Clearance of oxytocin and its potentially enzyme resistant analogues in the OXT‐receptor compartment of the potassium depolarized rat myometrium

The time–response behaviour of a group of oxytocin analogues structurally modified on potential sites of oxytocin splitting by tissue inactivation enzymes (“enzyme probes”) was investigated ex vivo on the potassium depolarized rat myometrium (at 30°C) and compared with the data obtained in the in vivo experiments. The modified oil‐immersion method by Kalsner and Nickerson was used to record time profiles after cessation of a steady state myometrium contraction triggered by analogues in a high potassium tissue medium. An exchange of the aqueous medium for mineral oil enables to suppress return diffusion of the peptide and to record its irreversible clearance near the corresponding receptor compartment. Response records were analysed by a nonlinear numeric procedure based on combination of steady state and kinetic terms that allows concomitant estimations of affinities from time–response measurements, in the given case for analogues on depolarized myometrium. Potential inactivation‐sensitive sites in the oxytocin chain are the Ν‐terminal peptide bond Cys1‐Tyr2 (aminopeptidase splitting), the intramolecular disulphide bridge (reduction and formation of the practically inactive linear peptide) and the C‐terminal Leu8‐GlyNH2 9 or the Pro7‐Leu8 (postprolin cleaving enzyme) bond, respectively. Clearance rate constants of single peptides in the OXT‐receptor compartment were in an interval of 0.025 to 0.28 min−1. The fragment contribution analysis reveals a significant linear additivity of individual structural changes and thus a predictivity of irreversible inactivation rate in the receptor compartment. The most potent inactivation of oxytocin is associated with aminopeptidase splitting; other enzymes may play some though nondecisive role. Less significant differences within the peptide group were found for rate constants for peptide transport between receptor compartment and its external aqueous medium. Besides rate constants, the evaluation of time–response data yields affinity values of the tested peptides and indicates a 25‐times desensitation of depolarized compared with a native state.

The time-response behaviour of a group of oxytocin analogues structurally modified on potential sites of oxytocin splitting by tissue inactivation enzymes ("enzyme probes") was investigated ex vivo on the potassium depolarized rat myometrium (at 30 C) and compared with the data obtained in the in vivo experiments. The modified oil-immersion method by Kalsner and Nickerson was used to record time profiles after cessation of a steady state myometrium contraction triggered by analogues in a high potassium tissue medium. An exchange of the aqueous medium for mineral oil enables to suppress return diffusion of the peptide and to record its irreversible clearance near the corresponding receptor compartment. Response records were analysed by a nonlinear numeric procedure based on combination of steady state and kinetic terms that allows concomitant estimations of affinities from time-response measurements, in the given case for analogues on depolarized myometrium. Potential inactivation-sensitive sites in the oxytocin chain are the Ν-terminal peptide bond Cys 1 -Tyr 2 (aminopeptidase splitting), the intramolecular disulphide bridge (reduction and formation of the practically inactive linear peptide) and the C-terminal Leu 8 -GlyNH 2 9 or the Pro 7 -Leu 8 (postprolin cleaving enzyme) bond, respectively. Clearance rate constants of single peptides in the OXT-receptor compartment were in an interval of 0.025 to 0.28 min À1 . The fragment contribution analysis reveals a significant linear additivity of individual structural changes and thus a predictivity of irreversible inactivation rate in the receptor compartment. The most potent inactivation of oxytocin is associated with aminopeptidase splitting; other enzymes may play some though nondecisive role. Less significant differences within the peptide group were found for rate constants for peptide transport between receptor compartment and its external aqueous medium. Besides rate constants, the evaluation of timeresponse data yields affinity values of the tested peptides and indicates a 25-times desensitation of depolarized compared with a native state. † Deceased.

