Cortical areas comprise multiple types of inhibitory interneurons, with stereotypical connectivity motifs that may follow specific plasticity rules. Yet, their combined effect on postsynaptic dynamics has been largely unexplored. Here, we analyze the response of a single postsynaptic model neuron receiving tuned excitatory connections alongside inhibition from two plastic populations. Synapses from each inhibitory population change according to distinct plasticity rules. We tested different combinations of three rules: Hebbian, anti-Hebbian, and homeostatic scaling. Depending on the inhibitory plasticity rule, synapses become unspecific (flat), anticorrelated to, or correlated with excitatory synapses. Crucially, the neuron's receptive field  depends on the modulatory state of inhibition. When both inhibitory populations are active, inhibition balances excitation, resulting in uncorrelated postsynaptic responses regardless of the inhibitory tuning profiles. Modulating the activity of a given inhibitory population produces strong correlations to either preferred or nonpreferred inputs, in line with recent experimental findings that show dramatic context-dependent changes of neurons' receptive fields. We thus confirm that a neuron's receptive field does not follow directly from the weight profiles of its presynaptic afferents. Our results show how plasticity rules in various cell types can interact to shape cortical circuit motifs and their dynamics.SIGNIFICANCE STATEMENT Neurons in sensory areas of the cortex are known to respond to specific features of a given input , but recent experimental studies show that such responses  depend on context. Inspired by the cortical connectivity, we built models of excitatory and inhibitory inputs onto a single neuron, to study how receptive fields may change on short and long time scales. We show how various synaptic plasticity rules allow for the emergence of diverse connectivity profiles and, moreover, how their dynamic interaction creates a mechanism by which postsynaptic responses can quickly change. Our work emphasizes multiple roles of inhibition in cortical processing and provides a first mechanistic model for flexible receptive fields. Inhibitory neurons exhibit large variability in morphology, connectivity motifs, and electrophysiological properties . InhibitThe state of balance is thought to be achieved and maintained by inhibitory plasticity, for example, a Hebbian-like inhibitory plasticity rule  increas. Other tGiven that cortical circuit motifs feature multiple interneuron types , we wondAltered receptive field properties have been widely observed  . In macaA), thus creating different connectivity profiles onto postsynaptic neurons (B), such as those observed for parvalbumin-positive (PV+) and somatostatin-positive (SOM+) interneurons , which results in a nonselective connectivity . This hypothesis extrapolates from evidence of cortical disinhibition during functional tasks  is the somatic voltage at time t, τm = RC is the membrane time constant , urest is the resting membrane potential, and EE and EI are the reversal potential for excitatory and inhibitory synapses, respectively. Synaptic conductances, gE (t) and gI (t), evolve according to the following:E and τI,, respectively. Presynaptic action potentials trigger increase in synaptic conductances through the sum of Dirac δ functions as follows:kjt is the time of the kth spike of presynaptic afferent j. The contribution of a given presynaptic afferent j to changes in conductances is given by the synaptic weight NE being the number of excitatory and NI of inhibitory presynaptic afferents.To investigate changes in neuronal response because of specific inhibitory connectivity motif, we simulated a postsynaptic leaky integrate-and-fire neuron (LIF) receiving excitatory and inhibitory afferents. Postsynaptic neuronal membrane potential dynamics is governed by the following:u(t) crosses the spiking threshold uth from below. The membrane potential is then instantaneously reset to ureset, being clamped at this value for the duration of the refractory period, τref. The postsynaptic spike train is described as a sum of Dirac deltas as follows:kt is the time of the kth spike of the postsynaptic neuron, or the time the membrane potential crosses the spiking threshold from below. Parameters used for the postsynaptic neuron are detailed in An action potential is triggered at the postsynaptic neuron once its membrane potential P signal groups  that share the same fluctuation in firing rate. We tested two cases: natural input and pulse input. Both are described below.To mimic experimentally observed synaptic input profiles , we diviOU is the time constant for the decaying process that changes because of a Gaussian noise term ξμ(t) with unitary standard deviation (SD). The mean value of the variable yμ is zero, and thus it assumes positive and negative values for long periods.For presynaptic activity mimicking a natural input, activity follows an inhomogeneous Poisson process that changes according to a modified Ornstein-Uhlenbeck (OU) process. We first defined an auxiliary variable for each pattern, X indicates the presynaptic population (X = E for excitatory and X = I for inhibitory). The spike trains of the afferents of signal group μ are generated by the following:X0 is the amplitude of the modulated firing rate fluctuations, and yμ(t), an afferent is half the time in the background state and half the time in the active state.The spike train of an afferent in a given signal group μ is given by the variable, Eref for excitatory and τIref for inhibitory inputs. Given the time step of the simulation Δt, spikes of a presynaptic afferent that is part of the signal group μ are generated with a probability X = E (excitatory) or X = I (inhibitory) afferent that is part of the signal group μ becomes the following:Presynaptic action potentials were generated as an inhomogeneous Poisson process according to the modified OU process described above and a fixed background firing rate. Additionally, we implemented a refractory period, τk being an integer larger or equal than zero and ν* = 5 Hz. Thus, presynaptic spikes are generated by the following:Xν is a scalar that sets the ratio of excitatory and inhibitory firing rate.To test transient responses to brief changes in presynaptic activity, we also quantified postsynaptic responses to pulse inputs. In this case, we simulated the postsynaptic neuron receiving inputs with constant background firing rate. For 100 ms, we increased the probability of presynaptic spikes for a given signal group μ by a factor Responses to the pulse input were divided in two bins: phasic and tonic. Phasic responses were defined as the postsynaptic activity elicited in the first 50 ms of the pulse input. Tonic activity was correspondingly defined as having occurred in the last 50 ms of the stimulus. We simulated 100 trials per input strength r0, b, and c are parameters defining the shape of the synaptic weight profile and μ0 defines the preferred signal group, which maximizes r(μ); r(μ0) = 1. Note that c is an even positive integer.Based on j as the signal group of which that afferent j is part. Thus, excitatory synapses are set as follows:wE0 is a normalization factor for excitatory weights, and ϵj is a noise term drawn from a uniform random distribution between For simplicity, we define ζInitial conditions for all inhibitory populations were flat with noise see , 7, 9, aIn all cases, except for one see , all inhw.Because of the small number of inhibitory afferents compared with the excitatory ones, and the difference in driving force, inhibitory weights were much larger than excitatory ones. Thus, we plotted excitatory weights multiplied by the parameter αjx(t) is the value of the trace of the spike train of presynaptic afferent j at time t; τSTDP is the time constant of the trace, and jS(t) is a sum of Dirac δ functions  is the postsynaptic trace, and Spost (t) is the spike train of the postsynaptic neuron  is given by the following:unctions  represenc neuron . We usedjth inhibitory synapse changes according to the following:H is the learning rate, and αH is a parameter that defines the postsynaptic firing rate. The first two terms on the right-hand side of Precise balance of excitatory and inhibitory inputs was learned by a Hebbian inhibitory plasticity rule . The weis is a learning rate, wIs is a reference weight, ρ0 is a firing rate reference value, chosen to be the same as the one for Hebbian plasticity rule, s is a term that sets the firing rate range for which synapses do not change. Postsynaptic neuron's firing rate is computed with a slow averaging of the postsynaptic activity through the following:scaling is the time constant for the postsynaptic activity and scaling so that ypost (t) is in units of rate. Synaptic depression is weight-dependent, whereas synaptic potentiation is not, which ensures that all synaptic weights tend to the same value. When the postsynaptic neuron is firing below a threshold s ρ0, all synapses increase in value by the same amount. Intuitively, these mechanisms ensure that all synapses converge to the same value for a long run (see below).One of the synaptic weight