BACKGROUND
the archaeon halobacterium salinarum swims by rotation of a semi-rigid right-handed flagellar bundle  <cit> .
each flagellar filament of the bundle extends the axis of a rotary motor to passively transduce the mechanical energy generated by the motor to the medium.
motors are anchored in the cell membrane and driven by atp  <cit> .
cells swim back and forth by switching the sense of flagellar rotation from clockwise to counterclockwise and vice versa  <cit> .
in adapted or unstimulated cells, switching occurs spontaneously.
active swimming and motor switching is superimposed with passive brownian motion of cell body and flagellar bundle  <cit> .
by the resulting random swimming paths, the cells explore their environment until they encounter a stimulus.
sensory stimulation of the photo- or chemoreceptors transiently modulates the probability of motor switching, resulting in a movement of the cell towards more favorable regions in the environment  <cit> .
rather than sensing absolute stimulus strengths, cells respond to relative changes by adapting to any stimulus of constant intensity  <cit> .
several lines of evidence suggest that in bacteria as well as in archaea this adaptation is at least partially caused by reversible methylation of methyl-accepting taxis proteins  <cit> .
proteins of this family, also called transducers, may act as sensory receptors for a specific stimulus, or they may bind to a specific, but different receptor protein to transduce the activation state of this respective receptor and relay it to the autophosphorylating histidine kinase chea  <cit> .
chea phosphorylates the chey protein, which is required for flagellar motor switching  <cit> , and the phosphorylation rate is thought to be stimulus-dependent.
the genome of h. salinarum encodes  <dig> orthologous methyl-accepting taxis proteins   <cit> .
while sensing and transmembrane regions of these orthologs are quite diverse, the cytoplasmic domains share a high degree of similarity.
the diversity allows monitoring different types of cellular and environmental parameters: light, oxygen, proton motive force, amino acids, temperature, and presumably others.
the similarity of the cytoplasmic domains of the transducers guarantees sensory integration by chea of all of these stimuli  <cit> .
the transducers physically interact with chea and the scaffolding proteins chew <dig> and chew <dig>  <cit>  to form r-twa complexes , and the transducers localize in clusters at the cell poles  <cit>  where the photosensory sensitivity is restricted to  <cit> .
with the help of two sensory rhodopsins, sri and srii, h. salinarum senses orange, uv and blue light .
the sensory rhodopsins directly act as photoreceptors through physical association with their cognate methyl-accepting proteins   <cit> .
the transducers form stable complexes with the sensory rhodopsins  <cit>  and the cytoplasmic domain of the transducer is essential for the functional interaction of the two molecules  <cit> .
after photoexcitation, which causes photoisomerization of the covalently bound retinal chromophor , a sensory rhodopsin molecule proceeds through a sequence of metastable intermediates and finally returns to the initial state through re-isomerization of the chromophor  <cit> .
this so-called photocycle is thermodynamically driven by part of the energy of the absorbed photon.
the conformational changes of the sensory rhodopsin molecule caused by photocycling are transduced to the complexed htr molecule and regulate chea activity  <cit> .
the enzymatic signaling mechanism does not involve changes in the membrane potential  <cit> .
differential regulation of motor switching is thought to be caused by differential regulation of the chea kinase activity.
orange and uv light are sensed by sri, suppressing or inducing motor switching respectively, and blue light is sensed by srii, inducing motor switching  <cit> .
most halobacterial transducer proteins carry  <dig> to  <dig> potential methylation sites  per molecule  <cit> .
as in bacteria  <cit> , the methyl-transferase cher transfers the methyl-group of s-adenosyl-methionine to a glutamate residue of the transducer signaling domain  <cit> .
after incubating cells with 3h-labeled methionine, transducer methylation is detected by fluorography  <cit> .
demethylation is catalyzed by the  methyl-esterase domain of cheb  <cit> .
in e. coli, phosphorylation  of the n-terminal, chey-like domain of cheb increases methyl-esterase activity  <cit> .
in h. salinarum, the chey-like domain of cheb is also present  <cit> , but it is not known whether it becomes phosphorylated in a stimulus-dependent manner or whether cheb-phosphorylation modulates methyl-esterase activity in vitro or in vivo.
transducer demethylation results in formation of methanol  <cit>  which can be quantitatively measured in a time-resolved manner with a so-called flow-assay .
exposure of h. salinarum to any step-like stimulus that causes taxis results in a transient release of methanol, no matter whether the stimulus induces or represses motor switching  <cit> .
the methanol release patterns observed in h. salinarum are similar in bacillus subtilis where the phenomenon is explained by the fact that transducers contain methylation sites that were shown to be functionally different  <cit> : one site is demethylated upon stimulation with attractant, another site is demethylated upon stimulation with repellent.
selective methylation has been shown to be regulated by chey  <cit>  and to depend on transducer/receptor conformation  <cit> .
in b. subtilis, the transducer deamidase ched regulates activity of the chey-phosphatase chec  <cit>  and the interplay of chec and ched is thought to provide an additional and methylation-independent adaptation system  <cit> .
deletion mutant studies also suggest that chec and ched are possibly involved in a coordination of selective methylation in b. subtilis .
chec and ched orthologs are also found in h. salinarum  <cit> , but their function is not clear.
in b. subtilis and in h. salinarum the demethylation reaction as measured in a flow assay cause adaptation to stimuli of constant strength, no matter whether a respective stimulus is attractive or repulsive  <cit> .
presumably, differential methylation resets the signaling activity of the transducers to the pre-stimulus level, resulting in sensory adaptation of the cell, although this has not been directly shown.
two mechanisms of stimulus-controlled transducer methylation seem possible: the stimulus-activated transducer molecule may be methylated/demethylated to reset its signaling activity to the pre-stimulus level, or other, i. e. non-stimulated transducers may be methylated/demethylated through a coupling mechanism or feedback loop to attenuate their constant signaling output.
because specific photoactivation of a htri mutant in which the methylation sites have been deleted, nevertheless causes both, sensory adaptation and methanol release, coupling between stimulated and unstimulated transducers in terms of reversible methylation seems obvious  <cit> .
a model of the halobacterial motor switch cycle quantitatively reproduces measurements on spontaneous and light stimulus-induced motor switching  <cit> .
in this model, the input to the motor switch is generated by a simple model of the sensory excitation and adaptation processes.
coupling of both models is sufficient to reproduce quantitative data on motor switching, but the simple model of excitation and adaptation does not explain reversible transducer methylation.
here we provide a predictive computational model of sensory adaptation and excitation based on experimental findings on reversible transducer methylation in wildtype and mutant cells.
RESULTS
modeling concepts
by iterative cycles of mathematical modeling , parameter estimation, and comparison of simulation and experimental data, we obtained a quantitative model of excitation and adaptation in halobacterial phototaxis and chemotaxis.
this model consistently explains physiological excitation, adaptation, and experimental data on transient transducer demethylation rates.
the model is based on the following experimental observations:
• in wildtype cells, transducer demethylation always increases transiently when previously adapted cells are stimulated, no matter whether an attractant or repellent is set on or off  <cit> .
the duration of the transient transducer demethylation approximately correlates with the kinetics of behavioral adaptation of the cells  <cit> .
transient transducer demethylation and cheyp concentration negatively correlate in response to attractant stimulation and positively correlate in response to repellent stimulation .
