Deciphering neural circuits for Caenorhabditis elegans behavior by computations and perturbations to genome and connectome
aa r X i v : . [ q - b i o . N C ] O c t Deciphering neural circuits for
C. elegans behavior bycomputations and perturbations to genome and connectome
Jan Karbowski , Nalecz Institute of Biocybernetics and Biomedical Engineering,Polish Academy of Sciences, 02-109 Warsaw, Poland; Institute of Applied Mathematics and Mechanics,University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland.
Abstract
Caenorhabditis elegans nematode worms are the only animals withthe known detailed neural connectivity diagram, well characterizedgenomics, and relatively simple quantifiable behavioral output. Withthis in mind, many researchers view this animal as the best candidatefor a systems biology approach, where one can integrate molecular andcellular knowledge to gain global understanding of worm’s behavior.This work reviews some research in this direction, emphasizing com-putational perspective, and points out some successes and challengesto meet this lofty goal.
Keywords : C. elegans behavior; Integrated system-level description; Genes and neu-rons affecting locomotion; Computational neuroscience; Models.Email: [email protected] 1 ntroduction.
Despite diverse goals and scopes, engineering and biological sciences share a commongeneral methodology. If engineers want to know how a device works, they usually breakor decomposes it into smaller parts and study them in isolation [1]. Subsequently,they gradually put the components together and investigate their interactions, whichgenerally leads to deciphering the workings of the device. A similar version of sucha reverse engineering is used also in biology. The functions of biological circuits areusually decoded by application of either molecular or cellular perturbations in the formof genetic mutations or cell elimination (laser ablations), with simultaneous observationof their consequences on the system performance [2].
Caenorhabditis elegans worms are unique biological organisms to study the structure-function relationship across different scales, from molecules to behavior, for the threemain reasons. (i) Their genome and protein networks are well characterized [3, 4],which represents a microscopic level. (ii) They have a very small nervous system com-posed of only 302 neurons and they are the only animals on the Earth with the knownwiring diagram of neural connections [5, 6, 7], called connectome, and this representsa mesoscopic level (for a comparison human brain contain 10 neurons and even asmall fruit fly brain has ∼ neurons). (iii) These worms can exhibit a broad rangeof behaviors (locomotion, olfaction, complex mating, sleep, learning and memory) thatcan be quantified, and this represents a macroscopic level [8]. It should be noted thatthe structure-function relationship has also been successfully studied in rodents [9] andin the fly [10]. However, these systems, despite recent progress in their connectome2tudies, still lack a detailed neuron-to-neuron wiring diagram.The above suggests that an integrated description of the nematode worms acrossdifferent spatial scales is in principle possible by merging the tools of separate disciplinessuch as genomics, connectomics, behavioral neurophysiology, and computational biol-ogy. There is an expectation that such a description might provided insights not onlyabout inner mechanisms employed by the worm to execute its behavioral program [4, 8],but also can shed some light on the biological mechanisms in more complex animalsbecause many molecular processes and their modularity are preserved across differentspecies [2, 11]. However, despite the apparent structural-behavioral simplicity of C. el-egans nematodes, the system-level approach is not as straightforward as it might seem.Foremost it requires a collaboration of researchers with different backgrounds and skillswho have to learn the basics of the other disciplines to communicate efficiently. Despitethis practical difficulty there are some studies that successfully merge and apply thetools from molecular genetics, behavioral neurophysiology [12], and/or computationalbiology [13, 14, 15, 16]. On the other hand, such a merging often requires a lot ofguess-work, since each of the levels (i-iii), although well characterized, contains some“knowledge gaps”, and moreover the levels are not easily related to one another.The goal of this review is to give a sense and examples of how the above three levelscould be potentially integrated using a system-level computational perspective, withhopes and challenges that have to be addressed and solved before systems biology of
C.elegans worms can fully materialized. We focus mainly on locomotion as it accompaniesa large part of the behavioral output of these worms [17, 18, 19]. Specifically, we3onsider the questions of locomotion robustness, locomotion encoding in
C. elegans nervous system, locomotory decision making, the type of synaptic signaling betweenpremotor command neurons, and the question about which neuronal models could bebest used for behavioral description?