| INTRODUCTION
Neurohypophyseal hormones-oxytocin and vasopressin-are rather short-acting peptides in current pharmacological in vivo experiments.
Their half-life in the blood plasma lies by human and animal species so far investigated between 1.5 and 8 min. 1 Regardless of the gender and the reproductive circle by female animals, the half-life of oxytocin was estimated in rats to 1.65 min 2 ; the related elimination rate constant is 0.6 min À1 . However, estimates of the so-called overall decay rate constants (k ρ ) 3 for its uterotonic and antidiuretic responses are considerably lower, 0.18 to 0.25 min À1 . In general, low k ρ values were reported in a number of reviews also for other neurohypophyseal peptide analogues [3][4][5][6][7] ; those for uterotonic response to peptides used in this communication are outlined in Table 1.
The time span of a response to neurohypophyseal peptides became an important factor in the clinical pharmacology. Structural changes potentially resulting in its prolongation were already subjects of early studies, 12   In order to investigate them more directly and to segregate the irreversible clearance from the peptide transport processes, we used a combination of the ex vivo* washout experiments and the oilimmersion method (assigned here as a "stopped-transport" procedure), introduced by Kalsner and Nickerson. 25,26 In our modification, 10,22,27 it consists in eliciting a steady-state tonic contraction of an isotonically or isometrically suspended muscle strip ex vivo by a uterotonic stimulant in an aqueous medium, and successively exchanging this medium for a mineral oil. The extreme hydrophobic barrier around the tissue prevents the reverse diffusion of the stimulating agents from the receptor compartment and hence allows following solely irreversible clearance in the response relaxation phase.
The peptide chain of oxytocin carries several potential sites exposed to enzymatic attacks reported in a number of reviews, [28][29][30][31] and outlined in Figure 1. Splitting the Ν-terminal peptide bond without opening the -S-S-bridge by the so-called oxytocinase, 32,33 a placental leucine aminopeptidase of the P-LAP family, was initially detected in the blood serum during pregnancy. Action of other aminopeptidases after enzymatic or nonenzymatic (thiol-disulphide interchange) reduction of the disulphide bond appears as a likely inactivation step but has not been proved experimentally. The C-terminal hydrolysis of the Leu 8 -GlyNH 2 9 bond by a carboxypeptidasetype enzyme, [34][35][36] and the Pro 7 -Leu 8 bond splitting 37 were identified in homogenates of rat and human uteri.

| Substances
The peptides used here as enzyme probes and their abbreviations are listed in Table 1. 1. Analogues modified on the N-terminal by removing, or altering, the amino group of 1-cystein are expected to assess sensitivity against aminopeptidase splitting.
2. Substitution of one or both sulphur atoms in the -S-S-bridge by a CH 2 group, 40 the so-called carba-analogues, may clarify the potential clearance role of disulphide reduction.
3. Analogues with a Leu 8 -Gly 9 peptide bond (see Figure 1) modified by insertion of aza-glycine in position 9 41 were introduced as probes of potential C-terminal cleavage.

| Evaluation routines
The software package Wolfram Mathematica™ (version 11.