profiles we used for inhibitory synapses was flat . To learn the flat profile from random initial weights, we implemented a scaling plasticity rule, partially based on experimental work that observed synaptic scaling on inhibitory synapses . Weightske train . The lasaH is a parameter to counterbalance the anti-Hebbian term . The resulting rule dictates that coincident events decrease inhibitory synapses, whereas noncoincident ones increase synaptic weights. Because of the unstable nature of this plasticity rule (see details below), we implemented a time-varying learning rate, which evolves according to the following:aH is the decay time constant for the learning rate, and MaH (t) is an external signal to transiently activate plasticity. We speculate that such signal could come from modulatory neurons, such as dopaminergic or cholinergic and assumed that the external signal peaks at a time t0 (beginning of the simulation), so thatt0 is the time when plasticity at these synapses is initiated. Parameters used for plasticity models are detailed in The third inhibitory plasticity rule we used is an anti-Hebbian rule inspired by experimental data , 2011 anpost (t) and the presynaptic firing rates as νj(t). The traces of both presynaptic afferent and postsynaptic neuron thus have an average of post (t), changes negatively with changes in inhibitory weights: increased inhibition generates fewer postsynaptic spikes and vice versa for decreased inhibition. This means that average firing rates are inversely linked to average inhibitory weights, as follows:We were interested in plasticity rules with stable dynamics. For a better intuition on fixed-point dynamics and stability, we consider here a simplified dynamics of a mean-field model for both the Hebbian  and the ectively . NeglectThe steady state is computed by considering the vanishing point of the equation above (we assume that the presynaptic activity is nonzero); thus,post(t) increases (via reduction in inhibitory efficacy) when below ρ0 and decreases when above ρ0, creating a stable fixed point for the postsynaptic firing rate.This means that the postsynaptic activity νThe opposite is true for the anti-Hebbian plasticity rule. Changes in postsynaptic firing rate (with the same assumption as for the Hebbian plasticity rule) follow the following:1 and decreases when it is below, this rule is unstable. The postsynaptic firing rate eventually explodes or vanishes. We chose the simplest way to overcome these problems by setting a time-varying learning rate. Other intricate mechanisms could be implemented, but this is not the scope of our work.Because postsynaptic activity increases when it is above threshold ρith interval in which LTD occurred and ith interval in which the synapse underwent LTP, we can combine jw(t), at time t as follows:TLTD and TLTP are the number of intervals with LTD and LTP, respectively. We assume that LTP is always followed by LTD in TLTD =TLTP ± 1. The first term on the right-hand side of i >> 1, or, from TLTP for small κ), as follows:0, and does not depend on the initial weight jw(0).Our scaling plasticity rule has two different mechanisms: one for LTD and one for LTP. LTD is multiplicative, and LTP is additive . The comfollows:wj(t)=wj(Zμ(t) is the firing rate of the signal group μ at time t, filtered with a time constant τZ. The postsynaptic activity is also computed through a low-pass filter of its spike train, as follows:Y(t) is the activity of the postsynaptic neuron at time t filtered with a time constant τY. The correlation is then computed as follows:cov is the covariance between variables z and y, σz is the SD of variable z, and We quantified the response of the postsynaptic neuron to natural inputs with the Pearson correlation between postsynaptic firing rate and input firing rate fluctuations, per signal group. We computed the firing rate of a signal groups as the low-pass filter of the spike trains of its excitatory afferents, as follows:C as the difference between the correlation measure for preferred (μ = 9) and nonpreferred (μ = 1) input signals, as follows:Subsequently, we computed a performance index ΔC = 1) means that the preferred signal group has maximum correlation (C9 = 1) while the nonpreferred signal group has maximum anticorrelation (C1 = −1), indicating that the postsynaptic neuron is responding solely to the preferred signal group. Consequently, ΔC = −1 indicates that the postsynaptic neuron is responding solely to the nonpreferred signal group. A flat response is indicated by ΔC = 0. Maximum ΔC (either positive or negative) is only achievable if the preferred  and nonpreferred  are strictly anticorrelated. This is unlikely given that all input signals are independent, and they will feature periods of coactivation. We define as best performance when ΔC = 0 for all inhibitory inputs active (control), ΔC = 1 (or ΔC > 0) for one inhibitory population inactive, and ΔC = –1 (or ΔC < 0) when the other inhibitory population is inactive. Parameters used for computing correlations are detailed in Maximum positive performance index  was computed with a 1 s bin. The coefficient of variation of the interspike interval  was calculated as the SD of the interspike interval (ISI) of the output spike train divided by the mean ISI.The SD of the output firing rate . Individual plots were generated with Gnuplot (http://www.gnuplot.info/). Figures were generated with Inkscape (https://inkscape.org/).Simulations were run in Fortran, compiled with Intel Fortran Compiler 19.0 on an Intel-based Linux computer . Codes are available online , allowing us to obtain two differently tuned populations (presumably types) of inhibition. Excitatory and inhibitory afferents belonging to the same group shared temporal fluctuations in firing rates, termed input patterns, even if they belonged to different populations. In our simulations, input patterns could either be natural or pulse. Natural inputs were generated through an inhomogeneous Poisson process based on a modified OU process , such that neurons of the same signal group also had temporally correlated firing patterns   was similar to experimentally observed spike patterns in vivo  see . The restop see . in vivo . We usedD), averaged over 100 trials. Separating responses in phasic and tonic allowed us to discriminate changes in output because of the input onset , when excitation outweighs inhibition (phasic period), and slower integration of the pulse , when excitation and inhibition are balanced (tonic period). The transient period is best captured by limiting the phasic window to 50 ms, and we thus set the tonic window to the same duration to keep both window sizes symmetric.In the alternative pulse input regimen, we analyzed transient responses with 100-ms-long pulses of varying amplitudes . Pulses Fig. 2A), in one of the two inhibitory populations, while the synapses of the other inhibitory and the excitatory population remained fixed. This learning rule has previously been shown to generate inhibitory weight profiles that mirror the excitatory synaptic weight profiles of a postsynaptic neuron, imposing a firing rate fixed point  by balancing excitation and inhibition  in the other population. The homeostatic scaling rule upregulates or downregulates the entire synapse population to reach a predetermined target firing rate. Notably, this plasticity rule was purely local, taking only synaptic weights and postsynaptic firing rate into account, similarly to the experimentally observed scaling of inhibitory synapses . Unlike its Hebbian counterpart, the anti-Hebbian rule leads to indefinite increases in the firing rate of the postsynaptic neuron because correlated activity decreases synaptic weights . The anti-Hebbian plasticity rule is thus unstable . We found that we could prevent catastrophe without incorporating additional, complex dynamics by using a variable learning rate for the anti-Hebbian rule. For simplicity, we decreased the learning rate exponentially over time , but this could also be achieved through top-down control (see Discussion).Learning was implemented via three distinct inhibitory plasticity rules , in threFig. 