J. theor. Biol. (1992) 157, 317-362
A Coupled-oscillator Model of Ovarian-cycle Synchrony Among Female Rats JEFFREY C. SCHANK t A N D M A R T H A
K. McCLINTOCK~§
t Committee on the Conceptual Foundations of Science and Department of Psychology, The University of Chicago and ~ Department of Psychology, The University of Chicago, 5730 Woodlawn Avenue, Chicago, Illinois 60637 U.S.A. (Received on 20 May 1991, Accepted in revised form on 25 March 1992) The ovarian cycles of female rats become synchronized when they live together, as do the cycles of many other mammals. Ovarian cycles also become synchronized when rats live apart if they share a common air supply, indicating that ovarian-cycle synchrony is mediated by pheromones. We developed a coupled-oscillator model of ovarian-cycle synchrony to test several hypotheses about its pheromonal and neuroendocrine mechanisms and to guide our experimental research. The model spans three levels of organization: the group, the rat, and the neuroendocrine components of the ovarian system. The ovarian system (not the ovaries themselves) are modeled as an oscillating system. Coupling among ovarian systems is mediated by the exchange of two pheromones, one that delays the phase of the ovarian system and one that advances it. Computer simulation experiments showed that this coupledoscillator model can explain the levels of ovarian-cycle synchrony observed in groups of female rats while, at the same time, matching an empirical distribution of ovariancycle lengths. By successfully matching computer simulation data with empirical data, we were able to infer theoretical predictions in a number of areas: (1) effect of initial conditions on the probability that a group will change to different synchrony level and phase relationships, i.e. the transition probability between all synchrony levels and phase relationships; (2) effects of individual differences in pheromone sensitivity on ovarian-cycle synchrony; (3) the timing of pheromone sensitivity during the ovarian cycle; and (4) the existence of partial luteinizing hormone surges, which may cause the "spontaneous" prolonged ovarian cycles associated with ovarian-cycle synchrony. The paper concludes by discussing the integrative role of this model for experimental research. In particular, we focus on the role of this model in interpreting theoretical aspects of ovarian-cycle synchrony as well as for guiding future experimental research into its mechanisms and functions.
1. Introduction
There are many examples of biological systems which undergo cyclic changes in physiology and behavior. Perhaps the most ubiquitous of biological cycles are circadian rhythms (i.e. daily rhythms in physiology and behavior that are close to 24 hr in length and remain nearly constant independent of external cues such as light and temperature). But, there are many other kinds of biological cycles in nature that § Author to whom reprint requests should be made. 317 0022-5193/92/1503 ! 7 + 46 $03.00/0
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exhibit interesting and complex behavior including the synchronization of cycles and even chaos (e.g. yon Hoist, 1969; Peskin, 1975; Winfree, 1980, 1987; Rinzel & Ermentrout, 1983; Glass & Mackey, 1988; Ermentrout, 1991). The goal of this paper is a better understanding of the mechanisms that produce ovarian-cycle synchrony among female rats and, in the long run, among females of the many other mammalian species that also exhibit ovarian synchrony (Miller, 1911; Reynold et al., 1952; Jolly, 1967; Fraser, 1968; Neal, 1970; McClintock, 1971, 1978, 1983b; Rasa, 1973; Harrington, 1974; Rood, 1974, 1975, 1978, 1980; van Horn, 1975; Abegglen, 1976; Estes, 1976; Dunbar & Dunbar, 1977; Rowell, 1977; Sinclair, 1977; Rowell & Hartwell, 1978; Frame et al., 1979; Keverne, 1979; Nishida, 1979; Rowell & Richards, 1979; Dunbar, 1980; Graham & McGrew, 1980; Handelmann et al., 1980; Russell et al., 1980; Hoek, 1981; McCracken & Bradbury, 1981; Quadagno et al., 1981 ; Buckley, 1982; Izard & Vandenbergh, 1982; Russell, I982; Iason & Guinness, 1985; Wallis, 1985, 1989; Matteo, 1987). There are a variety of mechanisms and signals that can cause the synchronization of biological cycles (e.g. see Winfree, 1980, 1987; Ermentrout, 1985; Glass & Mackey, 1988 for a discussion of some of these mechanisms and signals)t. In the case of circadian rhythms, light is an external time cue or signal that entrains circadian rhythms to the daily light-dark cycle. This kind of synchronization is due to an external periodic time cue--a Zeitgeber--that controls the synchronization of cycles. There are, however, other cases of the synchronization of biological rhythms for which there is no external Zeitgeber cueing synchronization. Among the most spectacular examples are the waves of synchronous flashing in swarming fire flies (Buck & Buck, 1968; Buck, 1988), and the collective synchronous behavior of cellular slime molds such as Dictyostelium discoideum (Bonner, 1967; Gerisch, 1968). In these cases and others, the synchronization of rhythmic changes in physiology or behavior is due to the mutual coupling of oscillating systems by physical signals such as flashes of light in fireflies (Buck, 1988; Ermentrout, 1991), or cyclic A M P in D. discoideum (Bonner, 1967; Gerisch, 1968; Winfree, 1980; Glass & Mackey, 1988). When female rats live together for three or four ovarian cycles, there is typically an increase in the number of females with synchronized ovarian cycles, although complete synchrony is rare (McClintock, 1978). Females that live apart synchronize their cycles to the same degree as females that live together if they share a common air supply (McClintock, 1978). Therefore, ovarian-cycle synchrony must be mediated by airborne chemosignals called pheromones (McClintock, 1983a). The fact that the ovarian system itself oscillates--though the ovaries alone do not oscillate (see Freeman, 1988 for review)--suggested to us that ovarian-cycle synchrony may be another t On the standard definitionof entrainment, two rhythms are entrained if and only if m cycles of one rhythm are locked to n cycles of the other (where m and n are integers and phase is the instantaneous state of a system; see Winfree, t980, 1987; Glass & Mackey, 1988). Synchrony is a special case of entrainment when there is a l-I locking (where re=n) and the cycles have essentiallyno differencein phase (Winfree, 1987). In this paper, we use the term synchronyin a similarsenseexceptthat we distinguish four equal stages or phases of the ovarian cycleand require a I-1 match only between these four phases of ovarian cycles. In this context, the term phase means a stage or interval of a cycle,which is in contrast to phase as the instantaneousstate of a system. We believethat these two uses of the term phase are clear in context.