| Kinetic analysis
The structure of the compartment system employed in oilimmersion experiments was described in a block box form in our recent communication. 22 We employed here its modified version focused on the comparison of clearance and transport rate constants ( Figure 2). It consists virtually of two distribution spaces: the receptor compartment (subscript r; see Section 4) and the external aqueous tissue medium (w). The rate of mass transport of agents through the tissue-medium interface (transport constants k r , k w ) is directly proportional to the rate constant of diffusion k (dimension: volume/time) and inversely proportional to the respective compartment volume V r , V w : for the receptor compartment k r = k/V r , for the medium k w = k/V w . The constant κ relates to the (irreversible) clearance rate from the receptor compartment (dimension: time À1 ).
The rate equations determining the time response of the peptide concentrations in the corresponding compartments (c r , c w ) are then wherein dotted symbols denote first derivatives with respect to time 1. In the stimulation phase, concentration c w is expected to be constant, c w = c 0 (and _ c w ¼ 0) within the time interval of stimulation; the integration of Equation 1b yields where c r,∞ is a steady state value of c r , F I G U R E 2 Phases of oil-immersion experiment in the oxytocin stimulated myometrium: compartment model and clearance kinetics (upper panels). The compartment system of peptide distribution (upper panels) consists of the receptor compartment as a part of the interstitial space (white background) and the aqueous tissue medium (light grey), suppressed in the oil-immersion phase by the mineral oil (dark grey). Upper part: stimulation phase (middle block), washout (left-hand block), insertion of oil (right-hand block; aqueous medium reduced from V w to v w ). The inserted block in the right-hand panel depicts a magnified membrane section with the potential remnant of the aqueous medium after the displacement by oil. Vertical arrows between two compartments indicate directions of the peptide transport, horizontal arrows its irreversible clearance. State (and steady state) equations for the receptor compartment (time change of the peptide concentration c r ) are indicated. Lower part: response profiles (isometric contraction) of the depolarized myometrium strip to oxytocin in the respective phase.
2. In the wash-out decay phase, the concentration in the external medium (c w ) is kept zero by a quick perifusion; c r,∞ is the initial value (t = 0), i.e., a c r steady state value before termination of the stimulation phase, The sum k r + κ stands for the cumulative clearance rate constant of the peptide in the receptor compartment.
3. The insertion of oil (oil-immersion decay phase) reduces the volume V w to a small residual aqueous layer v w around the tissue; obviously, v w ( V w and the corresponding modified mass trans- The integration of the homogenous linear system (1) brings forth a sum of two exponentials with exponential coefficients resulting from the roots λ of its characteristic polynomial, Supposed that the volume v w is very small, k 0 w ) κ þ k r , and the characteristic polynomial can be reduced to The resulting exponential coefficients are For small κ values (κ ( k 0 w ), the Maclaurin expansion for the variable κ (or alternatively v w ) about its zero value yields linear terms of the coefficients λ, The rate equation corresponding to Equation 5 runs Thus, still assuming that k 0 w ) κ, the concentration c r (t) in the oil-immersion phase follows approximately a single exponential course, 3.1.2 | Response kinetics: Combined steady state with exponential terms The intrinsic relaxation dynamics of the stimulated tissue is another factor of the muscle state change, potentially overlapping with the "pure" drug effect. A recent kinetic analysis of the uterotonic response to oxytocin and deaminooxytocin 22 indicates that such additional dynamic processes in myometrium are not rate determining.
The rectangular hyperbolic function commonly used to approximate steady state dose-response relationships may then describe a tran- wherein C E stands for an "intrinsic affinity" constant in the K + -depolarized state (in mol L À1 ), formally expressing a concentration c r that elicits the half-maximal response, that is, The response E(t) relative to its initial value (at the time t = 0; see The concentration functions c r (t) for the washout or the oilimmersion phase, respectively, consist of a common pre-exponential constant c r,∞ and a time dependent exponential term τ(t) of Equations 4, 9a and 9b, Then, where

| Numeric analysis of time-response profiles
A nonlinear regression analysis of the time-response data using the Gauss-Newton iteration routine was applied to Equation (12b) combined with the exponential terms τ(t) of Equations 4, 9a and 9b.
Concomitantly with the kinetic analysis, Equation 12 yields estimates of the intrinsic affinity C E (mol L À1 ) from the fitted constant C Ã E (Equation 12c) and rate constants k r and κ,

| Relationship between in vivo and ex vivo clearance descriptors
The in vivo total decay rate constants k ρ for the uterotonic response are reported in several communications and listed in Tables 1 and 2. They reflect, in analogy to the cumulative constants κ + k r , clearance processes in the receptor compartment within the framework of the intact organism, that is, in a native (nondepolarized) state of myometrium. Their numeric values, assessed from half-lives after cessation of a prolonged infusion 3 or from the slopes of the doseresponse curves 9 after doubling the stimulation doses, 7,52 were estimated earlier in several laboratories (cf. Table 1). Differences of mean values k ρ and (κ + k r ), tested by the paired t-test, are insignificant (p = 0.090), although displaying a slight, likely most experimentally caused, propensity toward k ρ < (κ + k r ). This supports the assumption that the kinetics of the peptide clearance processes in rat depolarized and "native" (nondepolarized) uterus do not differ. Hence, the time profiles in the-methodically preferable-depolarization state reflect the in vivo kinetics of oxytocin-like peptides in the OXTR compartment sufficiently well. As intuitively anticipated, a correlation between the data pairs κ, k ρ (Tables 1 and 2 Figure 4). The adjusted value (k ρ = 0.144) was obtained by linear interpolation using the MATLAB function interp1, and we suggest considering this value as a more probable one. However, the replacement of the deviating F I G U R E 3 Relationship between clearance (κ) and transport rate constant (k r ) within N (circles) and D (squares) analogue groups. Values of constants in Table 2. Arithmetic means and standard deviations (error bars). Correlations within the groups are highly significant. Upper panels: box plots of pooled κ, k r , and (κ + k r ) data. Each box represents the interquartile range (1st to 3rd quartile), the median (cross-line in the box), highest and lowest values (bars); t and p values indicate the significance of the N-D difference (t-test) value does not improve the correlation significantly (two-sample z test after Fisher's r to z transformation), but it yields a "sharper" value of the slope (1.066 ± 0.262). No k ρ value for HOT has been reported for uterotonic response, but its reliable value could be approximately estimated from the half-lives of OXT and HOT obtained for antidiuretic response. 6