How robust is
C. elegans locomotory behavior?
Sinusoidal locomotion is the basic short-term behavior of
C. elegans nematodes, andtherefore one can suppose that it must have been somehow optimized during evolution(see e.g. [20, 21]). Interestingly, most genetic mutations do not have a visible effect onlocomotion [22], and similarly, random elimination of neurons from the worm’s networkrarely alters the motion. To affect the locomotor output, e.g., to change mean velocity,frequency of body undulations, or the rate of changing direction (reversals), one has toapply targeted mutations or neural ablations [23]. But even in these cases, the propor-tional relationship between worm’s velocity and the frequency of neural oscillation ismostly preserved (Fig. 1). The exceptions that break this proportionality are rare, butif they happen they can have a very dramatic influence on motion (i.e. phenotype), in-cluding its cessation. The reason for a high degree of motor robustness against geneticmutations and neuron eliminations is that both protein and neural networks possessthe so-called “rich club” architecture [24]. This means that connectivity in these twotypes of networks is generally sparse, with only a small fraction of proteins and neuronsserving as “hubs” with dense connections [25]. (For neural connectome these are pri-marily locomotor interneurons [24].) Thus, random mutations or ablations would mostlikely hit a non-hub protein or neuron, and therefore can cause only a minor (i.e. local)4amage to network organization.Another manifestation of
C. elegans robustness and simplicity is the fact that itslocomotory output is low dimensional in a sense that at any given instant the worm’sposture can be represented as a linear combination of the same four basic shapes,the so-called “eigenworms” [26], across different genotypes (for wild-type and differentmutants) [14]. In sum, all this suggests a robust control mechanism of locomotion thatspans the three levels, form microscopic to macroscopic, and it resembles the concept of“robust yet fragile” architecture that possess many engineering and biological systems[27].
Why is it difficult to integrate the knowledge of connectome and neural dy-namics with nematode behavior?
The neural connectome is a static structure over the worm adulthood. On the otherhand, the worm behavior has a temporal aspect that can change depending on envi-ronmental input or internal neuronal activity. Simply saying, the same connectome canproduce a diverse behavioral output, which means that there is no a one-to-one map-ping between neuronal structure and behavior, or between mesoscopic and macroscopiclevels [28]. To understand a neuronal mechanism of a particular behavior one has torelate it to a corresponding neural dynamics. However, there are two problems here.One is that it is extremely difficult to record electric activity of
C. elegans neurons be-cause of the worm’s hydrostatic skeleton that can explode under the release of internalpressure upon dissection [29]. This problem has been circumvented in recent years bythe invention of optogenetic methods that enable imaging of calcium activity in many5eurons simultaneously [30, 31, 32, 33], which is possible due to
C. elegans transpar-ent body (see also below). Calcium level in neurons is a proxy for membrane electricvoltage, and hence there is a high hope that these type of imaging methods can yieldgreat insights about neuronal control of behavior not only in the nematode but also inother species [34]. A second problem is related to modeling of neural dynamics. Theactivity of a neural network is to a large extent dependent on neuronal communicationmediated by synapses and on different types of membrane ionic channels. Excitatoryand inhibitory synapses influence network dynamics in different ways [35], and thusrealistic modeling requires the knowledge of an identity of each synapses in the networkof interest. Unfortunately, we do not know the types of synapses in most neurons of
C.elegans , i.e., what kinds of neurotransmitters and postsynaptic receptors are used, andwhether a given synapse is excitatory, inhibitory or modulatory. Even worse, the sameneuron in
C. elegans can influence differently its downstream partners: it can excite oneneuron and inhibit another [36, 37], and this type of mixed signaling does not occur inmore complex organisms like mammals [38]. Similarly, we know that
C. elegans genomeencodes a large repertoire of various ion channels, which can exhibit a highly nonlineardynamics, but most of them remain uncharacterized [39]. Consequently, we have only alimited information on the types and properties of ionic channel for most neurons, andthus dynamic responses of single neurons are largely unknown (see however [29]). Nev-ertheless, we do know that
C. elegans neurons, in contrast to most vertebrate neurons,do not contain voltage-sensitive sodium channels (lack of genes coding for these chan-nels [3]), and hence they do not fire classic Na + -induced action potentials [29]. Instead,6hese neurons can be either depolarized in a graded fashion by Ca +2 ions [29, 40, 41], orthey can fire a broad calcium action potentials ( ∼
20 msec of width) driven by voltage-gated calcium channels [42]. This indicates that
C. elegans neurons can be engaged intwo different modes of communication, either analog or digital, for encoding externalsignals, which probably enhances the worm’s information processing capacity.