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example of the mutual entrainment of coupled oscillators, in this case, the mutual entrainment of rat ovarian systems coupled by the exchange of pheromones (McClinrock, 1983b). Moreover, on the basis of experimental evidence described in McClintock (1984a), we believe that coupling among oscillators is mediated by two distinct signals: one advances and the other delays the phase of the ovarian system. In order to test this coupled-oscillator hypothesis, we have built a model for computer simulation. The model proposes that synchrony among rats is produced by the pheromonal coupling of ovarian systems. The model focuses on representing the timing of interactions among the neuroendocrine, the physiological, and the pheromonal systems that interact to produce and entrain ovarian cycles in rats (section 2). Where there are gaps in our knowledge about these interactions, we have proposed auxiliary hypotheses that are biologically reasonable as a basis for developing a workable model (section 3). Data from computer simulation experiments, using this model matched empirical data, and thus allowed us to derive a number of testable theoretical predictions (section 4). Finally, we discuss several functions of the model, both for interpreting ovarian synchrony as well as for guiding future experimental work on its mechanisms and functions (section 5). 2. Ovarian-cycle Synchrony in Rats: An Overview In this section, we describe the empirical basis for our model and computer simulations. The information is presented in considerable detail, because it is important for identifying the key biological events and interactions that should be represented in a biologically realistic model of the rat ovarian system as well as the empirical data relevant to testing the model. We begin by describing the ovarian system: the phases of the ovarian cycle, the biological indicators of these phases, and the key physiological and endocrine events that control the timing of the ovarian cycle (section 2.1). We then describe the characteristics of ovarian-cycle synchrony in groups of female rats and its mediation by pheromones (section 2.2). Finally, we describe the effects of two different pheromones that are produced at different phases of the ovarian cycle: one that lengthens the ovarian cycles of recipient females and another that shortens their cycles (section 2.3). 2.1. T H E O V A R I A N C Y C L E
Ovulation in rats, as well as other mammals, is caused by a surge of luteinizing hormone (LH) from the anterior pituitary; the LH surge luteinizes several follicles in the ovary causing each to rupture and release its egg (see Feder, 1981; Freeman, 1988 for reviews). At the site of rupture, a corpus luteum forms, and although it is technically non-functional in the rat (i.e. it is short lived), it does secrete progesterone that can affect the length of the ovarian cycle (Feder, 1981 ; Freeman, 1988; S~mchezCriado et al., 1988). Just after ovulation, a new set of follicles begins to mature and releases increasing amounts of the ovarian steroid, estrogen, which primes the system for another surge of LH. Typically, the cycle repeats 4 or 5 days later when a new LH surge again triggers ovulation (see Feder, 1981 ; Freeman, 1988 for reviews).