| Segment contributions to rate constants κ and k r : Free-Wilson analysis
Under the assumption that distinct sites of the peptide chain potentially exposed to enzymatic attacks participate additively in the overall inactivation rate, the constant κ i of an ith peptide is expressed as where κ 0 stands for a backbone contribution (regarded as a common invariable molecular segment within the investigated set of peptides, in our case that of oxytocin) and ϕ jg for a segment contribution of the Effects of the reported site substituents on the transport constant k r (right-hand panel in Figure 5) are, in general, not significant. The only noteworthy exceptions are hydrophilic substituents in positions 1 (OH and NH 2 groups on C α of 1-hemicystin residue) and 4 (NH 2 of glutamine). Their overall effect on k r is, however, not overwhelming.

| Specific case of GOT and DGOT: Fragmentation of rate constants
An introduction of the glutamic acid δ-methyl ester in position 4 results in a significantly higher positive contribution to the κ values F I G U R E 4 Relationship between ex situ (κ) and in vivo (k ρ ) clearance rate constants (arithmetic means). Circles: reported k ρ (reference s.  Figure 5). This additional step is obviously a hydrolysis of the ester bond which seems to be a fast inactivation process. 10 This is an alternative to model represented by Equation 12b, whereε A (t), ε M (t) are response fractions of the respective primary agents and of its active metabolite(s) or, when the predetermined constant κ ( Table 2, κ = κ AM + κ c ) is inserted as a fixed parameter, F I G U R E 5 Segment analysis of rate constants κ and k r . Z-transformed segment contributions to the standardized backbone (Z-score = 0, horizontal broken line) for four sites of the oxytocin chain (upper part). Significance levels estimated by the regression analysis are marked with different horizontal bars shown in the inserted legend (right-hand).
Exponential constants for GOT and DGOT were obtained by the nonlinear regression analysis using numeric procedures described above and are summarized in Table 3. Obviously, nonlinear regression procedures applied to Equation 17b minimize the asymptotic errors of κ c but, sensu stricto, the derived κ MA estimates obtained as κ À κ c depend of previous computations and thus, are not fully independent; however, the two variants of Equation 17 generate congruent parameter values. Irrespective of the use of differing α values reported from different laboratories 5,10 (see Table 1 Table 2. In this way, the suggested analysis of these two unique oxytocin analogues enables a closer look at the weight proportion of distinct processes participating in the clearance in the receptor compartment.