3hibition , supporthibition . Next, wsynapses . Finallysynapses , 2011 anA, top). We followed previous work showing that the Hebbian plasticity rule (A) changes inhibitory synapses to provide precisely balanced inputs . Afferent synaptic weights of the excitatory population were set according to a receptive field tuning curve  while the efficacy of inhibitory afferents was governed by a synaptic plasticity rule for a period of 30 min. Learning was established by a Hebbian plasticity rule that potentiated synapses for coincident presynaptic and postsynaptic spikes and depressed synapses for sole presynaptic spikes (A). The plasticity rule was set to allow average postsynaptic firing rates of ∼5 Hz for natural inputs . We then tested the effect of changing the gain of all inhibitory afferents, while keeping their synaptic strengths fixed, by modulating their firing rates, from 50% to 150% of control rates. This change of input balance translated into changes in output rates  and spike patterns . When inhibition was equal or larger than excitation, the output was largely uncorrelated to any given input signal . When inhibitory firing rates fell below 90% of the control condition, the output first began to correlate with the preferred input signal. When inhibition became even weaker, the correlations increased, and even nonpreferred signals were articulated in the postsynaptic firing patterns .To begin, we constructed a standard cortical circuit motif with one excitatory and one inhibitory population  . Stimuli from nonpreferred afferents were largely ignored. This discriminability between transients of low- or high-amplitude pulses decreased when inhibition was downregulated  such that pulse stimuli from all signal groups caused a response. Increased inhibition, on the other hand, completely abolished transient responses to nonpreferred afferents . In all 3 cases , the postsynaptic neuron elicited most of its spikes within the phasic period of the total 100 ms input step . This indicates that strong postsynaptic responses are mostly driven by the onset of the presynaptic stimulation rather than the stimulus being integrated slowly over time, a consequence of the precise balance of excitatory and inhibitory inputs . The synapses of the excitatory and the other inhibitory population remained fixed (A).To study how plasticity can shape the emergence of distinct synaptic weight profiles, we incorporated inhibitory synaptic plasticity mechanisms into a model with two inhibitory populations. We started with a symmetric Hebbian plasticity rule in one of the two inhibitory populations: coincident presynaptic and postsynaptic spikes potentiated synapses, whereas sole presynaptic spikes depressed synapses  Fig. 3AAFig. 3A.ed fixed . Simulated fixed A.B), inhibitory weights of the plastic population stabilized (D–G). Whether the target firing rate  was reached depended on the synaptic strength of the other, static population of inhibitory synapses. If the static weights were weak, the plastic synapses increased their strength until the target firing rate was reached (C). If the static population provided strong inhibition (and thus kept postsynaptic firing below the target rate), weights from the plastic population would eventually vanish, before the target firing rate could be reached . Consequently, the shape of the static population determined the shape of the plastic population . As expected, the input/output correlation of the postsynaptic responses followed the effective synaptic weight profile , with distinct input/output correlations for turning either of the populations off . The Hebbian plasticity rule, because of the strengthening of synapses for coincident presynaptic and postsynaptic spikes, thus complemented additional inhibitory synaptic connectivity in establishing a state of detailed balance of excitatory and inhibitory inputs.After 30 min of stimulation with natural inputs compare B, inhibiabilized D–G. Wheting rate B,C was r reached C. If the reached C,G. Conspulation D,E. As eB; see Materials and Methods). With the homeostatic rule coactive, the Hebbian synapses, connections changing according to the Hebbian plasticity rule, developed a co-tuned profile from initially random weights , while the synapses following the scaling rule collapsed to a single value . Consequently, the postsynaptic neuron received precisely balanced inputs . The two plasticity rules cooperate to impose an average postsynaptic activity, and thus naturally work in harmony. Importantly, both plasticity rules are stable regarding their interaction with postsynaptic dynamics , and as such, not sensitive to initial conditions, and relatively robust to parameter choices, as long as the postsynaptic activity fixed point  imposed by both plasticity rules match.Next, we introduced plasticity to the second population of inhibitory afferents. We tested two different rules, beginning with a homeostatic plasticity rule, which (multiplicatively) scaled synapses down and additively potentiated synapses so that a fixed point for the postsynaptic firing rates was reached . We compared the output of the neuron in three scenarios: with both inhibitory populations active (control); with the co-tuned population inactive; and with the flat population inactive .We then studied the effects of differentially modulating the activity of the two inhibitory populations after their tuning curves had been established by the plasticity rules described above. First, we focused on the interaction of the connectivity created by Hebbian and the scaling plasticity rules , because the two populations (co-tuned and flat) created the same effect as the single (co-tuned) population. Deactivating either population had pronounced effects on postsynaptic responses. We increased the firing rate of the active inhibitory population to maintain the same average output firing rate of 5 Hz in the modulated conditions . Fluctuations in firing rate and membrane potential increased in both cases . When the co-tuned inhibitory population was turned off, the emerging imbalance of excitation and inhibition unmasked the excitatory tuning curve, thus increasing the chance of action potential generation when preferred signal populations were active . The compensatory increase in the activity of the flat population further quenched nonpreferred excitatory signals, leading to anticorrelated responses for nonpreferred input signals , reflecting the lack of postsynaptic firing during periods in which nonpreferred signals were active . The opposite effect could be observed when the flat population was deactivated. In this case, the lack of inhibition for nonpreferred signals gave rise to input/output correlations for nonpreferred signals, while preferred signals saw no response .With both populations active, the input/output correlation was indistinguishable from a model with one, homogeneous inhibitory population , were substantially increased for preferred inputs when the co-tuned population was deactivated, and the response to nonpreferred signals was completely diminished . When the flat population was deactivated, the postsynaptic neuron responded strongly to the nonpreferred inputs, but not to preferred inputs . Interestingly, modulating either of the inhibitory populations had similar effects on the postsynaptic response both in phasic and tonic periods, in contrast with the unmodulated control case, in which only phasic responses were postsynaptically elicited (E). Again, this reflects the state of balance between excitation and inhibition in the unmodulated control case, which only reveals transient input dynamics.Transient responses, when compared with the unmodulated control case E, top, wminished E, middled inputs E, bottomelicited E. Again,C). The anti-Hebbian rule, unlike the Hebbian, decreases synaptic weights for correlated activity, and sole presynaptic spikes increase synaptic weights. Such a rule can only either indefinitely increase the firing rate of the postsynaptic neuron or decrease it to zero . We accounted for the unstable nature of the anti-Hebbian plasticity rule  by controlling its learning rate, such that it decreased exponentially over time . With both Hebbian and anti-Hebbian rules active, initially random weights evolved into co-tuned and counter-tuned synaptic weight profiles (A). As learning slowed down because of the decreasing learning rate, the anti-Hebbian synapses (connections changing according to the anti-Hebbian plasticity rule) stabilized, and Hebbian synapses ceased to change once the target firing rate was reached . The anti-Hebbian plasticity rule, differently from the Hebbian one, is sensitive to initial conditions and choice of parameters because of its intrinsic instability . For example, different initialization of inhibitory weights requires distinct decay times for the learning rate (data not shown). Additional complexity in the formulation of the plasticity rule may solve these instability problems (Discussion).Instead of a purely homeostatic scaling rule, we also tried an experimentally inspired , 2011 anFig. 