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2.1.1. Cytological and behavioral indicators of the phase of the ovarian cycle Ovarian cyclicity is associated with cyclic changes in the frequency and intensity of specific sexual behaviors of unmated female rats, termed the estrous cycle (Feder, 1981)t. These behaviors include lordosis (a reflex elicited by flank stimulation) and soliciting the male. These sexual behaviors increase in frequency and intensity on the day of the LH surge, and in general, provide a reliable indicator of ovarian cyclicity in female rats (McClintock, 1984b). Ovarian cyclicity is also associated with cyclic changes in vaginal cytology (e.g. see Feder, 1981 for further discussion). On the basis of changes in behavior and vaginal cytology, it is conventional to distinguish four phases of the estrous cycle: proestrus, estrus, metestrus, and diestrus~. Each phase is 24 hr in length (for the prototypical 4-day cycle), and runs from midnight to midnight. The cyclic changes in behavior and vaginal cytology are dependent on the ovarian cycle, since ovariectomy resulted in the cessation of cycles in both behavior and vaginal cytology (Schwartz, 1969; Feder, 1981; Freeman, 1988). Using the estrous cycle as an indicator of the ovarian cycle, researchers have found that female rats typically have 4-day or 5-day ovarian cycles (Shnchez-Criado et al., 1988; LeFevre & McClintock, 1988). Nonetheless, rats also have a significant number of very prolonged cycles, up to 38 days in length (Long & Evans, 1922; LeFevre & McClintock, 1988). These prolonged cycles appear to be "spontaneous" and share characteristics in common with pseudopregnancies in rats (Long & Evans, 1922; Everett, 1963). In the Sprague-Dawley strain of rats, for which we have data, females typically exhibit 4-day ovarian cycles but with considerable variation in cycle lengths including "spontaneous" prolonged cycles (McClintock, 1978, 1983a; LeFevre & McClintock, 1988). In short, these cytological indicators of the estrous cycle are especially important for three reasons. First, they allowed us to measure increases or decreases in group synchrony (section 2.2). Second, they allowed us to measure the effects of pheromones on ovarian-cycle length (section 2.3)§. Third, they allowed us to generate an empirical cycle-length distribution, which was then used as a template against which to match simulation data (section 4). 2.1.2. Key mechanisms and the timing of ovarian cycle events Ovulation occurs early in the morning of estrus and is triggered by a surge of LH that is released the previous day, during the afternoon of proestrus. An ovulatory surge of LH is released by the pituitary once two conditions have been met. First, the pituitary must be primed by ovarian steroids (especially estrogen during diestrus
t The behavior during this phase of the ovarian cycle is termed estrus (the term "estrus" comes from the Latin term oestrus which means in a frenzy) and the periodic change in behavior is the estrous cycle. :~See footnote on p. 318 for the two senses of the term phase used in this paper. § These four phases of the estrous cycle are also used to describe cycles that are longer than 4 days in length (LeFevre & McClintock, 1988). For example, if a 5-day cycle is observed and there is an extra day with a large proportion of leukocyte cells, then this cycle would be called a 5-day cycle with a prolonged metestrous phase (i.e. 2 days of metestrus were observed).
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and early proestrus). In particu!ar, estrogen may act by increasing pituitary LH content and the number of luteinizing hormone releasing hormone (LHRH) receptors (or by affecting postreceptor mechanisms; see Fink, 1988; Freeman, 1988 for reviews). The pituitary is also primed by LHRH released from hypothalamic neurons into hypophysial-portal blood (during proestrus; Fink, 1988). Second, once the pituitary is fully primed, a surge of LHRH from hypothalamic neurons releases an ovulatory LH surge from the pituitary (Fink, 1988). There are also two conditions that must be met before the LHRH neurons of the hypothalamus release a surge of LHRH. First, these neurons must be primed by ovarian steroids (especially estrogen; see Feder, 1981; Freeman, 1988 for reviews). One effect of estrogen---especially in conjunction with progesterone--may be to increase the capacity of LHRH neurons to respond to depolarizing stimuli, and thereby facilitate the release of LHRH (Kordon & Drouva, 1990; see Freeman, 1988 for review of the priming effects of ovarian steroids on the hypothalamus). It also has been recently reported that estrogen stimulates the synthesis of LHRH mRNA (Rosie et al., 1990). Second, once the LHRH neurons are fully primed, a circadian signal of neural origin (i.e. from the anterior hypothalamus, including the suprachiasmatic nuclei and the medial preoptic areas) causes a cascade of events that triggers the primed LHRH neurons to release a surge of LHRH (see Fink, 1988; Freeman, 1988 for review). The precise timing of the daily neural-signal and of the priming of the pituitary and hypothalamus is known for Sprague-Dawley rats with regular 4-day cycles. The daily neural-signal that triggers the LHRH surge occurs during a very narrow critical period: every afternoon from 1400-1600 hr (Everett et al., 1949; Everett & Sawyer, 1950, 1953; Everett, 1956; Everett & Tejasen, 1967)t. In addition, priming of both the pituitary and hypothalamus is complete by 1200 hr of proestrus (Feder, 1981). Thus, if a neural signal is received by 1600 hr, and if the hypothalamus and pituitary have been fully primed by ovarian steroids, then an LHRH surge is triggered, rapidly causing the release of an LH surge from the pituitary in the late afternoon of proestrus, which in turn triggers ovulation early the following morning, on estrus. We are aware of the many other neuroendocrine events and mechanisms involved in this axis, e.g. the pulsatile release of LH (Levine & Ramirez, 1982; Fox & Smith, 1985), inhibin (Steinberger & Ward, 1988) and FSH (Schwartz, 1969). Our initial goal, however, was to select just those events and mechanisms directly responsible for the timing of the preovulatory LH surge, in a time frame of hours and days. Future elaborations of the model could incorporate the neuroendocrine mechanisms regulating the rate of ovarian development, i.e. follicular maturation and the life
t The timing of this critical period is relative to a constant light--dark cycle and entrained to the particular light-dark cycle under which rats are maintained (it is the same for 14 hr of light and 10 hr of dark or 12 hr of light and 12 hr of dark; (Everett et al., 1949; Everett & Sawyer, 1950, 1953; Everett & Tejasen, 1967). Finally, Everett & Tejasen (1967) emphasized differences in the critical period between Sprague-Dawley and Osborne-Mendel rats, but after examining the data they present in Everett & Tejasen (1967: fig. I, p. 791), it is clear that this difference is minimal and that Sprague-Dawley rats should be characterized as having a critical period between 1400 and 1600 hr.