• in a chey deletion mutant, transducer demethylation decreases transiently upon stimulation with attractants, and increases transiently upon stimulation with repellents  <cit>  .
• a mutant in which all putative methylation sites have been removed from the transducer htri still shows wildtype transducer demethylation patterns and sensory adaptation, even if stimulated through the methylation-deficient transducer htri, indicating that methyl-groups are turned-over on other transducers that did not receive or transduce the stimulus  <cit> .
the final mathematical model  was derived step by step , keeping the model structure  as simple as possible.
the model predicts that
• transducers are organized in clusters  of conformationally coupled molecules
• a cluster is composed of transducers with different input specificity in terms of photo-, chemo-, and other stimuli
• sensory adaptation occurs by attenuation of the signaling output through reversible methylation of two antagonistically active methylation sites of a transducer
• transducer activation by receptors and transducer methylation determines the signaling output of a cluster in a cooperative manner
• reversible transducer methylation is regulated through feedback via unphosphorylated chey
each feature of the model is essential in terms of reproducing transducer demethylation patterns  and experimental results described for the wildtype and the mutants.
the derived mathematical model is based on ordinary differential equations and algebraic equations for equilibrium conditions.
in dynamic simulations , the input was light and the outputs were methanol release and cheyp concentration.
methanol release from cells exposed to different photo- and chemo-stimuli was correlated quantitatively, and the change in cheyp concentration was correlated qualitatively to the motor response in terms of physiological adaptation.
adaptation of the cheyp-level in wildtype cells
the initial mathematical model  is based on the known molecular components of the phototaxis system and their known photo- and biochemical interactions .
two molecules of sensory rhodopsin i  form a stable complex  with two molecules of the sri-specific transducer .
the histidine kinase chea is bound via the scaffold protein chew to htri, which constitutes the r-twa complex .
the r-twa complex is assumed to occur in two conformations, active and inactive, which are in thermodynamic equilibrium.
photoexcitation of sri causes a transient shift in the equilibrium of the two conformations, and the behavioral response of the cell.
the behavioral response of the cell in terms of switching the flagellar motor depends on chea and chey.
chea autophosphorylates and transfers the phosphate group to chey.
transducers are methylated by the methyl-transferase cher and demethylated by the methyl-esterase cheb.
transducers contain one to three methylation sites and the number of sites varies according to the primary structure of the transducer.
receptor excitation causes a transient change in transducer demethylation.
the equilibrium of the r-twa complex depends on the free energy g of the active and inactive conformation/state.
for thermodynamic reasons, the state with lower free energy is preferred.
by direct molecular interaction sri shifts the equilibrium between the two activity states by changing the free energy of the r-twa complex depending on the photocycle-state and on the actual activity state of the r-twa complex.
the attractant photointermediate sri <dig>  for instance, favors the inactive state by lowering the free energy of the inactive state more compared to the active state .
according to the boltzmann distribution, the equilibrium probability a of being active can be determined  from the free energy of each possible combination of the photocycle-states of the two sri proteins with the activity states of the htri homodimer
with
as long as the photocycle-state of sri does not change, the probability of an r-twa complex of being active depends on the free energy  in the active and inactive state of the htri homodimer and is assumed to be determined by the structural properties of the protein  as well as by the methylation state of htri.
methylated transducers  are assumed to shift the equilibrium towards the active state , whereas unmethylated transducers  shift the equilibrium towards the inactive state :
the demethylation rate  is assumed to depend in a proportional manner  on the conformational state a of the r-twa complex
and the methylation rate  is assumed to be constant.
model  <dig> produces cheyp-peaks as expected and reversible transducer methylation allows adaptation of the cheyp level .
spudich and co-workers have shown that activation of htri by sri depends on the interface structure between sensory rhodopsin and its cognate transducer and mutations at or near this interface render wildtype strains into mutants that show an inverted response to orange-light  <cit> .
the phenotype of such mutants is generated in silico in our model by a variation of the free energy changes of the sri373-transducer complex such that  .
methanol release of wildtype cells and of a chey-deletion mutant
in simulations, model  <dig> failed  to reproduce the halobacterium-type methanol release pattern and instead, the e. coli-type pattern was obtained.
this result was insensitive to the numerical values of the rate constants for methylation and demethylation, insensitive to the values of free energy changes upon transducer methylation/demethylation, and insensitive to the rate constants of sri photocycling measured in wildtype cells.
an e. coli-type methanol release pattern was obtained no matter whether the transducers in the model carried one or more methylation sites.
moreover, the simulated methanol release pattern remained of the e. coli-type, no matter whether  transducer methylation favors active or inactive conformation, respectively.
in model  <dig>  we equipped each transducer with two antagonistically behaving methylation sites.
we assumed that both sites are accessible to cheb and cher in both conformational states of the r-twa complex and that methylation of the one site promotes the active state , whereas methylation of the other site promotes the inactive state .
adaptation then occurs by a shift in the equilibrium of methylation of the activating and the inactivating sites, respectively.
intuitively, one might expect that two antagonistically behaving methylation sites should always cause a net increase in methanol production no matter whether a repulsive or an attractive stimulus is given.
however, this is not necessarily the case, as discussed in the following.
let us assume that both methylation sites,  and , contribute additively to the free energy of the r-twa complex:
then, in the simplest case, the rates of demethylation of the activating  and the inactivating site  depend linearly on the active conformation a and inactive conformation i, respectively,
counterintuitively, numerical simulations show that this model always gives an e. coli-type methanol release pattern .
for certain parameter combinations, the methanol release pattern was e. coli-type with positive and negative peaks inverted, or no change in the net demethylation rate occurred at all.
for approximately linear dependence of the demethylation rates on changes in activity, Δa, the change of demethylation rates for the activating methylation site, Δdma ∝ Δa, compensates for the changes of demethylation rates of the inactivating methylation site, Δdmi ∝ Δi, and hence no net increase of demethylation occurs in response to attractant or repellent stimulation .
this holds for all tested numerical values of the rate constants for methylation and demethylation.
in a variation of model  <dig> , we assumed that chea phosphorylates cheb and that chebp has increased methyl-esterase activity :
however, this model was not capable of reproducing the halobacterium-type methanol release patterns  for all tested numerical values of the rate constants.
it seems that model  <dig> is too minimal to be able to reproduce the halobacterium-type demethylation kinetics.
perazzona and spudich showed that methanol release patterns depend on the presence of the chey protein  <cit> .
deletion of the chey gene converts the halobacterium-type methanol release pattern of the wildtype into an e. coli-type pattern, indicating that chey directly or indirectly interacts with the methylation/demethylation system of the transducers.