| Pharmacokinetic aspects
The clearance rate constants for the receptor compartment were assessed from the decay phase of the time-response profile using the combined exponential and hyperbolic response functions Its topology in rat myometrium based on histometric data has been discussed in more detail in our previous communication. 22 The concentration gradient of an amphiphilic substance-like peptides-near a biological membrane follows the Gouy-Chapman particle distribution around the negatively charged membrane surface 56   interaction site. Besides, capillary (or other hydrodynamic) forces may influence accumulation and depletion of particles within such a space.
All this makes the effective concentration in the close proximity of the receptor site (c r ), presently inaccessible to a direct assessment, difficult to express. Nevertheless, its apparent value can be expressed indirectly, as a concentration that elicits a measurable response. As follows from the analytical treatment of Equations (1) to (9), c r is a function of the concentration in the external aqueous medium (c 0 ), the clearance rate (κ) and the rate peptide transport (k r ) in the steady state where P r/w is a steady state partition coefficient of the stimulating agents between receptor and the adjacent extrinsic compartment, defined as a time invariable ratio of free concentrations c r /c w . As far as no extensive barriers occur, P r/w roughly equals unit. 22  Although the dissociation rate constant k off is low (0.017 to 0.27 min À1 ), the estimated "formal" receptor concentration in the receptor compartment is high (for a concentration corresponding to D 2 roughly 7 Â 10 À6 mol L À1 ) and thus, its effect on the oxytocin displacement rate is negligible. The spontaneous relaxation of the con- Finally, the question arises as to whether the clearance and transport descriptors recorded in the specific instance of a depolarised smooth muscle apply also for its "native" (polarised cell membrane) state. For investigations of biochemical/biophysical processes in the receptor compartment, the depolarized state offers the experimental advantage of yielding smooth time-response data for the tonic component in the decay phase. High K + /Na + ratio decreases the sensitivity of the contractile apparatus of myometrium cells by a factor of about 25 (Table 2) but does not substantially influence the clearance and the transport rate of the stimulating substance: the difference between cumulative clearance rate constants (estimated in the depolarized state) and response decay rate constants κ ρ (native state) is insignificant. Moreover, the linear correlation between the ex vivo (κ) and in vivo clearance constants (κ ρ ) (cf. Figure 4) provides a circumstantial support for the thesis that constants κ stand for irreversible (enzymatic) clearance processes in both in vivo and ex vivo systems.

| Rate constants of the clearance processes: Biochemical traits
The enzymatic clearance rate κ in Table 2 (Table 2) and the rate of residual clearance κ AM in the case of DGOT (Table 3, Figure 6) suggest that this splitting may account for about 30% to 45% of the total clearance. Nevertheless, the available evidence appears somewhat ambiguous. In vitro hydrolysis of the Leu 8 -GlyNH 2 9 34,35,57 and (concomitantly or alternatively) Pro 7 -Leu 8 bond 37,58 was detected in various tissue homogenates (human uterus, toad bladder, kidney). The latter bond is also cleaved by purified bovine chymotrypsin. 59 However, analogues substituted in position 9 by azaglycine-AOT and DAOT-reveal only slightly lower clearance rate constants κ compared with their 9-glycine-containing counterparts OXT and DOT ( Figure 5). One can infer that also their clearances do not differ substantially from each other, and that the Gly ! azaglycine substitution in position 9 does not exercise any appreciable inactivation protection. The insignificant difference of the two substituent segment contributions in position 9 ( Figure 5) may allow for two explanations. Firstly, that a splitting of the C-terminal bond Leu 8 -GlyNH 2 9 in the myometrium does not regularly occur, although it was observed in homogenized tissue. 34,35,57 Secondly, that the pseudo-peptide bond leucine-azaglycine (hydrazinecarboxylic acid, Remarkable is also the virtual identity of κ-constants found for oxytocin and hydroxyoxytocin. A cleavage of substrates with the N-terminal 2-hydroxy-3-β-mercaptopropionic acid by aminopeptidases has not been reported so far (and appears to be very unlikely), but another form of hydrolysis on the N-terminal peptide bond cannot obviously be excluded. Instead, the polarity of the N-terminal substituent of oxytocin analogues (N-D grouping) seems to be essential for the rate of the enzymatic clearance.

| Transport processes
The transport constant k r is defined as a ratio of the diffusion constant k and the volume V r of the receptor compartment. A low scatter of k r (Table 2) is rather astonishing, for it seems likely that the assumed vol-

| CONCLUSIONS
Conclusions derived from the investigations presented here are as follows: 1. An adapted version of the oil-immersion technique enables an assessment of clearance and transport rate constants in the receptor compartment of drugs eliciting tonic smooth muscle contraction. In the ex vivo rat myometrium, this state is optimally achieved in the K + -depolarized state.
2. A comparison of ex vivo and in vivo estimated clearance rate constants of oxytocin-like peptides supports the hypothesis that the response duration is mainly controlled by irreversible clearance in the receptor compartment. A peripheral clearance appears less efficient to these aims.