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span of the corpus luteum, if needed to develop a better model (e.g. see Lacker, 1981; Lacker & Peskin 1981; Lacker et al., 1987a, b for mathematical models of follicular maturation in mammals).
2.2. O V A R I A N - C Y C L E
SYNCHRONY
When female rats are placed in small groups, there is an increase in the synchrony of their ovarian cycles. Synchrony is manifested by an increase in the number of females in a group that are in the same phase of the cycle on the same day (e.g. in proestrus as indicated by sexual behavior and vaginal cytology; McClintock, 1978). Synchrony, in Sprague-Dawley rats, is also associated with a characteristic distribution of cycle lengths, including "spontaneous" prolonged ovarian-cycles (McClintock, 1983a). It takes about three cycles for synchrony to develop and it is maintained for at least 12 cycles (McClintock, 1978, 1983b). Complete synchrony is rare, however. In groups of five females, there are usually one or two females that are not synchronized with the others, which may reflect a balance of different reproductive strategies (see section 5.3.2; McClintock, 1978, 1983b). Ovarian-cycle synchrony is mediated by pheromones (airborne chemosignals), since females that share a recirculated air supply, but are otherwise physically isolated from each other, synchronize their cycles as rapidly, and to the same level, as females that are caged together (McClintock, 1978). This suggested to us that there are pheromones released during specific phases of the ovarian cycle that synchronize ovarian cycles within a group. If so, then ovarian-cycle synchrony can be conceptualized as the result of the mutual entrainment of ovarian cycles in a pheromonallycoupled system of oscillators (McClintock, 1983a, b, 1984a).
2.3. T H E
EFFECT
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In many coupled-oscillator systems, synchrony is caused by the interaction of two types of signals: one that phase delays the cycle and another that phase advances it (e.g. Aschoff, 1960; Buck & Buck, 1968; von Hoist, 1969; McClintock, 1983b, c). Given that pheromones mediate ovarian-cycle synchrony in rats, we hypothesized that there are two different pheromones released during specific phases of the ovarian cycle that have opposing effects on the recipient's ovarian cycle: one pheromone that phase-delays and therefore lengthens the cycle, and a second, released during a different phase, that phase advances and therefore shortens the cycle. In order to test this hypothesis, we identified three phases of the ovarian cycle that have distinct hormonal patterns and thus could produce different pheromones with different effects: ovulatory, luteal, and preovulatory phases. The ovulatory phase is characterized by high levels of estrogen, progesterone, and LH (Fig. 1). The luteal phase is characterized by high levels of progesterone, but low levels of estrogen and LH (Fig. 1). In contrast, the preovulatory phase is characterized by high levels of estrogen, but low levels of progesterone and LH (Fig. 1). We collected pheromones during a 24-hr period in each of these three phases (0500-0500 h) and continuously
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Estrogen Time of pheromone sampling
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Phase of ovarian cycle in days and phase scale [0,1] F1G. 1. A schematic representation of hormone levels during the rat's ovarian cycle: luteinizing hormone (LH) and the ovarian steroids, estrogen and progesterone. The horizontal axis represents both the
four phases of the ovarian cycle in days, estrus (E), metestrus (M), diestrus (D), and proestrus (P), as well as the phase scale [0, I] used in the model described below. The shaded bars indicate the times when different pheromones were sampled during McClintock's phase-resetting experiments (1984). Ovulatory odors were sampled when estrogen levels were high, progesterone was rising sharply and there was a surge of LH. Preovulatory odors were sampled when estrogen was rising, progesterone was decreasing, and LH was at baseline levels. Luteal odors were sampled when estrogen was low, progesterone was rising and LH was at baseline levels.
exposed female rats to them (see Fig. I for results and McClintock, 1983a, b, 1984a for experimental methods)t. Preovulatory pheromones shorten and regularize the ovarian cycles of recipient rats, in comparison to cycles of control rats exposed only to background odors; in fact all cycles are four days in length [Fig. 2 (a) and (b); see section 5.1 for an interpretation of this result]J;. Ovulatory pheromones have the opposite effect, they lengthen ovarian cycles and make them more irregular [Fig. 2(c)]. Luteal pheromones have no significant effect [Fig. 2(d)]. These experimental results clearly support the hypothesis that there are two signals mediating synchrony. Moreover, since these t The period from 0500 hr of estrus to 0500 hr of metestrus is part of the luteal phase but was not sampled in the experiment described below in order to control for duration of pheromone production (McClintock, 1984a). :[:The cycle-length data presented in Fig. 2(a)-(d) differs from the cycle-length data presented in McClintack (1984) in our reinterpretation of 2- and 3-day cyclic changes in vaginal cytology. Based on the literature and new hormonal data, we now interpret them as being part of the previous cycle rather than an extremely short cycle. For example, if a 5-day cycle was followed by a 3-day cycle, this was reinterpreted as a prolonged 8-day cycle. This reinterpretation affected less than 5% of the cycles.