3profiles A. As lea reached B,C. The A), that is, co-tuned and counter-tuned populations, were similar to that with co-tuned and flat inhibitory populations. In the unmodulated balanced state, output behavior is near identical to previous results . The main distinction between the models with counter-tuned or flat inhibitory profiles is how they complemented the co-tuned inhibitory currents: the flat inhibition produced currents that tracked the co-tuned inhibitory currents, whereas counter-tuned inhibition produced inhibitory currents that were largely uncorrelated to the co-tuned inhibitory currents .Postsynaptic dynamics with two inhibitory populations with tuning that resulted from the combination of the Hebbian and the anti-Hebbian plasticity rules A, that iB, middle and right). As before . Deactivation of the co-tuned population resulted in positive correlation between postsynaptic activity and preferred signals, and negative correlation between output and nonpreferred signals . For transient stimulation, there was no discernible difference to the model with flat inhibition in the control state .When either the co- or the counter-tuned inhibitory populations were inactivated, fluctuations in both firing rate and membrane potential increased considerably  also had similar results in the postsynaptic response as turning off the flat inhibition (compare B–E); that is, nonpreferred input produced output activity with positive correlation  and strong postsynaptic activity for transient activation . Unlike before, turning off co-tuned inhibition produced elevated firing rate responses also for transient stimuli from signals directly neighboring the preferred input .Turning off counter-tuned inhibition B–E also  compare B–E; thatrelation D, green tivation E, bottomCpref, and nonpreferred, Cnon-pref, signals . Ideally, the sensory system should present three distinct responses for the three different modulatory conditions, which are captured by different values of ΔC. With unmodulated input (control), the output neuron should present uncorrelated activity with all input groups, and thus C > 0 for correlated output/preferred signals, and ΔC < 0 for correlated output/nonpreferred signals.For a better understanding of the differences between the three conditions studied here , we compared different modulation schemes quantitatively. We introduced the parameter A, gray), reflecting low levels of correlation between output and input signals . With downregulated inhibition, ΔC increased slightly in the model with one homogeneous inhibitory population. ΔC increased more considerably in a two-population model in which the co-tuned population was inactive , confirming an increased correlation between preferred signal and output . When the flat or the counter-tuned inhibitory populations were inactivated, we observed postsynaptic responses even to nonpreferred input signals , which led to negative ΔC . Inactivating the flat inhibitory population resulted in a slightly better discrimination: larger positive ΔC  and larger negative ΔC .In the control condition, we observed similar l models A, gray,  signals B, top. Winactive A, purpled output B, middle signals B, bottomative ΔC A, green.itive ΔC A, purpleative ΔC A, green.C) as the number of responses with >50% of the maximum postsynaptic firing rate (D). The single inhibitory population model could only produce responses to preferred input signals, while co-modulation of two inhibitory populations could promote responses to nonpreferred input signals, as well. Counter-tuned population achieved better  postsynaptic control than flat inhibition (C).To compare pulse responses of the three models, we quantified which input signal groups elicited a substantial response to a pulse signal. We defined the number of signals recovered C as the ing rate D. The sihibition C.The addition of a second population of inhibitory inputs thus gives rise to a more flexible response to varying stimuli. In summary, our results shed light on the role of the many types of interneurons in cortical areas , and shoWe investigated how several distinctly tuned inhibitory connectivity profiles emerge through biologically reasonable plasticity rules and how they interact with a tuned excitatory connectivity profile in a receptive field-like paradigm. We found that the two aspects of selective attention (enhancing response to targets and suppressing the response to distractors) were implemented in our model by two types of disinhibition. Our results indicate a simple neuronal mechanism to help disentangle (or bind) parallel sensory input streams and may represent a step toward understanding the neural basis of intricate behaviors, such as the “cocktail party effect,” focusing on a single voice in a crowded, cacophonous place.Our findings fit well with recent experimental results showing that pyramidal neurons in sensory areas of the cortex change their response to external stimuli depending on the context of the signal or attentional state . For exa+ interneurons. As the main source of inhibition to pyramidal cells, PV+ interneurons target postsynaptic neurons with similar preferred orientation . These results suggest a plasticity rule that is Hebbian if the postsynaptic neuron's voltage is artificially kept below the reversal potential of chloride, but anti-Hebbian in normal conditions. The scaling plasticity rule acted locally but squeezed the distribution of all synaptic strengths to a narrow regimen, providing a parsimonious explanation for the untuned, blanket inhibition often encountered in experiments (To explore how different inhibitory synaptic populations could form and interact, we split the inhibitory afferents into two populations and implemented a Hebbian-like inhibitory plasticity rule  in one periments , and proIt is unclear how biological circuits would avoid such catastrophe, but in our model we could balance the effect of the two opposing rules and remain at plausible levels of postsynaptic activity by including a modulatory term that controlled the learning rate of the anti-Hebbian plasticity rule. While this mimics some of the observed modulatory control of plasticity through other neuronal types , the reaInterestingly, artificial networks have been shown to develop similar receptive field profiles to the ones explored here when they are trained to solve multiple tasks . Yang etTo explore the interaction between two distinct inhibitory plasticity rules without confounds, we made the simplifying assumption that excitatory synapses would remain fixed but see . ObviousIn conclusion, we predict that various GABAergic interneurons in the same cortical region must obey a range of different inhibitory synaptic plasticity rules, to restore or alter neuronal stimulus selectivity as appropriate and necessary. Such evidence would inform the theoretical framework presented here, and in turn inspire future computational modeling.


NO…H−N, with O…H distances of 2.15–2.23 Å. The N–O groups participating in the formation of H-bonds have greater bond lengths (~1.29 Å) as compared with nonparticipating groups (~1.27 Å). The nitronyl nitroxide and iminonitroxide diradicals showed an intramolecular antiferromagnetic interaction, with J = −77.3 and −22.2 cm−1, respectively (H = −2JS1⋅S2).In contrast to diradicals connected by alternant hydrocarbons, only a few studies have addressed diradicals connected by nonalternant hydrocarbons and their heteroatom derivatives. Here, the synthesis, structure, and magnetic properties of pyrrole-2,5-diyl–linked bis(nitronyl nitroxide) and bis(iminonitroxide) diradicals are described. The diradicals show characteristic electron spin resonance spectra in dilute glassy solutions, from which conclusions about the presence of distinct conformations, their symmetry, and interspin distance were made. X-ray diffraction analysis of the diradicals revealed that paramagnetic moieties lie in the plane of the pyrrole ring, because of the formation of an intramolecular hydrogen bond, O Delocalized high-spin organic compounds are actively studied with the aim of creating electrical conductors ,2,3, magEST|) in a disjoint system, the ground state might depend on π-systems to which it is applied and on inclusion of heteroatoms in such a system.Against the background of actively investigated diradicals linked by alternant hydrocarbons, there are only a few reports about diradicals that are linked by nonalternant systems ,26,27,281 and bis(iminonitroxide) 2 diradicals shown in 1 and 2, their X-ray diffraction (XRD) structures, electron spin resonance (ESR) spectra, and the temperature dependence of magnetic-susceptibility values. After analysis of the obtained magnetic data, values of the parameters of the intramolecular exchange interaction were compared with those in other bis(nitronyl nitroxide) and bis(iminonitroxide) diradicals with a five-membered aromatic linker. In this study, we focused on pyrrole-2,5-diyl as a nonalternant hydrocarbon spacer and fully investigated bis(nitronyl nitroxide) 1 and 2 were prepared by interaction of dicarbaldehyde 3 with 2 equivalents of bis-hydroxylamine 4 with subsequent oxidation of the product. If the condensation reaction is carried out in dimethylformamide in the presence of 4 equivalents of Me3SiCl, then diadduct 8, precipitating into a solid phase, contains virtually no impurities, and after oxidation, gives rise to 1 with the overall yield of 12% , biradical 7 (20% yield), and trace amount of mixed diradical 9 , an intermolecular process of condensation of hydroxylamine and aldehyde groups takes place, resulting in the formation of a dinitron bridge moiety between pyrrole rings and eventually—after oxidation—in the formation of biradical 7. Fortunately, after recrystallization from the CH2Cl2–heptane mixture, the biradical 7 precipitated into a solid phase in the form of crystals suitable for XRD analysis, which revealed the structure of this complicated compound  and 1.293(2) Å) are notably greater than the others (1.274(2) and 1.274(2) Å). In mixed diradical 9, the O atoms are disordered –1.242(4) and 1.243(3)–1.267(2) Å, respectively.The X-ray structural analysis of diradicals d, O…H−N , with O…1, the shortest intermolecular contacts with participation of nitroxide groups are five contacts between O atoms and H atoms of methyl groups (2.526–2.604 Å); in 2 there are pair contacts between O atoms and a C−H pyrrole