recombination (CSR) of Ig genes. SHM and CSR activities require separate regions within AID. A chromosome region maintenance 1 (CRM1)-dependent nuclear export signal (NES) at the AID C terminus is necessary for CSR, and has been suggested to associate with CSR-specific cofactors. CSR appeared late in AID evolution, during the emergence of land vertebrates from bony fish, which only display SHM. Here, we show that AID from African clawed frog (Xenopus laevis), but not pufferfish (Takifugu rubripes), can induce CSR in AID-deficient mouse B cells, although both are catalytically active in bacteria and mammalian cell systems, albeit at decreased level. Like mammalian AID, Takifugu AID is actively exported from the cell nucleus by CRM1, and the Takifugu NES can substitute for the equivalent region in human AID, indicating that all the CSR-essential NES motif functions evolutionarily predated CSR activity. We also show that fusion of the Takifugu AID catalytic domain to the entire human noncatalytic domain restores activity in mammalian cells, suggesting that AID features mapping within the noncatalytic domain, but outside the NES, influence its function.     

Origin of bistability in the lac Operon

Multistability is an emergent dynamic property that has been invoked to explain multiple coexisting biological states. In this work, we investigate the origin of bistability in the lac operon. To do this, we develop a mathematical model for the regulatory pathway in this system and compare the model predictions with other experimental results in which a nonmetabolizable inducer was employed. We investigate the effect of lactose metabolism using this model, and show that it greatly modifies the bistable region in the external lactose (Le) versus external glucose (Ge) parameter space. The model also predicts that lactose metabolism can cause bistability to disappear for very low Ge. We have also carried out stochastic numerical simulations of the model for several values of Ge and Le. Our results indicate that bistability can help guarantee that Escherichia coli consumes glucose and lactose in the most efficient possible way. Namely, the lac operon is induced only when there is almost no glucose in the growing medium, but if Le is high, the operon induction level increases abruptly when the levels of glucose in the environment decrease to very low values. We demonstrate that this behavior could not be obtained without bistability if the stability of the induced and uninduced states is to be preserved. Finally, we point out that the present methods and results may be useful to study the emergence of multistability in biological systems other than the lac operon.     

Implications of Rewiring Bacterial Quorum Sensing

Bacteria employ quorum sensing, a form of cell-cell communication, to sense changes in population density and regulate gene expression accordingly. This work investigated the rewiring of one quorum-sensing module, the lux circuit from the marine bacterium Vibrio fischeri. Steady-state experiments demonstrate that rewiring the network architecture of this module can yield graded, threshold, and bistable gene expression as predicted by a mathematical model. The experiments also show that the native lux operon is most consistent with a threshold, as opposed to a bistable, response. Each of the rewired networks yielded functional population sensors at biologically relevant conditions, suggesting that this operon is particularly robust. These findings (i) permit prediction of the behaviors of quorum-sensing operons in bacterial pathogens and (ii) facilitate forward engineering of synthetic gene circuits.     

Characterizing multistationarity regimes in biochemical reaction networks

Switch like responses appear as common strategies in the regulation of cellular systems. Here we present a method to characterize bistable regimes in biochemical reaction networks that can be of use to both direct and reverse engineering of biological switches. In the design of a synthetic biological switch, it is important to study the capability for bistability of the underlying biochemical network structure. Chemical Reaction Network Theory (CRNT) may help at this level to decide whether a given network has the capacity for multiple positive equilibria, based on their structural properties. However, in order to build a working switch, we also need to ensure that the bistability property is robust, by studying the conditions leading to the existence of two different steady states. In the reverse engineering of biological switches, knowledge collected about the bistable regimes of the underlying potential model structures can contribute at the model identification stage to a drastic reduction of the feasible region in the parameter space of search. In this work, we make use and extend previous results of the CRNT, aiming not only to discriminate whether a biochemical reaction network can exhibit multiple steady states, but also to determine the regions within the whole space of parameters capable of producing multistationarity. To that purpose we present and justify a condition on the parameters of biochemical networks for the appearance of multistationarity, and propose an efficient and reliable computational method to check its satisfaction through the parameter space.     

A Novel marRAB Operon Contributes to the Rifampicin Resistance in Mycobacterium smegmatis

The multiple-antibiotic resistance regulator (MarR) plays an important role in modulating bacterial antibiotic resistance. However, the regulatory model of the marRAB operon in mycobacteria remains to be characterized. Here we report that a MarR, encoded by Ms6508, and its marRAB operon specifically contribute to rifampicin (RIF) resistance in Mycobacterium smegmatis. We show that the MarR recognizes a conserved 21-bp palindromic motif and negatively regulates the expression of two ABC transporters in the operon, encoded by Ms6509–6510. Unlike other known drug efflux pumps, overexpression of these two ABC transporters unexpectedly increased RIF sensitivity and deletion of these two genes increased mycobacterial resistance to the antibiotic. No change can be detected for the sensitivity of recombinant mycobacterial strains to three other anti-TB drugs. Furthermore, HPLC experiments suggested that Ms6509–Ms6510 could pump RIF into the mycobacterial cells. These findings indicated that the mycobacterial MarR functions as a repressor and constitutively inhibits the expression of the marRAB operon, which specifically contributes to RIF resistance in M. smegmatis. Therefore, our data suggest a new regulatory mechanism of RIF resistance and also provide the new insight into the regulatory model of a marRAB operon in mycobacteria.     