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FIG. 2. The effectsof four different odor conditions on the cycle-lengthdistributions of female rats. In the control condition, femaleswere exposed to background colony odors (a). In the experimentalconditions, three kinds of odors were presented continuously (the sampling times for these three ovarian-cycle odors are indicated in Fig. 1). Preovulatory odors shortened and regularized ovarian cycles (b), while ovulatory odors lengthened ovarian cycles and made them more irregular (c). Luteal odors had no significant effect (d).
results precisely established the times when pheromones with opposing effects on ovarian-cycle length are released, they allowed us to incorporate the timing o f these opposing effects into the model described below.
3. The Model and Simulation Design We used the empirical information just described to design the coupled-oscillator model and computer simulations o f ovarian cycle synchrony proposed in this section. But, this empirical information is not by itself sufficient to design even a simple workable model of ovarian-cycle synchrony in groups of rats; it does not provide sufficient biological detail of neuroendocrine and pheromonal systems required to build a formal model. Therefore, we have also proposed auxiliary hypotheses, which are nevertheless biologically plausible, aimed at filling in the gaps in our knowledge about key features o f these systems (see Kauffman, 1971 for a classic account o f this kind o f exploratory modeling strategy, and Barinaga, 1990 for a brief discussion o f the use o f this strategy in neuroscierfce).
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A successful match between computer simulation and empirical data will support the empirical plausibility of the model; that is, it will confirm the main hypotheses, such as the pheromonal coupling of oscillating-ovarian systems, as well as lending empirical plausibility to the auxiliary hypotheses that we have proposed about specific neuroendocrine and pheromonal systems. In particular, because these auxiliary hypotheses are an essential part of this model, a match would also be a directive for future empirical work aimed at testing the predictions made by these auxiliary hypotheses.
3.1. A U X I L I A R Y H Y P O T H E S E S
3.1.1. Production of pheromones Although we do know that pheromones produced during the 24-hr period of the follicular, or preovulatory, phase (0500-0500 hr) have effects opposite to those of pheromones produced during the 24-hr period of the ovulatory phase (also 05000500 hr), we do not know exactly how either of these effects change within these 24hr periods. In the absence of this information, we have hypothesized that the effects of both pheromones wax and then wane, rather than dichotomously turning on and then off. Given that the phase-advance pheromone directly precedes the phase-delay pheromone, we decided to use a sinusoidal curve that spans half of an ovarian cycle" to representthe change in the effect of pheromones (i.e. spanning 0500 hr of diestrus to 0500 hr of estrus; see Fig. 4 below). It is also biologically reasonable to hypothesize that the effects of these pheromones dissipate quickly (i.e. over minutes or hours and not days), since otherwise the effects of these two pheromones would tend to "cancel" each other out during an ovarian cycle. This is in agreement with what we know about the chemical volatility of many pheromones in mammals (Albone, 1984). Thus the sinusoidal curve that we use combines both the waxing and waning of pheromone production with the dissipation of these pheromones. 3.1.2. Pheromone sensitivity: timing and duration If there are two pheromones that cause synchrony, sensitivity to pheromones must also wax and then wane. This is because mutual synchronization within a group requires that: (1) an oscillator that is just lagging behind the rest of the oscillators in a group receive a phase-advancing signal and (2) an oscillator that is just ahead of the group receive a phase-delaying signal (Winfree, 1980). If sensitivity to pheromones does not wax and then wane, this condition for synchronization cannot be met because the entrainment effects of the two opposing pheromones would cancel each other out over an entire cycle (see section 5.1 for further discussion). It is biologically reasonable to hypothesize that sensitivity to pheromones involves the olfactory system, and that cyclic variation in olfactory sensitivity of female rats could indicate when they are sensitive to ovarian-cycle pheromones. Pietras & Moulton (1974) systematically documented changes in olfactory sensitivity during the ovarian cycle of female Sprague-Dawley rats. Olfactory sensitivity increases from
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the early afternoon of proestrus (i.e. 1400 hr) and remains high until late in the evening ofestrus (i.e. 2200 hr). This places the center of olfactory sensitivity to odors at 0600 hr o f estrus. The increases and decreases in sensitivity to odors are sharp transitions, which have the form o f a square wave. Thus, we hypothesized that Sprague-Dawley rats are sensitive to pheromones only when their olfactory sensitivity is high: a 32-hr period centered at 0600 o f estrus, adequately approximated by a square wave (see Fig. 4 below).