In search of a biophysical model of neural dynamics and the role of opti-mization.
Missing data for synaptic signaling and ion channel types did not, however, preventseveral computational attempts to model neuron dynamics. One can broadly dis-tinguish three classes of models for studying individual neurons: passive or simple[13, 43, 44, 45, 46, 47], moderate [48, 49], and active or complex [16]. The passivemodels are simplified in the sense that they do not include ion channels except a lin-ear leak channel. For that reason, their dynamics seems unrealistic, unless synapticand gap-junction inputs are so strong that they dominate over ion channel dynamics.Indeed, there is some support for the dominant role of synaptic and gap-junction cur-rents at least for some locomotor interneurons, and this comes from an optimizationof the active/complex model where calcium and calcium activated potassium channelswere included on equal footing with the leak current [16]. This suggests that passivemodels [13, 43, 44, 45, 46, 47], although unrealistic in capturing dynamic complexity ofsingle neurons, do not have to lead to wrong dynamics on a network level if synapsesin this network are sufficiently strong. The mentioned active model [16], involves thecombination of two dynamic equations that are highly nonlinear, one for voltage and7nother for intracellular Ca +2 concentration, in contrast to the passive models that aredescribed only by a single equation for the voltage. Moderate models, in turn, eitherconsider an ion channel nonlinearities in an abstract way by including a switch-liketerm in a single voltage dynamics equation [48], or consider a spatial distribution ofcalcium concentration dynamics using three simple linear equations [49]. From this, itfollows that only two models, the active one [16] and the moderate model in [49], can inprinciple be related to the dynamics of Ca +2 in imaging experiments of freely movingworms [30, 31, 32], and thus can link computations or theory with experimental data.Out of these two models, the active model [16] is much more grounded biophysically(Hodgkin-Huxley type model), and therefore has a potential for future improvementsin adding more relevant channels and their optimization.To summarize, we know which neuron is connected to which, but we are uncertainhow they talk to each other and what is their intrinsic dynamic repertoire, which is a bigobstacle for realistic modeling of worm’s neural circuits and relating them to behavior.For these reasons, it appears that it does not make sense to model the dynamics of thewhole large-scale C. elegans neural network, despite the knowledge of its connectome,because the result is very likely to be distinct from the real network activity (see however[47]). A way around these problems is to use sophisticated computational techniquesrelying on evolutionary optimization that would allow us to predict or determine withhigh probability the neuronal and synaptic parameters by relating connectome to be-havior [16, 45]. Such approaches minimize an appropriately chosen multivariable costfunction, and find optimal set of neural network parameters for a given behavior. An8ptimization approach could be used, e.g., to infer the range of ion channel parametersin the biophysical model used in [16]. It seems that a natural cost function for thisproblem could be related to a difference between input-output characteristics for theexperimental neuron [29] and theoretical neuron [16].
How genetic and neuronal perturbations help us to decipher neural mecha-nism of worm’s behavior?