chey/cheyp might directly interact with the r-twa complexes, cheb, or cher through a feedback mechanism, e.g.
by alternating the rate of phosphorylation of cheb by chea.
we found  that halobacterium-type methanol release patterns are obtained in the simulation of model  <dig> if the demethylation rates depend on the transducer activity in a particular nonlinear, e. g. quadratic, manner:
this observation together with the fact that methanol release patterns in halobacterium depend on chey leads to a simple kinetic model for feedback of chey/cheyp on the transducer demethylation rate :
feedback of chey/cheyp on the transducer increases the demethylation rates and simultaneously introduces an approximately quadratic dependence of the demethylation rate on the transducer activity .
in the absence of the chey protein, the rates in the model become approximately linear , which explains both, the phenotypes of wildtype  and of the chey deletion mutant .
demethylation and methylation rates in equation  depend on chey and cheyp concentration, respectively.
hence the model suggests that chey regulates demethylation of both methylation sites depending on its phosphorylation state and depending on the activity of the r-twa complex .
however, an alternative kinetic mechanism yields a similar behavior of the system, namely if only the unphosphorylated form of the chey protein inhibits demethylation of the activating methylation site and simultaneously enhances demethylation of the inactivating methylation site , e. g.:
here, inhibition and activation is modeled by kinetics of the michaelis-menten-type.
yet another and similar regulatory mechanism results if only cheyp modulates the demethylation rates , e. g.:
feedback mechanisms  <dig> and  <dig>  i. e. regulation of demethylation through the unphosphorylated or the phosphorylated form of the chey protein, respond differently to the genetic deletion of chey.
if the modification rates were regulated by chey only , then chey deletion  would increase dma to a· and, contrarily, would decrease dmi to i. the resulting steady state equilibrium is then shifted towards lower activity of the r-twa complexes .
a drop of activity down to zero  would then cause an overall drop of demethylation.
upon saturating stimulation with repellents , an overall increase of demethylation would occur , as experimentally observed in the chey deletion mutant  <cit> .
dependency on cheyp alone  would produce the opposite methanol release pattern , in contradiction to the experimental observations.
thus, in the model, the unphosphorylated form of chey  is the active component in regulating transducer demethylation at the two antagonistically active sites.
the remaining possibility ) is that both chey and cheyp regulate demethylation of the two sites, however in a reciprocal manner.
the steady-state would then be barely shifted in a chey deletion mutant.
parameters can be found that reproduce the halobacterium-type methanol release patterns.
however, the resulting model turned out to be very sensitive to parameter variations when rate constants were fitted to experimental data.
in addition to not being robust with respect to parameter variations, the model is not minimal, i. e. would need more parameters and interactions to explain the data.
we therefore continue with the simplest model in which demethylation of the two sites is only regulated by the unphosphorylated form of the chey protein.
accordingly, feedback by the chey protein  was incorporated into model  <dig> to give model  <dig> fbm <dig> and the effect of different numerical values of the reaction rates was analyzed.
parameter combinations that produced halobacterium-type methanol release patterns were easily obtained , while positive and negative peaks of cheyp were obtained as expected.
the fact that cheb in h. salinarum has a chey-like domain  may lead to alternative kinetic models in which cheb/chebp-feedback is responsible for producing the halobacterium-type methanol release patterns.
if both cheb and chey compete for phosphate from chea, then the absence of the chey-protein could cause an increased phospho-transfer to cheb.
if, in addition, chebp has increased demethylation activity , then this would result in a higher  demethylation rate for repellent stimuli, and a lower  demethylation rate for attractant stimuli.
the methanol release in a chey deletion mutant would then be of the e. coli-type, as experimentally observed.
to analyze the possibility of a cheb/chebp-based mechanism, we assumed cheb and chebp-dependent demethylation rates  of the form
the additional parameters k <dig> ≥  <dig> and k <dig> ≥  <dig> were introduced to account for possible cooperative effects.
for an appropriate choice of the parameters k <dig> and k <dig>  cheb and chebp introduce a nonlinear dependence on activity/inactivity which may be approximative quadratic - similar as for chey/cheyp in equation  - and may then produce the halobacterium-type pattern observed in the wildtype.
we found parameters for models  with a cubic  dependence on cheb/chebp for which the wildtype methanol release pattern could be reproduced.
however, only model 3b fbm <dig> with a linear  dependence on activity/inactivity could predict the e. coli-type methanol release patterns of the chey deletion mutant.
we did not favor the possibility of a cheb/chebp-based feedback mechanism , because the wildtype/halobacterium-type methanol-release patterns are still observed in a b. subtilis mutant in which the chey-like domain of cheb is deleted  <cit> .
adaptation of cells with methylation-deficient htri
cells expressing htri with all putative methylation sites disabled by site-directed mutagenesis are able to respond and to adapt to light, and transiently release methanol as observed in the wildtype  <cit> .
since model  <dig> fbm <dig> failed to reproduce this experimental finding, it had to be extended to a model in which excitation of the sri-htri complex is communicated to a different transducer type with different substrate specificity, which in turn is reversibly demethylated.
presumptive mechanisms of functional coupling might be conformational coupling of different transducer types, or feedback by modulating the methyl-esterase and methyl-transferase activity at transducers other than the actually stimulated transducers.
extending model  <dig> fbm <dig> by an additional, non-stimulated and methylation-efficient transducer type  yields model  <dig>  looking at wildtype cells, now two different r-twa populations are coupled via chey that feeds back on both transducer types .
due to the conformationally independent but functionally coupled populations, the overall activity is given by the linear superposition/weighted mean of both activities
where ku and ks represent the contributions of unstimulated  and stimulated  transducers due to different expression levels.
in the wildtype case, parameters for simulating halobacterium-type methanol release with adaptation of the cheyp level were found .
however, when simulating the model with one methylation-deficient transducer population and one transducer population where reversible methylation is normal, we could not find any set of parameters that reproduced the experimentally observed wildtype halobacterium-type methanol release pattern and adaptation .
as the activity of the unstimulated transducers stays constant and as the mutated, stimulated transducers cannot be methylated, any change of the demethylation rates in the model can only occur through feedback by chey the concentration of which is changed by the stimulated transducers.
then the demethylation rates become linear
and cannot explain the halobacterium-type methanol release .
hence, in the framework of this model, feedback by chey alone cannot be the only mechanism that mediates cross-talk between stimulated and non-stimulated transducers.
phosphorylation of cheb through the stimulated transducers and an increased demethylation of the non-stimulated transducers by phosphorylated cheb could provide such a cross-talk mechanism.
however, we found no parameters in such a model  that predicted the halobacterium-type methanol release pattern of the non-methylatable htri mutant .
the missing additional mechanism could be conformational coupling among different transducer types/species within a  unit, and this is considered in model  <dig>
in model  <dig>  all r-twa complexes within a unit contribute to the overall activity in a nonlinear and cooperative manner via the phototaxis transducers and cognate photoreceptors, via the binding state of the chemotaxis transducers/receptors, and via the methylation state of all transducers within the unit.