3. 1.3. Indioidual differences in pheromone sensitioity There are individual differences in the distribution of ovarian-cycle lengths among young female Sprague-Dawley rats (ages 3-6 months; LeFevre & McClintock, 1991 ; see also Long & Evans, 1922: table 37). Some females exhibit nearly all 4-day cycles. Other females exhibit a mix o f 4- and 5-day cycles. Still fewer females exhibit predominantly 5-day cycles or a mix of 4- and 6-day cycles with an occasional prolonged cycle or spontaneous pseudopregnancies. Long & Evans (1922) hypothesized that the 4-day cycle is normal for female rats and that any deviation indicates poor health of the animal. But, contrary to Long & Evans (1922), the young animals in our laboratory colony were in excellent health (McClintock, 1978, 1984a). Thus, individual variation in our cycle-length data is not likely due to individual differences in the health of animals. Indeed, any factor that affects the rate o f follicular development could account for the individual differences observed in ovarian-cycle length in female rats. As a first approximation, we can begin by distinguishing between intrinsic and extrinsic factors affecting cycle length. An example o f an intrinsic factor would be individual differences in the initial state o f maturity of follicles recruited to start a new ovarian cycle, which has been shown theoretically to lead to differences in ovarian-cycle length in mammals (Lacker, 1981 ; Lacker & Peskin, 1981). An example of an extrinsic factor would be ovarian-cycle pheromones, which presumably act in some manner to alter the rate o f follicular development. In our model, we are particularly interested in the effects o f pheromones on ovarian-cycle length and therefore we have made the idealizing assumption that in healthy young female rats, pheromones are the only source o f individual differences in ovarian-cycle lengtht. Although this assumption is an idealization, we will show below that it does a remarkably good job o f explaining our empirical data, which strongly suggests that individual differences in cycle lengths-measured in days in female rats--has its main source in the exchange o f ovariancycle pheromones (also see section 5.1 for further discussion o f this hypothesis)~. t Another extrinsic factor that is likely to be important for determining the individual differencesin the sequence of cycles of different length is the specificconfiguration of ovarian-cyclephases within the group. This configuration is important because the ovarian-cyclephases of these other rats will determine what type of pheromones a female rat is exposed to when she is sensitive to pheromones. :l:The circadian regulation of the timing of ovulation in rats tends to support this idealization. Small intrinsic individual differencesin rates of follicular development or timing of LH surges, which are measured on a time scale of minutes or hours, are truncated to a time scale of days via circadian modulation. Thus, even though there may be intrinsic individual differencesamong females in rates of follicular development or timing of LH surges, in the absence of extrinsic factors such as pheromones, cycle lengths in female rats will typically be 4 days in length.
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3.1.4. Priming the pituitary and the hypothalamus: a mechanism for variation in cycle length Although ovarian cycles in rats are typically 4 days long, there is considerable variation in cycle length, including cycles of up to 38 days or longer (Long & Evans, 1922; LeFevre & McClintock, 1991). Cycles that are 5-7 days long typically appear as extended 4-day cycles, that is, with extended metestrus and/or diestrus-estrus phases (Nequin et al., 1979; LeFevre & McClintock, 1988). There is another class of long cycles, 8 days or more in length, that we term prolonged ovarian cycles. These prolonged cycles are often described as occurring "spontaneously" and are sometimes referred to as "spontaneous" pseudopregnancies (e.g. Long & Evans, 1922; Everett, 1963). Close examination of changes in vaginal cytology during these "spontaneous" prolonged cycles has revealed subliminal cycles, in the proportion of cell types, that are 4-7 days in length (McClintock, unpublished data)t. Since the length of "spontaneous" prolonged cycles can be interpreted as multiples of shorter, more typical cycles (i.e. 4-, 5-, 6-, and 7-day cycles), this suggested to us a possible mechanism for their "spontaneous" occurrence. That is, a mechanism that would enable the ovarian system to "reset" without also triggering the full ovulation that normally begins a new cycle. Such a mechanism could produce subliminal anovulatory cycles that together would comprise a prolonged cycle with a length that is a multiple of shorter-cycle lengths. Our proposed mechanism has two thresholds: one for full and the other for partial steroid priming of the pituitary and hypothalamus. When ovarian steroid levels reach the full-priming threshold, the daily neural signal triggers a full LH surge and ovulation, which begins a new cycle (see section 2). When ovarian steroid levels reach only the partial-priming threshold, which is slightly lower than the full-priming threshold, the neural signal will only trigger a partial LH surge. A partial LH surge can reset the ovarian cycle but cannot cause ovulation (i.e. there is some luteal activity and folliculogenisis, but not complete follicular rupture). These anovulatory cycles should be 4-7 days in length, as are short ovulatory cycles bounded by full LH surges. A sequence of one or more anovulatory cycles will be observed as a prolonged cycle (i.e. a prolonged cycle is bounded by full LH surges, but contains one or more subliminal cycles, each indicated by a partial LH surge). If ovarian steroids do not reach either of the two thresholds by the time of the daily neural signal, then ovarian development continues until the next daily signal and the cycle is lengthened by only 1 or more days. For these short cycles, the cycle length is directly proportional to the rate of ovarian development. This is in contrast to prolonged cycles, which are longer than would result simply from delayed ovarian development.
t More specifically, subliminal cycling in vaginal cytology means that there are 4- to 5-day cyclic patterns of increase and decrease of nucleated and cornified epithelial cells in the daily smears within prolonged cycles. The subliminal variation in the percentage of leukocytes in these prolonged cycles does not reach the criterion of >80% in the smear, which indicates proestrus, ovulation, and a new cycle onset (McClintock, 1978).