The advantage of possessing a well characterized nervous system and the genome isthat we can apply perturbations to these two systems and record subsequent changesin worm’s behavior. There is a large body of evidence showing that neural connectiv-ity is correlated with the gene expression pattern, meaning that denser connections,associated with hubs, require more gene activity [50, 51]. Therefore by mutating ordeleting specific genes that target specific neural connections, we can alter the worm’sbehavioral output. If we additionally can quantify that output, we can go back and inprinciple infer some unknown properties of the neural circuit underlying that particularbehavior. An example of the approach along similar lines was performed in Ref. [13].In that work, combining genetic perturbations with computational modeling, locomo-tion of mutants with altered synaptic transmission, channel conductance, and musclestructure was measured and compared with predictions of a large-scale neural circuitmodel. It was found, among other things, that the head network was the likely sourceof worm’s sinusoidal oscillations (the so-called Central Pattern Generator, CPG), andthat the frequency of neuronal oscillations depends bimodally on the synaptic couplingstrength, the latter in agreement with slo-1 mutants and their variants [13]. This work9s also an example that mathematical modeling does not have to act posteriorly to theexperiment, but instead can induce experimentation by proposing a certain hypothesis:in this case the location of CPG. A recent experimental quest to resolve that question,involving genetic constructs and neural ablations, suggest a slightly more complex pic-ture: there are probably more than one CPG (some perhaps secondary), distributedalong the worm’s body [52]. Also there is an evidence that CPG can be strongly modu-lated by proprioceptive feedback [53], which can help in coordination of various CPG’sand stabilization of the worm’s movement.Cellular perturbations to a specific neural circuit can help us also in revealing theidentity of neural connections [16, 46]. Systematic ablations of neurons in the pre-motor interneuron network were performed, and based on this, the likely polaritiesof interneurons and their connections were inferred using a computational approach,involving evolutionary optimization [16, 46]. Unexpectedly, it turned out that all in-terneuron connections should be inhibitory. This prediction is partly supported byrecent data showing that the connection from AVA interneuron to one of the down-stream motor neurons is mediated by lgc-46 chloride postsynaptic receptor [54], whichshould act as inhibition since influx of negative Cl − ions decreases membrane voltage[55]. However more specific neurophysiological experiments must be performed to ver-ify this strong prediction. The works in Refs. [16, 46] have provided a substrate fora more realistic modeling of premotor interneuron network, and in addition they shedsome light on how the locomotory output is represented on the interneuron level. Thedominant synaptic inhibition means that interneurons mutually suppress one another,10nd this could be good for saving metabolic energy in the interneuron network duringlocomotion. Such low activity is in agreement with a study showing that only a smallfraction of C. elegans sensory neurons is activated upon an external stimulation [56].Taken together, this suggests that sensory and premotor interneuron circuits could usesparse neural representations to encode locomotion [16]. Such sparseness is energeticallyadvantageous because neurons and synapses are known to be metabolically expensive[57, 58, 59, 60].It should be noted that a sheer perturbation like cell ablations can have “off target”effects [61]. This means, e.g., that removing a certain neuron from a circuit of interestcan affect the input coming to this circuit from other neighboring networks, becauseof the possible recurrent connections between them. This undesirable effect would beamplified if the ablated neuron were a hub neuron. It seems that it is difficult to controlthis type of influence or even estimate its magnitude; nevertheless one has to be awareof such possibilities, especially in the modeling studies.
Optogenetics as a method for perturbing and monitoring neural dynamics.
Optogenetics is an experimental method that has an equal or even more potential thancell ablation, since it enables a selective activation or silencing of some neurons withoutaffecting the network structure [62]. The main idea is to express, using genetic methods,artificial ion channels or pumps in neuron’s membrane that upon light stimulationconduct various ions (e.g. Na + , K + , Ca , Cl − , H + ), leading to changes in neuronalvoltages. Because the light stimulation can be changed at will, it allows a temporalcontrol of the circuit dynamics [62]. The large-scale neural activity can be subsequently11onitored using calcium imaging in real time [30, 31, 32, 33].It must be stressed again, that since optogenetics affects mainly ion channels, onehas to use biophysical neuron model with realistic basic channel dynamics in orderto compare computational modeling with calcium optogenetic data. Thus, an activeneuron model, such as the one in Ref. [16], or its extension, is essential for a meaningfulconnection between theory and data. How locomotory program of