A simple electrostatic switch important in the activation of type I protein kinase A by cyclic AMP

Cyclic AMP activates protein kinase A by binding to an inhibitory regulatory (R) subunit and releasing inhibition of the catalytic (C) subunit. Even though crystal structures of regulatory and catalytic subunits have been solved, the precise molecular mechanism by which cyclic AMP activates the kinase remains unknown. The dynamic properties of the cAMP binding domain in the absence of cAMP or C-subunit are also unknown. Here we report molecular-dynamics simulations and mutational studies of the RIalpha R-subunit that identify the C-helix as a highly dynamic switch which relays cAMP binding to the helical C-subunit binding regions. Furthermore, we identify an important salt bridge which links cAMP binding directly to the C-helix that is necessary for normal activation. Additional mutations show that a hydrophobic "hinge" region is not as critical for the cross-talk in PKA as it is in the homologous EPAC protein, illustrating how cAMP can control diverse functions using the evolutionarily conserved cAMP-binding domains.     

Mitotic exit in two dimensions

Metaphase of mitosis is brought about in all eukaryotes by activation of cylin-dependent kinase (Cdk1), whereas exit from mitosis requires down-regulation of Cdk1 activity and dephosphorylation of its target proteins. In budding yeast, the completion of mitotic exit requires the release and activation of the Cdc14 protein-phosphatase, which is kept inactive in the nucleolus during most of the cell cycle. Activation of Cdc14 is controlled by two regulatory networks called FEAR (Cdc fourteen early anaphase release) and MEN (mitotic exit network). We have shown recently that the anaphase promoting protease (separase) is essential for Cdc14 activation, thereby it makes mitotic exit dependent on execution of anaphase. Based on this finding, we have proposed a new model for mitotic exit in budding yeast. Here we explain the essence of the model by phaseplane analysis, which reveals two underlying bistable switches in the regulatory network. One bistable switch is caused by mutual activation (positive feedback) between Cdc14 activating MEN and Cdc14 itself. The mitosis-inducing Cdk1 activity inhibits the activation of this positive feedback loop and thereby controlling this switch. The other irreversible switch is generated by a double-negative feedback (mutual antagonism) between mitosis inducing Cdk1 activity and its degradation machinery (APC(Cdh1)). The Cdc14 phosphatase helps turning this switch in favor of APC(Cdh1) side. Both of these bistable switches have characteristic thresholds, the first one for Cdk1 activity, while the second for Cdc14 activity. We show that the physiological behaviors of certain cell cycle mutants are suggestive for those Cdk1 and Cdc14 thresholds. The two bistable switches turn on in a well-defined order. In this paper, we explain how the activation of Cdc20 (which causes the activation of separase and a decrease of Cdk1 kinase activity) provides an initial trigger for the activation of the MEN-Cdc14 positive feedback loops, which in turn, flips the second irreversible Cdk-APC(Cdh1) switch on the APC(Cdh1) side).     

Switches and latches: a biochemical tug-of-war between the kinases and phosphatases that control mitosis

Activation of the cyclin-dependent kinase (Cdk1) cyclin B (CycB) complex (Cdk1:CycB) in mitosis brings about a remarkable extent of protein phosphorylation. Cdk1:CycB activation is switch-like, controlled by two auto-amplification loops--Cdk1:CycB activates its activating phosphatase, Cdc25, and inhibits its inhibiting kinase, Wee1. Recent experimental evidence suggests that parallel to Cdk1:CycB activation during mitosis, there is inhibition of its counteracting phosphatase activity. We argue that the downregulation of the phosphatase is not just a simple latch that suppresses futile cycles of phosphorylation/dephosphorylation during mitosis. Instead, we propose that phosphatase regulation creates coherent feed-forward loops and adds extra amplification loops to the Cdk1:CycB regulatory network, thus forming an integral part of the mitotic switch. These network motifs further strengthen the bistable characteristic of the mitotic switch, which is based on the antagonistic interaction of two groups of proteins: M-phase promoting factors (Cdk1:CycB, Cdc25, Greatwall and Endosulfine/Arpp19) and interphase promoting factors (Wee1, PP2A-B55 and a Greatwall counteracting phosphatase, probably PP1). The bistable character of the switch implies the existence of a CycB threshold for entry into mitosis. The end of G2 phase is determined by the point where CycB level crosses the CycB threshold for Cdk1 activation.