ring (O…C 3.361 Å) to form ribbons; in 9 there are contacts between O atoms and HCH3 atoms lying in the range of 2.553–2.708 Å.In all nitroxides, there are no short intermolecular contacts between nitroxide groups. In the crystal structure of 1, 2, and 9 are typical of diradicals with S = 1 and comprise a characteristic spectrum in the region 340 mT (g = 2) and a weak line in half-field. Continuous-wave ESR spectra of diluted glassy solutions of D and E, and the value of D provided an estimate of the distance between the effective point dipoles as D = 3/2(g2β2r−3), while the E/D ratio gave an indirect measure of the degree of coplanarity of the two radical moieties in the molecule. The spectra were modeled within the framework of second-order perturbation theory to account for a rather noticeable asymmetry, using the expressions from ref.  and spin2 and 9, the spectrum is a superposition of spectra of two distinct diradicals with well-defined and quite different geometry , a single conformation is sufficient to reproduce the spectrum of 1. Furthermore, the symmetry of this molecule is so high that the spectrum contains explicitly displayed hyperfine interactions with four equivalent nitrogen atoms, which could be reproduced in modeling by augmenting the Hamiltonian with the relevant 1, the relative intensity of the doublet at the spectrum center decreases with decreasing diradical concentration  mT, also indicating high symmetry of this diradical in a diluted glassy solution. 1. Although for tion see ; this fi2 was modeled as a superposition of two spectra  indicates that the symmetry of the corresponding conformation of the diradical is far from axial; a resolved doublet structure appears in the center of the spectrum. In contrast to the other two diradicals, in the experimental spectra of 9, this central doublet did not depend on the concentration of the diradical  dependencies was performed using a model of an exchange-coupled dimer (spin Hamiltonian H = −2JS1⋅S2). The best-fit values of the g-factor and exchange coupling parameter J are 1.99 (±0.02) and −77.3 (±1.2) cm−1 for 1 and 2.01 (±0.01) and −22.2 (±0.1) cm−1 for 2, respectively. Magnetochemical analysis is in agreement with the results of theoretical studies by S. Datta . Th. Thp-phep-phenylene parity, which explains the observed intramolecular exchange interactions of antiferromagnetic character.Thus, in this study, nitronyl- and imino-nitroxyl diradicals with the pyrrole-2,5-diyl coupler were synthesized and thoroughly investigated. In these diradicals, the paramagnetic parts lie in the plane of the pyrrole ring because of the formation of an intramolecular H-bond: O…H−N. ESR spectroscopy gave insight into the structures of the diradicals in glassy solutions and provided a quantitative estimate of spin–spin distances. An additional useful outcome of the ESR analysis, covered in more detail in H-Pyrrole-2,5-dicarbaldehyde 1/2, where NA, μB, and k are the Avogadro number, Bohr magneton, and Boltzmann constant, respectively.Magnetic susceptibility measurements were taken on SQUID magnetometer Quantum Design MPMSn,m)/NEVPT2 level were done using the ORCA 4.0 package [Quantum-chemical calculations were performed at the X-ray geometries. Computations at the BS-DFT level were done via the Gaussian 09 package , whereas package .The high-spin and broken-symmetry single determinants were calculated using the B3LYP functional in conjunction with the 6-311+G basis set. The internal stability of all SCF solutions was confirmed by stability analysis. The isotropic exchange parameter was estimated in accordance with the spin-projected scheme proposed by Yamaguchi and coworkers .n,m)/NEVPT2 calculations, the def2-TZVP basis set was utilized. In the CASSCF/NEVPT2 method, the reference wave function is calculated at the CASSCF level, and then the remaining electron correlation is included via the multiconfigurational NEVPT2 approach. The SA- and SS-CASSCF procedures were employed to obtain the MOs to be used at the NEVPT2 step. The SA-CASSCF MOs were obtained from the average of the lowest singlet and triplet states with equal weights. The restricted open-shell Hartree-Fock/second-order Moller-Plesset perturbation theory natural MOs optimized for the triplet state served as an initial guess. The SS-CASSCF MOs were obtained starting from the corresponding SA-CASSCF MOs. The CASSCF energy and orbital gradient convergence tolerances were set to 10−9 and 10−6, respectively. The RI approximation was applied throughout. The J values shown in In the CASSCF(


UPLC-MS/MS was used to detect the probes and their metabolites in rat plasma and rat liver microsomes. The in vitro results revealed that the half-maximal inhibitory concentration values of bupropion and tolbutamide in RLMs were 8.79 and 20.17 μM, respectively, indicating that poziotinib showed varying degrees of inhibition toward cyp2b1 and cyp2c11. Poziotinib was a competitive inhibitor of cyp2b1 and cyp2c11, with Ki values of 16.18 and 17.66 μM, respectively. No time- or concentration-dependence of inhibition by poziotinib was observed toward cyp2b1 and cyp2c11 in RLMs. Additionally, no obvious inhibitory effects were observed on the activity of cyp1a2, cyp2d1, cyp2e1, and cyp3a1/2. In vivo analysis revealed that bupropion, tolbutamide, phenacetin, and chlorzoxazone showed significantly different pharmacokinetic parameters after administration (p < 0.05); there was no significant difference in the pharmacokinetic parameters of dextromethorphan and midazolam. These results show that poziotinib inhibited cyp2b1 and cyp2c11, but induced cyp1a2 and cyp2e1 in rats. Thus, poziotinib inhibited cyp2b1 and cyp2c11 activity in rats, suggesting the possibility of interactions between poziotinib and these CYP substrates and the need for caution when combining them in clinical settings.Poziotinib is an orally active, irreversible, pan-HER tyrosine kinase inhibitor used to treat non-small cell lung cancer, breast cancer, and gastric cancer. Poziotinib is currently under clinical investigation, and understanding its drug-drug interactions is extremely important for its future development and clinical application. The cocktail method is most suitable for evaluating the activity of cytochrome P450 enzymes (CYPs). As poziotinib is partially metabolized by CYPs, cocktail probes are used to study the interaction between drugs metabolized by each CYP subtype. Midazolam, bupropion, dextromethorphan, tolbutamide, chlorzoxazone, phenacetin, and their metabolites were used to examine the effects of poziotinib on the activity of cyp1a2, 2b1, 2d1, 2c11, 2e1, and 3a1/2, respectively. The  Drug-drug interaction (DDI) occurs during the co-administration of two or more drugs and may increase toxicity or weaken the therapeutic effect of the drugs, leading to the occurrence of serious clinical complications such as adverse drug reactions or treatment failure . DDI is CYP is a superfamily of oxygenases with mixed functions that are involved in the metabolism of endogenous and exogenous substances and are abundantly present in the liver and intestines . CYPs arCYP2C is the second most abundant isoenzyme subfamily. Its main isoenzymes are CYP2C9 and CYP2C19 can metabolize ∼25% of all drugs, of which CYP2C9 metabolizes 16% of all drugs, e.g., oral anticoagulants, non-steroidal anti-inflammatory drugs, various fatty acids, and steroid hormones . CYP1A2 The cocktail method, involving the simultaneous use of several probe substrates, has been used to investigate DDIs and examine changes in CYP activity in drug metabolism . The FDAEGFR and HER2 exon 20 mutations (Poziotinib (HM781-36B) is a new, orally active, irreversible pan-HER tyrosine kinase inhibitor . Poziotiutations . Analyseutations . This evin vivo and in vitro. The results of this study will help to understand the potential drug interactions of poziotinib.It is extremely important to select the appropriate probe substrate for each CYP450 enzyme. Studies reporting the cocktail probe approach have used phenacetin for CYP1A2, bupropion for CYP2B6, tolbutamide for CYP2C9, dextromethorphan for CYP2D6, chlorzoxazone for CYP2E1, and midazolam for CYP3A4 (Poziotinib (purity > 98%) was purchased from the Beijing Sunflower and Technology Development Co. Ltd. . Bupropion hydrochloride (purity > 98%) and phenacetin (purity > 99%) were purchased from TCI Chemicals . Tolbutamide (purity > 97.5%) and chlorzoxazone (purity > 98%) were purchased from J&K Chemical Ltd. (Shanghai China). α-Naphthoflavone (purity > 98%), Ticlopidine (purity > 98%), sulfaphenazole (purity > 98%), quinidine (purity > 98%), sodium diethyldithiocarbamatre (purity > 97%), ketoconazole (purity > 99%) were purchased from Aladdin. Midazolam injection was obtained from Nhwa Pharma. Co.  and NADPH from Roche . The internal standard (IS) of diazepam (purity > 98%) was purchased from the Tianjin KingYork Pharmaceutical Co. Ltd. . Chromatographic grade methanol and acetonitrile were purchased from Merck Co. Ltd. . Rat liver microsomes (RLMs) were prepared in our laboratory . All othSamples were analyzed by a UPLC-MS/MS system equipped with a triple quadrupole mass spectrometer  and Acquity UPLC BEH C18 column  at 40°C. The mobile