C. elegans is encoded in neural dynamics?
Large-scale optogenetic calcium imaging study has shown that worm locomotory statesare correlated not only with the dynamics of peripheral motor and command neurons,but also and mostly with distributed neural dynamics across the whole nervous system[15]. Moreover, this global neuronal representation of locomotion is highly coordinatedto the extent that its dynamics can be reduced to just few dimensions [15]. A principalcomponent analysis associated with cross-correlations between neurons revealed that agiven locomotion state (moving forward, backward, turning, slowing) can be preciselymapped into a particular region of a low dimensional neuronal state manifold (in thespace of principal components). This manifold has a continuous and cyclic character,reflecting a long-term repeatable sequence of the worm motor actions [15]. This showsthat
C. elegans locomotory phases are encoded in the nervous system collectively in asimple, yet abstract, but a straightforward way. Interestingly, the low dimensionalityof neural dynamics underlying locomotion is consistent with the low dimensionality ofworm’s locomotory shapes discussed earlier [14, 26]. Additionally, it is very similarto neural representations in other species [63, 64], which might suggest some form of12euronal universality across different animals with dramatically different brain sizes.How robust is the low dimensional neuronal state manifold? It turns out that itstopological structure is quite stable against various perturbations, including an inhi-bition of a hub locomotor interneuron (AVA), or stimulation of chemosensory neurons[15]. In addition, the manifold structure is also preserved during
C. elegans starvation,which surprisingly affects only a few neurons [65]. Nevertheless, the global neuronalmanifold can collapse to a single stationary fixed point during the worm’s quiescence,presumably global sleep brain state, in which the majority of neurons throughout thebrain is inactive [65]. Thus, it appears that the global neuronal state representing lo-comotion is stable if perturbations are local, but it can be destroyed when activities ofmany neurons are significantly reduced. This temporal neural organization of behaviorpoints again towards the engineering concept of “robust yet fragile” [27], suggestingsome similarities between global organization in man-made devices and evolutionaryshaped biological systems.Is the global neuronal manifold energy efficient? The data show that about 40%of head neurons is involved in the neuronal manifold [15, 65], which is a substantialfigure and clearly should lead to a large metabolic expenditure on a global neural scale.This contrasts with the above results showing sparse sensory representation [56] andmutual synaptic suppression of premotor interneurons [16], and indicates that energymight be minimized locally, but not globally. Moreover, the high percentage of neuronsparticipating in the global manifold suggests that the worm must invest some amountof energy to perform its living functions, i.e. to execute its exploration-exploitation13rade-off [66], and a sheer saving of metabolic energy is not a viable strategy.
Locomotory decision making in
C. elegans and macroscopic level.
The macroscopic level where the worm’s behavior takes plays is influenced both by thenematode nervous system and by an environmental input that can change in a stochasticmanner [67, 53]. Interestingly, the neural network in itself can generate variability evento deterministic stimuli, as for instance in the olfactory circuit of
C. elegans [68], and thisseems to be a generic feature of neural circuits also in higher animals [69]. This impliesthat behavioral level of the worm can be described in probabilistic terms using Markovchains, with dynamically changing probabilities representing states with forward andbackward motions and stop phases [16, 46, 70]. Experimental data involving geneticmutations in the premotor interneurons and motor neurons indicate that transitionsbetween locomotor states are driven by a difference in the activities of motor neuronscontrolling forward and backward motion [71]. Specifically, if motor neurons belongingto class B are more active than those belonging to class A, then the worm more likelywill move forward, and vice versa [71]. Both motor neuron classes are modulated bythe upstream interneurons, which in turn are influenced by sensory input. Hence, theprobabilistic decision to move in a particular direction or to stop is made collectively,and presumably with some delay, by the whole interacting large-scale neural network,whereas the execution of the decision is performed by the asymmetric activities of thetwo classes of peripheral motor neurons.How can we reconcile this probabilistic picture of locomotor output with the abovecontinuous dynamics of global neuronal manifold where each locomotory state is mapped14o a specific manifold region [15, 65]? It seems that these two descriptions are mutu-ally complementary: the first is the macroscopic (behavioral) view, while the secondis its abstract neuronal representation. It must be also remembered that the neuronalmanifold representation does not include time explicitly, and hence stochastic temporaleffects are hidden. Nevertheless, these effects are captured by a thickness of the neuronalmanifold [15]. Moreover, from a mathematical point of view, the probabilistic Markovchain picture can be formally mapped into continuous dynamics of a relevant variable(e.g. velocity) perturbed by stochastic noise [72]. Thus, these two, seemingly distinct,descriptions can be made formally similar under suitable mathematical transformations(see Box 1).Another issue is how we can use biophysical neural models to describe locomotorytransitions in a simple and efficient way, i.e., how mesoscopic level can describe themacroscopic one? It appears that solely biophysical description of locomotory behavioris impractical, since there is no a unique neural variable that relates directly to motoroutput. Instead, it seems that a better approach is to use a hybrid picture: biophys-ical modeling of neural dynamics combined with probabilistic Markov model for thedescription of behavior, as it was done in [16]. The two models meet at the level ofmotor neuron activity, which links mesoscopic and macroscopic dynamics.
Summary and conclusions.