by formulating the free energy changes of every possible state of the r-twa signaling unit, the probability of being active can be derived from the boltzmann distribution in a similar manner as for the sri-htri heterotetramer.
suitable parameter values for simulating experimentally observed methanol release patterns and adaptation of the cheyp level for wildtype cells, chey-deficient or non-methylatable htri mutants were easily obtained .
fitting of the final model to quantitative experimental data
each feature of model  <dig> is essential in the sense that its omission produces a model that contradicts one of the experimental observations.
to validate whether model  <dig> is able to reproduce experimental data quantitatively, we had to take into account the influence of the measurement technique used and extended the model by radio-labeling and methanol release kinetics .
the final model  was fitted to the results of flow assay experiments  and it quantitatively reproduced experimental data .
discussion
we presented the first quantitative, predictive model of excitation and adaptation in halobacterial phototaxis and chemotaxis which explains the methanol release patterns in response to attractant and to repellent stimulation in the wildtype, in a chey deletion mutant, and in a mutant in which the stimulated transducer species is methylation-deficient.
essential elements of our model are two antagonistically active methylation sites, demethylation rates that depend on feedback by chey, and conformationally coupled heterologous receptors/transducers assembled in cooperative signaling units.
the model integrates proposed mechanistic features both from e. coli and b. subtilis, the combination of which allows to quantitatively reproduce the experimental data on stimulus-induced methanol release in halobacterium, once the appropriate parameter values are chosen.
features from e. coli are cross-talk of heterologous transducer species by direct conformational coupling within a  unit   <cit> .
features from b. subtilis are two methylation sites on the transducers that behave antagonistically in response to attractant and to repellent stimulation, and a feedback of chey/cheyp on reversible receptor methylation  <cit> .
feedback of chey on transducer demethylation is based on direct experimental evidence by  <cit>  who showed that the normal halobacterium-type methanol release pattern  is converted into an e. coli-like pattern .
however, feedback by chey was not sufficient to explain the experimental finding that release of methanol is caused by stimulation of a mutant transducer in which all putative methylation sites have been experimentally deleted  <cit> .
within the cooperative unit of heterologous receptors/transducers, methylation deficiencies as well as different equipment with methylation sites  are compensated allowing the mutant to adapt.
an alternative potential mechanism for feedback might perhaps occur by reversible phosphorylation of the response regulator domain on cheb  <cit> .
in e. coli, methyl-esterase activity of cheb is increased by phosphorylation of the response regulator domain  <cit> , which presumably forms a feedback loop in vivo that controls the basal activity and the speed of motor response  <cit> .
phosphorylation of cheb in e. coli is also considered to increase robustness of adaptation  <cit>  in chemotaxis, while it seems not to be required for precise adaptation  <cit>  for which receptor conformation dependent demethylation is sufficient  <cit> .
in b. subtilis, cheb also has a phosphorylation domain but the role of cheb-phosphorylation is not known in detail.
a mutant strain with deleted cheb response regulator domain still produces the identical methanol release patterns, albeit at a generally higher turn-over/basal-level  <cit> .
thus, the methanol release in response to attractant and to repellent stimulation is independent of cheb phosphorylation in b. subtilis  <cit> .
as we have no experimental evidence for stimulus-dependent cheb phosphorylation in halobacterium, we have computationally analyzed the effect of cheb phosphorylation by assuming that methyl-esterase activity of cheb is increased by phosphorylation.
cheb phosphorylation could not reproduce the wildtype methanol-release pattern for linear demethylation rates , nor could cheb phosphorylation mimic the effects mediated by cooperative transducer interaction in terms of methanol release caused by stimulation through a non-methylatable mutant transducer .
furthermore, in a extension of the final model  <dig> by cheb-phosphorylation, halobacterium-type methanol release patterns were still obtained, which suggests that cheb phosphorylation does not interfere with the proposed kinetic mechanisms of our model.
we have also analyzed the possibility that the halobacterium-type methanol release patterns are generated by a cheb/chebp-based feedback mechanism .
we found parameters in model 3b fbm <dig> that predict the patterns of the wildtype and of the chey deletion.
in any case, it is not possible by an analysis of the mathematical models to exclude or disprove a direct or indirect role of cheb phosphorylation in methylation-dependent adaptation.
to discriminate experimentally between a chey-based and a cheb/chebp-based feedback mechanism, we propose to measure the methanol release patterns of a mutant in which the chey-like domain of cheb has been deleted.
if halobacterium-type patterns are still obtain in such a mutant, then this would suggest that cheb-phosphorylation is not part of the feedback-mechanism which generates the halobacterium-type patterns.
since the halobacterium-type patterns are still observed in a corresponding b. subtilis mutant  <cit> , we did not favor the cheb/chebp-based feedback mechanisms.
additional feedback-loops of methylation independent adaptation processes such as in b. subtilis via the interplay of ched, chec and cheyp  <cit>  may further contribute to adaptation in halobacterium, but we have no experimental evidence for this.
we included enzymatic hydrolysis of cheyp by a chec phosphatase in a variation of model  <dig> to analyze the potential effect of a phosphatase on methanol release and cheyp levels.
again, for a wide range of parameters the additional mechanism of chec-phosphatase did not interfere with or destroyed the halobacterium-type patterns qualitatively or quantitatively.
as expected due to the proposed phosphatase activity of chec, the level of cheyp in the adapted state was significantly lower as predicted by the model lacking chec.
for repellents, the cheyp level was severalfold higher compared to the adapted level.
experimental results regarding stimulus-induced changes in transducer methylation in halobacterium measured by gel fluorography as published by different authors are contradictory  <cit>  and have therefore not been taken into account for our model.
instead, we focused on reliable, reproducible, and temporally resolved quantitative data on the demethylation rates as measured with the flow assay.
however, for the simplest case of constant methylation rates , our model suggests that the transducer methylation level initially drops in response to all kind of stimuli and subsequently slowly returns to the pre-stimulus level, as it was experimentally observed in b. subtilis  <cit> .
parameters in the final model were fitted to experimental data from different groups.
parameters from e. coli and b. subtilis  served as starting values and a parameter set was found that quantitatively reproduced the experimental data.
further parameter optimizations or accounting for yet unmodeled mechanistic details  might improve fitting results further, but additional model extensions are not sufficiently supported by currently available experimental data in h. salinarum.
CONCLUSIONS
we provided a kinetic model for signal processing in photo- and chemotaxis in the archaeon h. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a chey-dependent feedback on transducer demethylation.
further iterative cycles of experiments and mathematical modeling are required to reduce the number of undetermined parameters and to incorporate more mechanistic details.
nevertheless, the predictive computational model and the parameter set obtained now allows to infer cheyp concentration changes upon excitation and adaptation and to correlate these changes to the measurable response of the flagellar motor switch.
this will lead to a data-based coherent model of excitation, adaptation, and motor response in halobacterial phototaxis.