phase consisted of acetonitrile (A) and 0.1% formic acid (B) with a linear gradient elution at 0.4 ml/min for 3 min. The elution procedure was as follows: 0.0–0.6 min (rapidly rising from 10 to 50% A), 0.6–1 min (increasing from 50 to 80% A), 1–2 min (increasing from 80 to 95% A), 2–2.5 min (maintained at 95% A), and 2.5–2.6 min (reduced to 10% A).Mass spectrometer contained a triple quadrupole and an ESI source. The optimized parameters of multiple reaction monitoring detection included a source temperature of 150°C and desolvation temperature of 500°C. The MS conditions, chemical structure, and chromatograms for the probe drugs and IS are presented in 50) of poziotinib was determined with all of the CYPs. Phenacetin, bupropion, tolbutamide, dextromethorphan, chlorzoxazone, and midazolam  were mixed to form a cocktail of probe substrates for measuring CYP450 activity. To this cocktail, 1 mg/ml of RLMs, 100 mM potassium phosphate buffer (pH 7.4), poziotinib  were added to obtain a final volume of 200 μL. After pre-incubation of this mixture for 5 min in a shaking water bath at 37°C, 1 mM NADPH was added to start the reaction. The reactions were allowed to proceed for 30 min, after which 200 μL of acetonitrile and 20 μL of IS were added to terminate the reactions. The mixtures were vortexed for 30 s and centrifuged again at 13,000 rpm for 5 min. Then, 2 μL of the supernatant was injected into the UPLC-MS/MS system for analysis.The cocktail method was employed to analyze the effects of poziotinib on cyp1a2, cyp2b1, cyp2c11, cyp2d1, cyp2e1, and cyp3a1/2. First, 100 μM poziotinib was used to test its direct inhibitory effects RLMs. Then half-maximal inhibitory concentration , and NADPH was pre-incubated at 37°C for 0, 5, 10, and 20 min; Methanol instead of poziotinib was performed as control. Then 20 μM bupropion or 100 μM tolbutamide was added and incubated at 37°C for 30 min. The reactions were carried out and analyzed in triplicate as described in 2.3.ad libitum for 2 weeks for acclimation. All of the experimental procedures followed the guidelines for the care and use of laboratory animals and were approved (No. wydw 2019-650) by the Animal Experimental Ethical Inspection of Laboratory Animal Center, Wenzhou Medical University.Male Sprague-Dawley rats were supplied by the Animal Experimental Center of the Wenzhou Medical University . Animals were kept under standard conditions with a 12-h day-night cycle and were provided water and food Twelve male Sprague-Dawley rats (230 ± 20 g) were randomly divided into treated and control groups, with 6 in each group. Dose of probe substrate mixture  was dissolved in 0.5% CMC-Na solution: 10 mg/kg, Toluamide: 1 mg/kg. After 7 days of continuous oral administration of poziotinib  to the experimental group, the two group rats were treated with an oral gavage of probe substrate mixture. After 0.083, 0.25, 0.5, 1, 2, 3, 4, 6, 8, 12, and 24 h following administration of poziotinib, 300 μL blood was collected from the tail vein of each rat, transferred to a heparinized centrifuge tube, and immediately centrifuged at 4,000 rpm for 10 min. The supernatant was mixed with 200 μL of acetonitrile and 20 μL of 0.5 μg/ml diazepam (IS), vortexed for 30 s, centrifuged at 13,000 rpm for 5 min, and the supernatant was injected into the UPLC-MS/MS system for analysis.p < 0.05 was considered statistically significant. GraphPad  was used to calculate IC50 and plot the plasma concentration-time curves and inhibition plots .Pharmacokinetic parameters were calculated using DAS software (Version 3.2.8). SPSS software  was used to analyze the significance of differences between the main pharmacokinetic parameters. 50 values of the six probe substrates  from those of the control group ((0–t), AUC (0–∞), and Cmax values of the treated group were significantly reduced by 56.08, 55.81, and 48.06%, respectively. In addition, t1/2, Vz/F, and CLz/F values were significantly increased by 45.45, 203.82, and 116.85%, respectively. The higher AUC and Cmax values and lower Tmax values of the control group indicated that poziotinib induces cyp1a2 activity, thus accelerating the metabolism of phenacetin and reducing its plasma drug concentration in rats.The pharmacokinetic parameters of phenacetin were used to describe the inhibitory effects of poziotinib on cyp1a2 activity. The area under the plasma concentration-time curve of phenacetin  in the tol group . Compare(0–t), AUC(0–∞), MRT(0–t), and Tmax values in the treated group were 1.39, 1.46, 1.41, and 1.63-fold higher than those of the control group, respectively, whereas the CLz/F and Vz/F values were 1.47 and 1.04-fold lower than those of the control group, respectively  and AUC (0–∞) values were significantly higher in the treated group than in the control group (p < 0.05), increasing by 45.87 and 51.60%, respectively, whereas CLz/F was significantly lower than control group by 50% , AUC(0–∞), and Cmax values of the treated group were significantly reduced to 1.95, 1.94 and 2.51-fold that of the control group, respectively. The MRT (0–t), MRT (0–∞), Vz/F, and CLz/F of the treated group were 1.60, 1.56, 1.75, and 1.96-fold higher than those of the control group  > IC50 (tolbutamide) > IC50 (dextromethorphan) > IC50 (phenacetin) > IC50 (chlorzoxazone) > IC50 (midazolam). According to literature, IC50 < 1 μM is considered to be strong inhibition, 1 μM < IC50 < 10 μM moderate inhibition, and IC50 > 10 μM weak inhibition (50 = 8.79 μM) and CYP2C11 (IC50 = 20.17 μM), respectively, whereas its inhibitory effect on the other four CYPs was not obvious . A more detailed investigation of the inhibitory effect of poziotinib on cyp2b1 and 2c11 revealed that the inhibition of both cyp2b1 and 2c11 by poziotinib was competitive, with Ki values of 16.18 and 17.66 μM, respectively.The results of hibition . Our resAs the approved EGFR inhibitor, poziotinib is a quinazoline derivative, same as afatinib, erlotinib, gefitinib, dacomitinib. The above quinazoline derivatives are all metabolized by CYP 2D6 and CYP 3A4, however, they have different impacts on CYPs activity. Afatinib has no inhibition or induction on cytochrome P450 (CYP) enzymes . ErlotinThis competitive inhibition indicates that the inhibitor, poziotinib, and the enzyme substrate compete at the binding site, thereby interfering with the binding of the substrate to the enzyme and reducing enzymatic activity. In addition, we did not observe any time- and concentration-dependent inhibitory effects of poziotinib on cyp2b1 and 2c11 in RLMs, which implies that the activity of these enzymes did not change over time during the incubation period. These results indicate that cyp2b1 and cyp2c11 were reversibly inhibited by poziotinib. Therefore, attention should be paid to the combined use of poziotinib and drugs to look for possible interactions of poziotinib with drugs that are metabolized by cyp2b1 or cyp2c11 to prevent the occurrence of serious adverse reactions.(0–t) and CLz/F values of the treated group were 1.40 and 0.68-fold that of the control group values, respectively. Similarly, for cyp2c11 and tolbutamide, the AUC(0–t) and CLz/F values of the treated group were 1.43 and 0.5-fold that of the control group values, respectively. These results indicate that the activity of cyp2b1 and 2c11 was inhibited by poziotinib, which resulted in increased systemic exposure of bupropion and tolbutamide in rats and slower clearance rates. This was consistent with the results of the in vitro incubation with RLMs, confirming the inhibitory effect of poziotinib on the activity of cyp2b1 and 2c11.We compared pharmacokinetic parameters of the six CYP probe substrates as a result of their interaction with poziotinib in rats. For cyp2b1 and bupropion, the AUCmax values in the treated groups were significantly lower than those in the respective control groups, whereas CLz/F values were much higher than those in the control groups. Thus, poziotinib accelerated the elimination rates and reduced the plasma concentrations of phenacetin and chlorzoxazone in rats. However, our in vitro results did not reveal any inhibitory effect of poziotinib on cyp1a2 and 2e1. This could imply that the observed induction in rats may be caused by gene regulation, which increased protein synthesis and accelerated the metabolism of the probe substrates; however, further research is needed to confirm this hypothesis (in vivo or in vitro.This inhibition could be attributed to the direct binding of poziotinib to the substrate binding site in the enzymes, leading to a decrease in the metabolic activity of these two enzymes. Another study had postulated that long-term use of poziotinib may affect the expression of metabolic enzymes . In addipothesis . PoziotiIn conclusion, this study shows that poziotinib competitively and reversibly inhibited the metabolism of cyp2b1 and cyp2c11 substrates to varying degrees without any time- or concentration dependence. Poziotinib had no obvious inhibitory effect on the other four CYPs. The results of this study will help in further study of poziotinib in humans and draw attention to its potential DDIs when combined with other drugs metabolized by cyp2b1 and cyp2c11 to enable clinically effective and safe use of poziotinib.