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This idea--that there is a second threshold for partial steroid priming of the hypothalamus and pituitary and that partial LH surges can lead to anovulatory resetting of the ovarian cycle--is a novel hypothesis. Nonetheless, it is supported by the literature in several respects. A few studies of the full LH surge also report anecdotally very small or partial surges of LH (e.g. less than 20% of full surge levels; Carrillo & Sawyer, 1978; Allen & Kalra, 1986). These partial LH surges, however, are typically dismissed as anomalies or measurement errors with no functional significance. There is, however, in vitro evidence that small amounts of LH (i.e. as small as 5% of the normal LH surge) can cause luteal steroidogeisus without ovulation (Peluso, 1990). If confirmed in vivo, this mechanism would explain how partial LH surges reset the ovarian system without causing full ovulation, producing an anovulatory cycle. Finally, evidence also comes from a classic series of elegant studies by Everett and colleagues (Everett et al., 1949; Everett & Sawyer, 1950, 1953; Everett & Tejasen, 1967) which showed that by partially blocking a full LH surge during the circadian critical period, partial ovulation or anovulation often results. In the model, we have specified that: (1) Full steroid priming, in both the pituitary and hypothalamus, is reached by 1200 hr of proestrus in regular 4-day cycling rats (Feder, 1981 ; Wise et al., 1981). (2) Partial priming is hypothesized to have a lower threshold, which is achieved 3 hr earlier, at 0900 hr. We based this hypothesis on experimental evidence, which has established that this is the time when LHRH concentrations in the hypothalamus increase significantly in Sprague-Dawley rats (Wise et al., 1981). An increase in the hypothalamic concentration of LHRH indicates steroid priming in both the hypothalamus and the pituitary, and in turn, triggers the release of LH from the pituitary. (3) Prior to 0900 hr of proestrus LHRH concentrations are not significantly above baseline (Wise et al., 1981), and thus we hypothesized that neither the hypothalamus nor pituitary are primed prior to 0900 hr of proestrus during a regular 4-day cycle. In short, if full priming is achieved by the end of the critical period for the neuralcircadian signal (1600 hr), then a full LH surge will be triggered, causing ovulation and resetting of the ovarian cycle. If, however, only partial priming is achieved by the end of the critical period, then there will only be a partial LH surge and the ovarian cycle will reset without ovulation, ceasing an anovulatory cycle. If neither threshold is reached by the end of the critical period, then the cycle will be prolonged by at least another day--until the time of the neural signal on the next day. 3.1.5. Summary o f the main auxiliary hypotheses The principle auxiliary hypotheses described above are worth emphasizing again: (H 1) Sensitivity to pheromones starts at 1400 hr of proestrus and ends at 2200 hr of estrus. (H2) There are individual differences among female rats in their sensitivity to pheromones. (H3) If ovarian steroids reach only the partial-priming threshold by the end of the critical period for the daily neural signal, then the neural signal will trigger only a partial LH surge.
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(H4) Partial LH surges cause anovulatory cycles, which are part of prolonged ovulatory cycles. (H5) Ovarian-cycle pheromones (specifically, ovulatory pheromones) increase the likelihood of partial LH surges by delaying ovarian-cycle development, which, in turn, delays the priming of the hypothalamus and pituitary. (H6) Individual differences among female rats in pheromone sensitivity are primarily responsible for individual differences in ovarian-cycle length.
3.2. T H E M O D E L
The interactions among the components of this multi-level model are presented schematically in Fig. 3. These include interactions among: the neuroendocrine components of the ovarian system, ovarian and pheromonal systems, and rats living in groups. A simple mathematical model of this multi-level system is presented below in terms of finite difference equationst. In this model, the ovaries can cycle only if there is hormonal input from the pituitary; thus the ovaries are not modeled as simple clocks. Full or partial LH surges from the pituitary reset the ovaries (ovarian phase, Oi, resets from 1, the maximum value for ovarian phase, to 0). If there is a full LH surge from the pituitary, P~(t) = 2, the ovaries reset to onset and ovulation is assumed to occur. If there is only a partial LH surge, P,(t) = 1, the ovaries also reset to onset but no ovulation (or only partial ovulation) is assumed to occur. With each change in time, At, the phase of the ovarian system changes by a constant proportion, AO, which is modulated by the state of the pheromonal-sensitivity system, PSi(t). The current ovarian phase, O~(t), is changed by AO[1 + PSi(t)], if the result is less than l, the maximum value for ovarian phase. Once it reaches its maximum value, ovarian phase does not change further until it is triggered to onset by an LH surge from the pituitary. 010
O,(t+ l) = 0
,(t)+AO[I+PS~(t)]
if Pi(t) = 2 if Pt(t) = l if O,{t)+AO[l+PSi(t)]
A Coupled-oscillator Model of Ovarian-cycle Synchrony Among Female Rats JEFFREY C. SCHANK t A N D M A R T H A
K. McCLINTOCK~§