 the archaeon halobacterium salinarum swims by rotation of a semi-rigid right-handed flagellar bundle. each flagellar filament of the bundle extends the axis of a rotary motor to passively transduce the mechanical energy generated by the motor to the medium. motors are anchored in the cell membrane and driven by atp. cells swim back and forth by switching the sense of flagellar rotation from clockwise to counterclockwise and vice versa. in adapted or unstimulated cells, switching occurs spontaneously. active swimming and motor switching is superimposed with passive brownian motion of cell body and flagellar bundle. by the resulting random swimming paths, the cells explore their environment until they encounter a stimulus. sensory stimulation of the photo- or chemoreceptors transiently modulates the probability of motor switching, resulting in a movement of the cell towards more favorable regions in the environment. rather than sensing absolute stimulus strengths, cells respond to relative changes by adapting to any stimulus of constant intensity. several lines of evidence suggest that in bacteria as well as in archaea this adaptation is at least partially caused by reversible methylation of methyl-accepting taxis proteins. proteins of this family, also called transducers, may act as sensory receptors for a specific stimulus, or they may bind to a specific, but different receptor protein to transduce the activation state of this respective receptor and relay it to the autophosphorylating histidine kinase chea. chea phosphorylates the chey protein, which is required for flagellar motor switching, and the phosphorylation rate is thought to be stimulus-dependent. the genome of h. salinarum encodes orthologous methyl-accepting taxis proteins. while sensing and transmembrane regions of these orthologs are quite diverse, the cytoplasmic domains share a high degree of similarity. the diversity allows monitoring different types of cellular and environmental parameters: light, oxygen, proton motive force, amino acids, temperature, and presumably others. the similarity of the cytoplasmic domains of the transducers guarantees sensory integration by chea of all of these stimuli. the transducers physically interact with chea and the scaffolding proteins chew and chew to form r-twa complexes, and the transducers localize in clusters at the cell poles where the photosensory sensitivity is restricted to. with the help of two sensory rhodopsins, sri and srii, h. salinarum senses orange, uv and blue light. the sensory rhodopsins directly act as photoreceptors through physical association with their cognate methyl-accepting proteins. the transducers form stable complexes with the sensory rhodopsins and the cytoplasmic domain of the transducer is essential for the functional interaction of the two molecules. after photoexcitation, which causes photoisomerization of the covalently bound retinal chromophor, a sensory rhodopsin molecule proceeds through a sequence of metastable intermediates and finally returns to the initial state through re-isomerization of the chromophor. this so-called photocycle is thermodynamically driven by part of the energy of the absorbed photon. the conformational changes of the sensory rhodopsin molecule caused by photocycling are transduced to the complexed htr molecule and regulate chea activity. the enzymatic signaling mechanism does not involve changes in the membrane potential. differential regulation of motor switching is thought to be caused by differential regulation of the chea kinase activity. orange and uv light are sensed by sri, suppressing or inducing motor switching respectively, and blue light is sensed by srii, inducing motor switching. most halobacterial transducer proteins carry to potential methylation sites per molecule. as in bacteria, the methyl-transferase cher transfers the methyl-group of s-adenosyl-methionine to a glutamate residue of the transducer signaling domain. after incubating cells with 3h-labeled methionine, transducer methylation is detected by fluorography. demethylation is catalyzed by the methyl-esterase domain of cheb. in e. coli, phosphorylation of the n-terminal, chey-like domain of cheb increases methyl-esterase activity. in h. salinarum, the chey-like domain of cheb is also present, but it is not known whether it becomes phosphorylated in a stimulus-dependent manner or whether cheb-phosphorylation modulates methyl-esterase activity in vitro or in vivo. transducer demethylation results in formation of methanol which can be quantitatively measured in a time-resolved manner with a so-called flow-assay. exposure of h. salinarum to any step-like stimulus that causes taxis results in a transient release of methanol, no matter whether the stimulus induces or represses motor switching. the methanol release patterns observed in h. salinarum are similar in bacillus subtilis where the phenomenon is explained by the fact that transducers contain methylation sites that were shown to be functionally different: one site is demethylated upon stimulation with attractant, another site is demethylated upon stimulation with repellent. selective methylation has been shown to be regulated by chey and to depend on transducer/receptor conformation. in b. subtilis, the transducer deamidase ched regulates activity of the chey-phosphatase chec and the interplay of chec and ched is thought to provide an additional and methylation-independent adaptation system. deletion mutant studies also suggest that chec and ched are possibly involved in a coordination of selective methylation in b. subtilis. chec and ched orthologs are also found in h. salinarum, but their function is not clear. in b. subtilis and in h. salinarum the demethylation reaction as measured in a flow assay cause adaptation to stimuli of constant strength, no matter whether a respective stimulus is attractive or repulsive. presumably, differential methylation resets the signaling activity of the transducers to the pre-stimulus level, resulting in sensory adaptation of the cell, although this has not been directly shown. two mechanisms of stimulus-controlled transducer methylation seem possible: the stimulus-activated transducer molecule may be methylated/demethylated to reset its signaling activity to the pre-stimulus level, or other, i. e. non-stimulated transducers may be methylated/demethylated through a coupling mechanism or feedback loop to attenuate their constant signaling output. because specific photoactivation of a htri mutant in which the methylation sites have been deleted, nevertheless causes both, sensory adaptation and methanol release, coupling between stimulated and unstimulated transducers in terms of reversible methylation seems obvious. a model of the halobacterial motor switch cycle quantitatively reproduces measurements on spontaneous and light stimulus-induced motor switching. in this model, the input to the motor switch is generated by a simple model of the sensory excitation and adaptation processes. coupling of both models is sufficient to reproduce quantitative data on motor switching, but the simple model of excitation and adaptation does not explain reversible transducer methylation. here we provide a predictive computational model of sensory adaptation and excitation based on experimental findings on reversible transducer methylation in wildtype and mutant cells.  modeling concepts by iterative cycles of mathematical modeling, parameter estimation, and comparison of simulation and experimental data, we obtained a quantitative model of excitation and adaptation in halobacterial phototaxis and chemotaxis. this model consistently explains physiological excitation, adaptation, and experimental data on transient transducer demethylation rates. the model is based on the following experimental observations: • in wildtype cells, transducer demethylation always increases transiently when previously adapted cells are stimulated, no matter whether an attractant or repellent is set on or off. the duration of the transient transducer demethylation approximately correlates with the kinetics of behavioral adaptation of the cells. transient transducer demethylation and cheyp concentration negatively correlate in response to attractant stimulation and positively correlate in response to repellent stimulation. • in a chey deletion mutant, transducer demethylation decreases transiently upon stimulation with attractants, and increases transiently upon stimulation with repellents. • a mutant in which all putative methylation sites have been removed from the transducer htri still shows wildtype transducer demethylation patterns and sensory adaptation, even if stimulated through the methylation-deficient transducer htri, indicating that methyl-groups are turned-over on other transducers that did not receive or transduce the stimulus. the final mathematical model was derived step by step, keeping the model structure as simple as possible. the model predicts that • transducers are organized in clusters of conformationally