This paper investigates the underlying driving force in strategic decision-making. From a conceptual standpoint, few studies empirically studied the decision-maker’s intrinsic state composed of entropy and uncertainty. This study examines a mutual information theory approach integrated into a state of qualia complexity that minimizes exclusion and maximizes the interactions of the information system and its dynamic environment via logical metonymy, illusion, and epigenetics. The article questions whether decision-makers at all levels of the organization are responding from the consciousness of an objective quale from a more subjective qualia awareness in the narrow-sense perspective of individual instances of their conscious experience. To quantify this research question, we explore several hypotheses revolving around strategic information system decisions. In this research, we posit that the eigenvalues of factor analysis along with the reduction in the uncertainty coefficients of the qualia entropy will be balanced by the quale enthalpy of our information theory structural equation model of trust, flexibility, expertise, top management support, and competitive advantage performance. We operationalize the integration of the aforementioned top management support, information systems competencies, and competitive advantage performance concepts into the qualia consciousness awareness and information theory quale framework. One of the basic principles of quantum mechanics revolves around the energy of the system. In this context, the Hamiltonian is the operator corresponding to the total energy of the system. It is the set of possible outcomes for the total energy of a system and is of fundamental importance in the evolution of quantum theory. In determining the Hamiltonian of a quantum system, eigenvectors are used to determine the different energy eigenstates, and their eigenvalues are the corresponding energy levels used to find the eigenvectors. In this article, we propose that information systems (IS) follow these same principles ,2,3,4,5.The second law of thermodynamics states that systems tend to reach a state of equilibrium. In other words, any organization, group of individuals, or information system, no matter how highly organized it may be at any given instant, tends toward greater disorder or randomization, called entropy (S). Entropy can be related to the random movements of molecules and can be measured by T∆S, where T is the absolute temperature of the system. When the system is at equilibrium, there is no net reaction and the system has maximum entropy with no capacity to do useful work: Q = T∆S. Work can be done by systems tending toward equilibrium, and a measure of this work is W′ = −∆H + T∆S. Free energy is defined as ∆G = ∆H − T∆S, where ∆G = −W′, such that when the measure of W′ is positive and can do useful work, then the measure of ∆G is negative and vice versa.A system at equilibrium has three characteristics: There are two opposing tendencies or reactions; both reactions are in full operation at equal speeds, and any change in the conditions, such as concentration, pressure, or temperature, produces a corresponding change in the system. Any change in conditions forces the system to settle down into a new state of equilibrium with new proportions of reactants and products that correspond to these new conditions. In the study of dynamical systems, discrimination of the presence of correlations in time series emerges as one key task. Given a time series, one of the most natural measures of disorder and, thus, the absence of correlation, is Shannon entropy , which sThe reduction of uncertainty can be quantified as mutual information (MI). MI can also be described in terms of P2 as MI = H[P] + H[Q] − H[PQ], where Q is another discrete probability distribution . Let X aTsuchiya et al.  claim thFor example, if an organization has a trusting IS–business relationship, then it can continue to have trust, or there can be no trust and trust is developed, or there is trust that turns to no trust, or finally, there is no trust that leads to no trust. Uncertainty can be designated as having no trust in the IS–business relationship. Decision-makers are viewing trust, expertise, top management support, and flexibility in the present state. The amount of information lost is known as integrated information. Here, we would look at trust, expertise, top management support, and flexibility in view of performance and competitive advantage. All possible subsets of a system determine the composition and, therefore, we must study the system ceteris paribus, as there are conceivably an infinite number of variables. Despite this understanding of the importance of IS competencies in business performance, little research examined how a firm refines IS competencies over time. This article fills this gap in the literature by examining empirically how a firm refines IS competencies such as top management support in the context of competitive advantage performance. Below, we define the concept of IS competencies in this context. Based on this categorization, we define IS competencies as those attributes of IS that cannot be easily imitated by other IS units in different firms . A flexible IS infrastructure allows for the sharing of data and applications through communication networks. It pertains to arrangements of hardware, software, and networks such that data and applications can be accessed and shared within and between suppliers, customers, and vendors. A flexible IS infrastructure helps in integrating disparate and geographically distributed manufacturing systems and ensures the cost effectiveness of the operation and support of IS applications. Therefore, a flexible infrastructure becomes a critical source of advantage and performance for the firm.Porto de Albuquerque and Christ  studied A flexible infrastructure with shared IS business expertise is a critical source of advantage and performance for the firm.Hypothesis 1: IS infrastructure flexibility will have a positive relationship with IS business expertise.Hypothesis 2: Competitive advantage performance will have a positive relationship with IS expertise.Makkonen and Vuori  pointed Hypothesis 3: A trusting IS–business relationship will have a positive relationship with competitive advantages.The literature does not provide a consistent picture of payback for IT investment  of the IS infrastructure flexibility will proceed toward a greater equilibrium and the organization will evolve toward greater competitive advantage.From the ITQ perspective, data were analyzed using hierarchical regression analysis and structural equation modeling (SEM) to understand the broad objective relationship of top management support with IS competencies and competitive advantage performance. The QCA data were analyzed utilizing both factor analysis eigenvalues and entropy uncertainty coefficients.We used the following items to measure trusting IS–business relationships: “our business managers and IS personnel share responsibility in setting business strategy”; “our business managers and IS personnel jointly set business strategy”; “our business managers and IS personnel appreciate each other’s contributions in setting business strategy”; “our business managers and IS personnel periodically consult each other in setting business objectives”; and “our business managers and IS personnel trust each other in setting business objectives”.Finally, we used the following items to measure competitive advantage: “employees are important to competitive advantage performance”; “external reports are important to competitive advantage performance”; “competitors are important to competitive advantage performance”; and “top managers seek outside information to competitive advantage performance.”Given the multiple relationships in our model, we used LISREL for our quale data analysis. One of its primary strengths is its simultaneous estimation of the measurement and structural models. We used SEM to test our hypotheses see .2 = 237, degrees of freedom (df) = 94, comparative fit index = 0.933, goodness-of-fit index = 0.960, normed fit index = 0.895, root-mean-square error of approximation = 0.0671, p ≤ 0.00452. Our results supported all seven hypotheses: Hypothesis 1, IS infrastructure flexibility will have a positive relationship with IS business expertise (B = 0.67); Hypothesis 2, competitive advantage performance will have a positive relationship with IS expertise (B = 0.58); Hypothesis 3, IS business expertise will have a positive relationship with a trusting IS–business relationship (B = 0.29); Hypothesis 4, competitive advantage performance will have a positive relationship with IS top management support (B = 0.77); Hypothesis 5, IS top management support will have a positive relationship with a trusting IS–business relationship (B = 0.34); Hypothesis 6, IS top management support will have a positive relationship with IS business expertise (B = 0.63); and Hypothesis 7, IS top management support will have a positive relationship with IS infrastructure flexibility (B = 0.49).R2 of 0.415; this means that nearly 42% of the variance in the dependent variable (competitive advantage performance) was explained by the independent variable flexibility of the IS infrastructure, top management support, IS business expertise, and trust. p ≤ 0.000. p ≤ 0.01. Expertise 2 and 3 had significances of p ≤ 0.001 and p ≤ 0.002, respectively. Trust 3 had p ≤ 0.001, and top management support 1, 2, and 3 all had p ≤ 0.000.LISREL was used for our quale data analysis. We checked the measures by assessing their reliability and unidimensionality. We iteratively revised the measurement model by dropping, one at a time, the items that shared a high degree of residual variance with other items. Cronbach’s alpha for all 17 items was 0.855, as illustrated in p = 0.000. The interactive effects of