C. elegans worms exhibit a robust low-dimensional locomotory behavior, which can bemildly perturbed by genetic and cellular means to decipher its neuronal representation.However, to describe and understand the neuronal basis of locomotion, we need more15eliable biophysical neural models, and models linking directly neural dynamics withdifferent locomotor states. We also need a more specific molecular perturbations, whichcould be straightforwardly related to specific parameters in the models. Optogeneticmethods, in combination with optimization techniques, will allow a comparison betweenpredictions of neural theory with experimental data, and thus can select better models.Once this happens, the genuine systems biology approach, from genes through neuronsand their networks to behavior, could be successfully applied in
C. elegans . Such com-bined approaches might uncover neuronal principles of behavior in the worm that couldhave a universal character and apply to other, more complex, animals as well, sinceevolution acts in many respects by repeating the same microstructures and mechanisms[2, 11].Finally, we did not discuss other biological functions, like learning and memory,which are known to exist in
C. elegans [73, 74]. For instance, some neurons can par-ticipate in diverse behaviors, e.g. olfactory sensing and encoding, which is a form ofmemory [75, 76]. This is interesting because it links sensory and locomotory circuitswith learning and memory, which currently lacks understanding. Clearly, there is apotential here for using computational modeling that would give us more insight aboutsuch a complex behavior. 16 ox 1: Link between probabilistic and continuous descriptions of locomotion.
It is shown below that the probabilistic Markov model of
C. elegans locomotionemployed in [16, 70] is approximately equivalent to continuous noisy dynamics of worm’svelocity. The general form of the Markov model is given by dynamics of probabilities p n ( t ) that the system is in a particular state n :˙ p n = α n +1 p n +1 + β n − p n − − ( α n + β n ) p n , (1)where the dot denotes the time derivative, and α n , β n are the transition probabilities pertime unit. In the minimal models of C. elegans locomotion only 3 states are considered:forward movement, backward movement, and stop phase [46, 16, 70], and these statescorrespond respectively to n = 1, n = −
1, and n = 0 in Eq. (1). We can extend theseminimal models to the model with 2 N + 1 states, where N ≫
1, in which n = 1 , , ..., N correspond to the states with different velocities for forward motion, the states n = − , − , ..., − N correspond to different velocities for backward motion, and the state n = 0 refers to the stop phase.The goal is to transform the discrete Eq. (1) into a quasi-continuous equivalentequation. To achieve this, we define a quasi-continuous velocity v as v = nǫ , where ǫ is the experimental resolution of velocity or its measurement error. The next stepis to introduce two quasi-continuous functions A ( v ) and B ( v ), related respectively todeterministic and stochastic components of the dynamics, by making the followingrescaling transformations: 17 n ( t ) = ǫP ( v, t ) ,α n = 12 " B ( v ) ǫ − A ( v ) ǫ ,β n = 12 " B ( v ) ǫ + A ( v ) ǫ , (2)where P ( v, t ) is the distribution of probability for v . Note that nonzero A ( v ) introducesasymmetry between elementary jumps that increase ( β n ) and decrease ( α n ) velocity.A quasi-continuous version of Eq. (1) is obtained by expanding p n ± , α n +1 , and β n − for small ǫ to O ( ǫ ) order. For example, p n ± = ǫP ( v ± ǫ, t ) = ǫ [ P ( v ) ± ǫP ′ ( v ) + ǫ P ′′ ( v ) + O ( ǫ )], where the prime and double-prime denote first and second derivativeswith respect to v . These expansions lead to a partial differential equation for probabilitydistribution P ( v, t ) of quasi-continuous velocity as ∂P ( v, t ) ∂t = − ∂∂v [ A ( v ) P ( v, t )] + 12 ∂ ∂v [ B ( v ) P ( v, t )] + O ( ǫ ) , (3)which formally is known as a Fokker-Planck equation [72]. This equation in turn ismathematically equivalent to a continuous dynamics of velocity v influenced by noise[72] ˙ v = A ( v ) + q B ( v ) η, (4)18here η is the Gaussian white noise with unit variance. Note that in this picture,the function A ( v ) is related to a deterministic part of acceleration, while B ( v ) to itsstochastic part. Both of these functions can in principle be experimentally measured,which should enable us to determine the transition rates α n , β n in the phenomenologicalmodel given by Eq. (1). 19 cknowledgments The author thanks an anonymous reviewer for useful comments. The work was sup-ported by the Polish National Science Centre (NCN) grant no. 2015/17/B/NZ4/02600.20 of special interest ∗∗ of outstanding interest References
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