coupled molecules • a cluster is composed of transducers with different input specificity in terms of photo-, chemo-, and other stimuli • sensory adaptation occurs by attenuation of the signaling output through reversible methylation of two antagonistically active methylation sites of a transducer • transducer activation by receptors and transducer methylation determines the signaling output of a cluster in a cooperative manner • reversible transducer methylation is regulated through feedback via unphosphorylated chey each feature of the model is essential in terms of reproducing transducer demethylation patterns and experimental results described for the wildtype and the mutants. the derived mathematical model is based on ordinary differential equations and algebraic equations for equilibrium conditions. in dynamic simulations, the input was light and the outputs were methanol release and cheyp concentration. methanol release from cells exposed to different photo- and chemo-stimuli was correlated quantitatively, and the change in cheyp concentration was correlated qualitatively to the motor response in terms of physiological adaptation. adaptation of the cheyp-level in wildtype cells the initial mathematical model is based on the known molecular components of the phototaxis system and their known photo- and biochemical interactions. two molecules of sensory rhodopsin i form a stable complex with two molecules of the sri-specific transducer. the histidine kinase chea is bound via the scaffold protein chew to htri, which constitutes the r-twa complex. the r-twa complex is assumed to occur in two conformations, active and inactive, which are in thermodynamic equilibrium. photoexcitation of sri causes a transient shift in the equilibrium of the two conformations, and the behavioral response of the cell. the behavioral response of the cell in terms of switching the flagellar motor depends on chea and chey. chea autophosphorylates and transfers the phosphate group to chey. transducers are methylated by the methyl-transferase cher and demethylated by the methyl-esterase cheb. transducers contain one to three methylation sites and the number of sites varies according to the primary structure of the transducer. receptor excitation causes a transient change in transducer demethylation. the equilibrium of the r-twa complex depends on the free energy g of the active and inactive conformation/state. for thermodynamic reasons, the state with lower free energy is preferred. by direct molecular interaction sri shifts the equilibrium between the two activity states by changing the free energy of the r-twa complex depending on the photocycle-state and on the actual activity state of the r-twa complex. the attractant photointermediate sri for instance, favors the inactive state by lowering the free energy of the inactive state more compared to the active state. according to the boltzmann distribution, the equilibrium probability a of being active can be determined from the free energy of each possible combination of the photocycle-states of the two sri proteins with the activity states of the htri homodimer with as long as the photocycle-state of sri does not change, the probability of an r-twa complex of being active depends on the free energy in the active and inactive state of the htri homodimer and is assumed to be determined by the structural properties of the protein as well as by the methylation state of htri. methylated transducers are assumed to shift the equilibrium towards the active state, whereas unmethylated transducers shift the equilibrium towards the inactive state: the demethylation rate is assumed to depend in a proportional manner on the conformational state a of the r-twa complex and the methylation rate is assumed to be constant. model produces cheyp-peaks as expected and reversible transducer methylation allows adaptation of the cheyp level. spudich and co-workers have shown that activation of htri by sri depends on the interface structure between sensory rhodopsin and its cognate transducer and mutations at or near this interface render wildtype strains into mutants that show an inverted response to orange-light. the phenotype of such mutants is generated in silico in our model by a variation of the free energy changes of the sri373-transducer complex such that. methanol release of wildtype cells and of a chey-deletion mutant in simulations, model failed to reproduce the halobacterium-type methanol release pattern and instead, the e. coli-type pattern was obtained. this result was insensitive to the numerical values of the rate constants for methylation and demethylation, insensitive to the values of free energy changes upon transducer methylation/demethylation, and insensitive to the rate constants of sri photocycling measured in wildtype cells. an e. coli-type methanol release pattern was obtained no matter whether the transducers in the model carried one or more methylation sites. moreover, the simulated methanol release pattern remained of the e. coli-type, no matter whether transducer methylation favors active or inactive conformation, respectively. in model we equipped each transducer with two antagonistically behaving methylation sites. we assumed that both sites are accessible to cheb and cher in both conformational states of the r-twa complex and that methylation of the one site promotes the active state, whereas methylation of the other site promotes the inactive state. adaptation then occurs by a shift in the equilibrium of methylation of the activating and the inactivating sites, respectively. intuitively, one might expect that two antagonistically behaving methylation sites should always cause a net increase in methanol production no matter whether a repulsive or an attractive stimulus is given. however, this is not necessarily the case, as discussed in the following. let us assume that both methylation sites, and, contribute additively to the free energy of the r-twa complex: then, in the simplest case, the rates of demethylation of the activating and the inactivating site depend linearly on the active conformation a and inactive conformation i, respectively, counterintuitively, numerical simulations show that this model always gives an e. coli-type methanol release pattern. for certain parameter combinations, the methanol release pattern was e. coli-type with positive and negative peaks inverted, or no change in the net demethylation rate occurred at all. for approximately linear dependence of the demethylation rates on changes in activity, Δa, the change of demethylation rates for the activating methylation site, Δdma ∝ Δa, compensates for the changes of demethylation rates of the inactivating methylation site, Δdmi ∝ Δi, and hence no net increase of demethylation occurs in response to attractant or repellent stimulation. this holds for all tested numerical values of the rate constants for methylation and demethylation. in a variation of model, we assumed that chea phosphorylates cheb and that chebp has increased methyl-esterase activity: however, this model was not capable of reproducing the halobacterium-type methanol release patterns for all tested numerical values of the rate constants. it seems that model is too minimal to be able to reproduce the halobacterium-type demethylation kinetics. perazzona and spudich showed that methanol release patterns depend on the presence of the chey protein. deletion of the chey gene converts the halobacterium-type methanol release pattern of the wildtype into an e. coli-type pattern, indicating that chey directly or indirectly interacts with the methylation/demethylation system of the transducers. chey/cheyp might directly interact with the r-twa complexes, cheb, or cher through a feedback mechanism, e.g. by alternating the rate of phosphorylation of cheb by chea. we found that halobacterium-type methanol release patterns are obtained in the simulation of model if the demethylation rates depend on the transducer activity in a particular nonlinear, e. g. quadratic, manner: this observation together with the fact that methanol release patterns in halobacterium depend on chey leads to a simple kinetic model for feedback of chey/cheyp on the transducer demethylation rate: feedback of chey/cheyp on the transducer increases the demethylation rates and simultaneously introduces an approximately quadratic dependence of the demethylation rate on the transducer activity. in the absence of the chey protein, the rates in the model become approximately linear, which explains both, the phenotypes of wildtype and of the chey deletion mutant. demethylation and methylation rates in equation depend on chey and cheyp concentration, respectively. hence the model suggests that chey regulates demethylation of both methylation sites depending on its phosphorylation state and depending on the activity of the r-twa complex. however, an alternative kinetic mechanism yields a similar behavior of the system, namely if only the unphosphorylated form of the chey protein inhibits