expertise, infrastructure, and trust contributed significantly to competitive advantage, and the least-squares regression was weighted by top management support. To assess discriminant validity, we set some regression weights to 1 and did not estimate them to determine whether their correlations were significantly different from unity. When competitive advantage increased by 1, expertise 1 increased by 1 as well. The same was true for competitive advantage on top management support 1. The probability of obtaining a critical ratio as large as the absolute value was less than 0.0001 for most of the regression weights. The regression weight for the latent variable competitive advantage in the prediction of expertise 2 (0.522 ***) was significantly different from 0 at the 0.000 level. The same was true for the regression weight for competitive advantage on top management support 2 (0.661 ***). The standard error shows how accurately the values of the free parameters were estimated. The standard error was small, 0.08 (competitive advantage); therefore, we believe that the parameters were estimated correctly. For each free parameter, the parameter estimate divided by its standard error produces a t-value. If a t-value is between –1.96 and 1.96, it is not significantly different from zero; thus, fitting it to zero will not make the fit of the model significantly worse. For example, the relationship between competitive advantage and expertise had an estimate of 0.58 ** and a standard error of 0.08.The initial factor analysis report in Our ITQ quale results generally supported the validity of our decision-makers’ broad objective contribution to the validity of our research model. We showed, from a quale perspective, that top management support enhanced IT infrastructure flexibility, a trusting IS–business relationship, IS business expertise, and competitive advantage performance. In turn, IS business expertise increased competitive advantage performance. Top management support generated IS competencies, and this directly impacted the firm’s ability to improve competitive advantage performance. We showed that the flexibility of the IT infrastructure is a critical organizational IT capability for improving competitive advantage performance. In other words, IT infrastructure flexibility is a capability that has strategic ramifications and provides top management with the ability to respond rapidly to critical requirements for firm survival and success. In a similar manner, trust between IS personnel and their business partners, as well as IS expertise to run flexible IS, all benefit competitive advantage performance through the support of top management. We showed that top management support coupled with IT infrastructure flexibility, a trusting IS–business relationship, and IS expertise enabled organizations to perform at a higher level through the competitive advantage performance that they generated.Through the QCA qualia results, we were able to show that decision-makers conveyed, through their conscious awareness, that they were able to lower the entropy of the organization when information needs changed, and that they were able to reconfigure and adapt their IT infrastructure according to their information-processing needs. Decision-makers’ individual subjective narrow awareness in their consciousness is instrumental in generating relevant and timely information in the ITQ sense so that firms are more likely to develop competitive advantages to improve their performance. By following this thought process, top management decision-makers are better equipped to exploit existing competencies of trust, expertise, and flexibility to generate long-term performance opportunities for competitive advantage.Although our study used the same respondents to provide data on both our independent and dependent variables, we attempted to overcome this common method bias by both measuring a broad objective ITQ quale approach and balancing it with the narrower subjective QCA qualia consciousness of the decision-makers. The combined results indicate that this bias did not seem to be a major problem. However, we recognize that it still may have biased our results. Another limitation that we tried to overcome was the static cross-sectional snapshot of top management support, capabilities, and competitive advantage. Although this approach makes it difficult to address the interaction of these issues, we built on the data and findings of a previous similar study  to improve the longitudinal perspective of how top management support, IT capabilities, and trust lead to competitive advantage performance that is created over time.Our ITQ SEM quale approach showed that IT infrastructure flexibility, top management support, trust, and expertise can generate competitive advantage and, thus, increase a firm’s ability to leverage performance enhancement. Top management is able to funnel its subjective QCA consciousness into more broad-based objective ITQ information to respond to market opportunities, thereby creating improvements in competitive advantage and firm performance. For example, our study showed that it is important that decision-makers overcome their subjective narrow QCA qualia to lower the entropy of the organization to develop IT infrastructures that can facilitate the leveraging of competitive advantage performance by the organization. Our study showed the importance of the intersection of QCA qualia consciousness with ITQ and the value of decreasing entropy within the organization as demonstrated in Although entropy can describe globally the level of disorder of a process, there is also the probability that an analysis of time series using solely Shannon entropy could be incomplete. The reason for this is that an entropy measure does not quantify the degree of structure or patterns present in a process. Consequently, we used our framework to propose that ITQ statistical complexity is necessary to characterize a system and explore the QCA mindset of decision-makers. To observe more clearly the temporal changes in ITQ informational efficiency, we computed the uncertainty coefficient and used eigenvalues from factor analysis to measure entropy in all of the QCA decision variables studied. We hypothesized that if the value of the Shannon S interpretation is 2/3lnk < S ≤ lnk, then the organizational system has a high level of disorder, entropy, and uncertainty. However, if 1/3lnk < S ≤ 2/3lnk, then the organizational system is somewhat ordered and we should determine whether any of the factors should be strengthened. Finally, if 0 < S ≤ 1/3lnk, then the organizational system is highly ordered, with certainty and enthalpy, and the variables used to measure organizational sustainability are grouped around a common low uncertainty, high efficiency, and low entropy point.In other words, we adopted a variation in the information theory approach that involves the main concepts of entropy and uncertainty. These properties permit a consideration of entropy as a measure of the uncertainty of random QCA variables and provides the theoretical basis for measuring our model ITQ information. As our ITQ information increases, our knowledge of our organizational model decreases the degree of QCA uncertainty. By utilizing the concept of entropy, we can precisely measure the degree of uncertainty of the QCA random variables describing the ITQ information relationship between trust, expertise, flexibility, and competitive advantage in our organizational system. For example, trust and infrastructure competencies (IS competencies) were an important area of inquiry for both top managers and academicians. It is now widely believed that, to achieve a sustainable competitive advantage, a firm must be able to renew IS personnel, IS business trust, and infrastructure flexibility. Although the literature discussed the importance of competitive advantage through IS, little is known about how top management support renews IS competencies and helps in achieving competitive advantage. Even less is known about trust and the organization’s ability to form a relationship between IS groups and business groups so that these groups can work together to solve organization-wide problems. This is considered a critical attribute of IS competencies.In this research, we took a step in this direction by analyzing the relationship between IS competencies for business advantages and investigating IS infrastructure, expertise, trust, and top management support. We collected data through a survey of 339 IS and business managers from service and manufacturing participants. We found that top management support was positively related to IT infrastructure flexibility and trust from both an ITQ quale and a QCA qualia perspective. Moreover, IS infrastructure flexibility and trust were both positively related to competitive advantage performance. Finally, IS business expertise was positively related to competitive advantage performance. These results show the importance of top management support for refining IS trust and infrastructure competencies. Our results generally support the validity of the proposed research model. Top management support enhances IS flexibility infrastructure, IS business expertise, and IS trust relationships, as well as impacts competitive advantage. Furthermore, IS business expertise has a positive relationship with competitive advantage. We conclude that top management support has an impact on IS capabilities and competitive advantage performance. We showed that it is important that top managers develop scalable, modular, and compatible IT infrastructures that can lead to competitive advantage through trust and expertise. Most important, we validated many of the findings of the Bhatt et al.’s (2010) study, leading to a longitudinal inroad into understanding these constructs through the adoption of our QCA ITQ framework. Survey items can be found in