demethylation of the activating methylation site and simultaneously enhances demethylation of the inactivating methylation site, e. g.: here, inhibition and activation is modeled by kinetics of the michaelis-menten-type. yet another and similar regulatory mechanism results if only cheyp modulates the demethylation rates, e. g.: feedback mechanisms and i. e. regulation of demethylation through the unphosphorylated or the phosphorylated form of the chey protein, respond differently to the genetic deletion of chey. if the modification rates were regulated by chey only, then chey deletion would increase dma to a· and, contrarily, would decrease dmi to i. the resulting steady state equilibrium is then shifted towards lower activity of the r-twa complexes. a drop of activity down to zero would then cause an overall drop of demethylation. upon saturating stimulation with repellents, an overall increase of demethylation would occur, as experimentally observed in the chey deletion mutant. dependency on cheyp alone would produce the opposite methanol release pattern, in contradiction to the experimental observations. thus, in the model, the unphosphorylated form of chey is the active component in regulating transducer demethylation at the two antagonistically active sites. the remaining possibility ) is that both chey and cheyp regulate demethylation of the two sites, however in a reciprocal manner. the steady-state would then be barely shifted in a chey deletion mutant. parameters can be found that reproduce the halobacterium-type methanol release patterns. however, the resulting model turned out to be very sensitive to parameter variations when rate constants were fitted to experimental data. in addition to not being robust with respect to parameter variations, the model is not minimal, i. e. would need more parameters and interactions to explain the data. we therefore continue with the simplest model in which demethylation of the two sites is only regulated by the unphosphorylated form of the chey protein. accordingly, feedback by the chey protein was incorporated into model to give model fbm and the effect of different numerical values of the reaction rates was analyzed. parameter combinations that produced halobacterium-type methanol release patterns were easily obtained, while positive and negative peaks of cheyp were obtained as expected. the fact that cheb in h. salinarum has a chey-like domain may lead to alternative kinetic models in which cheb/chebp-feedback is responsible for producing the halobacterium-type methanol release patterns. if both cheb and chey compete for phosphate from chea, then the absence of the chey-protein could cause an increased phospho-transfer to cheb. if, in addition, chebp has increased demethylation activity, then this would result in a higher demethylation rate for repellent stimuli, and a lower demethylation rate for attractant stimuli. the methanol release in a chey deletion mutant would then be of the e. coli-type, as experimentally observed. to analyze the possibility of a cheb/chebp-based mechanism, we assumed cheb and chebp-dependent demethylation rates of the form the additional parameters k ≥ and k ≥ were introduced to account for possible cooperative effects. for an appropriate choice of the parameters k and k cheb and chebp introduce a nonlinear dependence on activity/inactivity which may be approximative quadratic - similar as for chey/cheyp in equation - and may then produce the halobacterium-type pattern observed in the wildtype. we found parameters for models with a cubic dependence on cheb/chebp for which the wildtype methanol release pattern could be reproduced. however, only model 3b fbm with a linear dependence on activity/inactivity could predict the e. coli-type methanol release patterns of the chey deletion mutant. we did not favor the possibility of a cheb/chebp-based feedback mechanism, because the wildtype/halobacterium-type methanol-release patterns are still observed in a b. subtilis mutant in which the chey-like domain of cheb is deleted. adaptation of cells with methylation-deficient htri cells expressing htri with all putative methylation sites disabled by site-directed mutagenesis are able to respond and to adapt to light, and transiently release methanol as observed in the wildtype. since model fbm failed to reproduce this experimental finding, it had to be extended to a model in which excitation of the sri-htri complex is communicated to a different transducer type with different substrate specificity, which in turn is reversibly demethylated. presumptive mechanisms of functional coupling might be conformational coupling of different transducer types, or feedback by modulating the methyl-esterase and methyl-transferase activity at transducers other than the actually stimulated transducers. extending model fbm by an additional, non-stimulated and methylation-efficient transducer type yields model looking at wildtype cells, now two different r-twa populations are coupled via chey that feeds back on both transducer types. due to the conformationally independent but functionally coupled populations, the overall activity is given by the linear superposition/weighted mean of both activities where ku and ks represent the contributions of unstimulated and stimulated transducers due to different expression levels. in the wildtype case, parameters for simulating halobacterium-type methanol release with adaptation of the cheyp level were found. however, when simulating the model with one methylation-deficient transducer population and one transducer population where reversible methylation is normal, we could not find any set of parameters that reproduced the experimentally observed wildtype halobacterium-type methanol release pattern and adaptation. as the activity of the unstimulated transducers stays constant and as the mutated, stimulated transducers cannot be methylated, any change of the demethylation rates in the model can only occur through feedback by chey the concentration of which is changed by the stimulated transducers. then the demethylation rates become linear and cannot explain the halobacterium-type methanol release. hence, in the framework of this model, feedback by chey alone cannot be the only mechanism that mediates cross-talk between stimulated and non-stimulated transducers. phosphorylation of cheb through the stimulated transducers and an increased demethylation of the non-stimulated transducers by phosphorylated cheb could provide such a cross-talk mechanism. however, we found no parameters in such a model that predicted the halobacterium-type methanol release pattern of the non-methylatable htri mutant. the missing additional mechanism could be conformational coupling among different transducer types/species within a unit, and this is considered in model in model all r-twa complexes within a unit contribute to the overall activity in a nonlinear and cooperative manner via the phototaxis transducers and cognate photoreceptors, via the binding state of the chemotaxis transducers/receptors, and via the methylation state of all transducers within the unit. by formulating the free energy changes of every possible state of the r-twa signaling unit, the probability of being active can be derived from the boltzmann distribution in a similar manner as for the sri-htri heterotetramer. suitable parameter values for simulating experimentally observed methanol release patterns and adaptation of the cheyp level for wildtype cells, chey-deficient or non-methylatable htri mutants were easily obtained. fitting of the final model to quantitative experimental data each feature of model is essential in the sense that its omission produces a model that contradicts one of the experimental observations. to validate whether model is able to reproduce experimental data quantitatively, we had to take into account the influence of the measurement technique used and extended the model by radio-labeling and methanol release kinetics. the final model was fitted to the results of flow assay experiments and it quantitatively reproduced experimental data. discussion we presented the first quantitative, predictive model of excitation and adaptation in halobacterial phototaxis and chemotaxis which explains the methanol release patterns in response to attractant and to repellent stimulation in the wildtype, in a chey deletion mutant, and in a mutant in which the stimulated transducer species is methylation-deficient. essential elements of our model are two antagonistically active methylation sites, demethylation rates that depend on feedback by chey, and conformationally coupled heterologous receptors/transducers assembled in cooperative signaling units. the model integrates proposed mechanistic features both from e. coli and b. subtilis, the combination of which allows to quantitatively reproduce the experimental data on stimulus-induced methanol release in halobacterium, once the appropriate parameter values are chosen. features from e. coli are cross-talk of heterologous transducer species by direct conformational coupling within a unit. features from b. subtilis are two methylation sites on the transducers that behave antagonistically in response to attractant and to repellent stimulation, and a feedback of chey/cheyp on reversible receptor methylation. feedback of chey on transducer demethylation is based on direct experimental evidence by who showed that the normal halobacterium-type methanol release pattern is converted into an e. coli-like pattern. however, feedback by chey was not sufficient to explain the experimental finding that release of methanol is caused by stimulation of a mutant transducer in which all putative methylation sites have been experimentally deleted. within the cooperative unit of heterologous receptors/transducers, methylation deficiencies as well as different equipment with methylation sites are compensated allowing the mutant to adapt. an alternative potential mechanism for feedback might perhaps occur by reversible phosphorylation of the response regulator domain on cheb. in e. coli, methyl-esterase activity of cheb is increased by phosphorylation of the response regulator domain, which presumably forms a feedback loop in vivo that controls the basal activity and the speed of motor response. phosphorylation of cheb in e. coli is also considered to increase robustness of adaptation in chemotaxis, while it seems not to be required for precise adaptation for which receptor conformation dependent demethylation is sufficient. in b. subtilis, cheb also has a phosphorylation domain but the role of cheb-phosphorylation is not known in detail. a mutant strain with deleted cheb response regulator domain still produces the identical methanol release patterns, albeit at a generally higher turn-over/basal-level. thus, the methanol release in response to attractant and to repellent stimulation is independent of cheb phosphorylation in b. subtilis. as we have no experimental evidence for stimulus-dependent cheb phosphorylation in halobacterium, we have computationally analyzed the effect of cheb phosphorylation by assuming that methyl-esterase activity of cheb is increased by phosphorylation. cheb phosphorylation could not reproduce the wildtype methanol-release pattern for linear demethylation rates, nor could cheb phosphorylation mimic the effects mediated by cooperative transducer interaction in terms of methanol release caused by stimulation through a non-methylatable mutant transducer. furthermore, in a extension of the final model by cheb-phosphorylation, halobacterium-type methanol release patterns were still obtained, which suggests that cheb phosphorylation does not interfere with the proposed kinetic mechanisms of our model. we have also analyzed the possibility that the halobacterium-type methanol release patterns are generated by a cheb/chebp-based feedback mechanism. we found parameters in model 3b fbm that predict the patterns of the wildtype and of the chey deletion. in any case, it is not possible by an analysis of the mathematical models to exclude or disprove a direct or indirect role of cheb phosphorylation in methylation-dependent adaptation. to discriminate experimentally between a chey-based and a cheb/chebp-based feedback mechanism, we propose to measure the methanol release patterns of a mutant in which the chey-like domain of cheb has been deleted. if halobacterium-type patterns are still obtain in such a mutant, then this would suggest that cheb-phosphorylation is not part of the feedback-mechanism which generates the halobacterium-type patterns. since the halobacterium-type patterns are still observed in a corresponding b. subtilis mutant, we did not favor the cheb/chebp-based feedback mechanisms. additional feedback-loops of methylation independent adaptation processes such as in b. subtilis via the interplay of ched, chec and cheyp may further contribute to adaptation in halobacterium, but we have no experimental evidence for this. we included enzymatic hydrolysis of cheyp by a chec phosphatase in a variation of model to analyze the potential effect of a phosphatase on methanol release and cheyp levels. again, for a wide range of parameters the additional mechanism of chec-phosphatase did not interfere with or destroyed the halobacterium-type patterns qualitatively or quantitatively. as expected due to the proposed phosphatase activity of chec, the level of cheyp in the adapted state was significantly lower as predicted by the model lacking chec. for repellents, the cheyp level was severalfold higher compared to the adapted level. experimental results regarding stimulus-induced changes in transducer methylation in halobacterium measured by gel fluorography as published by different authors are contradictory and have therefore not been taken into account for our model. instead, we focused on reliable, reproducible, and temporally resolved quantitative data on the demethylation rates as measured with the flow assay. however, for the simplest case of constant methylation rates, our model suggests that the transducer methylation level initially drops in response to all kind of stimuli and subsequently slowly returns to the pre-stimulus level, as it was experimentally observed in b. subtilis. parameters in the final model were fitted to experimental data from different groups. parameters from e. coli and b. subtilis served as starting values and a parameter set was found that quantitatively reproduced the experimental data. further parameter optimizations or accounting for yet unmodeled mechanistic details might improve fitting results further, but additional model extensions are not sufficiently supported by currently available experimental data in h. salinarum.  we provided a kinetic model for signal processing in photo- and chemotaxis in the archaeon h. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a chey-dependent feedback on transducer demethylation. further iterative cycles of experiments and mathematical modeling are required to reduce the number of undetermined parameters and to incorporate more mechanistic details. nevertheless, the predictive computational model and the parameter set obtained now allows to infer cheyp concentration changes upon excitation and adaptation and to correlate these changes to the measurable response of the flagellar motor switch. this will lead to a data-based coherent model of excitation, adaptation, and motor response in halobacterial phototaxis. 
the model correctly predicts experimentally observed transducer demethylation in response to attractant and repellent stimuli of wildtype cells, a chey deletion mutant, and a mutant in which the stimulated transducer species is methylation-deficient. we provide a kinetic model for signal processing in photo- and chemotaxis in the archaeon h. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a chey-dependent feedback on transducer demethylation. both, methylation and demethylation reactions are involved in sensory adaptation and are modulated by the response regulator chey. receptor activation by light or a change in receptor occupancy by chemical stimuli results in reversible methylation of glutamate residues of the transducer proteins. by mathematical modeling we infer the kinetic mechanisms of stimulus-induced transducer methylation and adaptation. photo- and chemotaxis of the archaeon halobacterium salinarum is based on the control of flagellar motor switching through stimulus-specific methyl-accepting transducer proteins that relay the sensory input signal to a two-component system.
 photo- and chemotaxis of the archaeon halobacterium salinarum is based on the control of flagellar motor switching through stimulus-specific methyl-accepting transducer proteins that relay the sensory input signal to a two-component system. certain members of the transducer family function as receptor proteins by directly sensing specific chemical or physical stimuli. others interact with specific receptor proteins like the phototaxis photoreceptors sensory rhodopsin i and ii, or require specific binding proteins as for example some chemotaxis transducers. receptor activation by light or a change in receptor occupancy by chemical stimuli results in reversible methylation of glutamate residues of the transducer proteins. both, methylation and demethylation reactions are involved in sensory adaptation and are modulated by the response regulator chey.  by mathematical modeling we infer the kinetic mechanisms of stimulus-induced transducer methylation and adaptation. the model correctly predicts experimentally observed transducer demethylation in response to attractant and repellent stimuli of wildtype cells, a chey deletion mutant, and a mutant in which the stimulated transducer species is methylation-deficient.  we provide a kinetic model for signal processing in photo- and chemotaxis in the archaeon h. salinarum suggesting an essential role of receptor cooperativity, antagonistic reversible methylation, and a chey-dependent feedback on transducer demethylation. 