t Committee on the Conceptual Foundations of Science and Department of Psychology, The University of Chicago and ~ Department of Psychology, The University of Chicago, 5730 Woodlawn Avenue, Chicago, Illinois 60637 U.S.A. (Received on 20 May 1991, Accepted in revised form on 25 March 1992) The ovarian cycles of female rats become synchronized when they live together, as do the cycles of many other mammals. Ovarian cycles also become synchronized when rats live apart if they share a common air supply, indicating that ovarian-cycle synchrony is mediated by pheromones. We developed a coupled-oscillator model of ovarian-cycle synchrony to test several hypotheses about its pheromonal and neuroendocrine mechanisms and to guide our experimental research. The model spans three levels of organization: the group, the rat, and the neuroendocrine components of the ovarian system. The ovarian system (not the ovaries themselves) are modeled as an oscillating system. Coupling among ovarian systems is mediated by the exchange of two pheromones, one that delays the phase of the ovarian system and one that advances it. Computer simulation experiments showed that this coupledoscillator model can explain the levels of ovarian-cycle synchrony observed in groups of female rats while, at the same time, matching an empirical distribution of ovariancycle lengths. By successfully matching computer simulation data with empirical data, we were able to infer theoretical predictions in a number of areas: (1) effect of initial conditions on the probability that a group will change to different synchrony level and phase relationships, i.e. the transition probability between all synchrony levels and phase relationships; (2) effects of individual differences in pheromone sensitivity on ovarian-cycle synchrony; (3) the timing of pheromone sensitivity during the ovarian cycle; and (4) the existence of partial luteinizing hormone surges, which may cause the "spontaneous" prolonged ovarian cycles associated with ovarian-cycle synchrony. The paper concludes by discussing the integrative role of this model for experimental research. In particular, we focus on the role of this model in interpreting theoretical aspects of ovarian-cycle synchrony as well as for guiding future experimental research into its mechanisms and functions.
1. Introduction
There are many examples of biological systems which undergo cyclic changes in physiology and behavior. Perhaps the most ubiquitous of biological cycles are circadian rhythms (i.e. daily rhythms in physiology and behavior that are close to 24 hr in length and remain nearly constant independent of external cues such as light and temperature). But, there are many other kinds of biological cycles in nature that § Author to whom reprint requests should be made. 317 0022-5193/92/1503 ! 7 + 46 $03.00/0
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exhibit interesting and complex behavior including the synchronization of cycles and even chaos (e.g. yon Hoist, 1969; Peskin, 1975; Winfree, 1980, 1987; Rinzel & Ermentrout, 1983; Glass & Mackey, 1988; Ermentrout, 1991). The goal of this paper is a better understanding of the mechanisms that produce ovarian-cycle synchrony among female rats and, in the long run, among females of the many other mammalian species that also exhibit ovarian synchrony (Miller, 1911; Reynold et al., 1952; Jolly, 1967; Fraser, 1968; Neal, 1970; McClintock, 1971, 1978, 1983b; Rasa, 1973; Harrington, 1974; Rood, 1974, 1975, 1978, 1980; van Horn, 1975; Abegglen, 1976; Estes, 1976; Dunbar & Dunbar, 1977; Rowell, 1977; Sinclair, 1977; Rowell & Hartwell, 1978; Frame et al., 1979; Keverne, 1979; Nishida, 1979; Rowell & Richards, 1979; Dunbar, 1980; Graham & McGrew, 1980; Handelmann et al., 1980; Russell et al., 1980; Hoek, 1981; McCracken & Bradbury, 1981; Quadagno et al., 1981 ; Buckley, 1982; Izard & Vandenbergh, 1982; Russell, I982; Iason & Guinness, 1985; Wallis, 1985, 1989; Matteo, 1987). There are a variety of mechanisms and signals that can cause the synchronization of biological cycles (e.g. see Winfree, 1980, 1987; Ermentrout, 1985; Glass & Mackey, 1988 for a discussion of some of these mechanisms and signals)t. In the case of circadian rhythms, light is an external time cue or signal that entrains circadian rhythms to the daily light-dark cycle. This kind of synchronization is due to an external periodic time cue--a Zeitgeber--that controls the synchronization of cycles. There are, however, other cases of the synchronization of biological rhythms for which there is no external Zeitgeber cueing synchronization. Among the most spectacular examples are the waves of synchronous flashing in swarming fire flies (Buck & Buck, 1968; Buck, 1988), and the collective synchronous behavior of cellular slime molds such as Dictyostelium discoideum (Bonner, 1967; Gerisch, 1968). In these cases and others, the synchronization of rhythmic changes in physiology or behavior is due to the mutual coupling of oscillating systems by physical signals such as flashes of light in fireflies (Buck, 1988; Ermentrout, 1991), or cyclic A M P in D. discoideum (Bonner, 1967; Gerisch, 1968; Winfree, 1980; Glass & Mackey, 1988). When female rats live together for three or four ovarian cycles, there is typically an increase in the number of females with synchronized ovarian cycles, although complete synchrony is rare (McClintock, 1978). Females that live apart synchronize their cycles to the same degree as females that live together if they share a common air supply (McClintock, 1978). Therefore, ovarian-cycle synchrony must be mediated by airborne chemosignals called pheromones (McClintock, 1983a). The fact that the ovarian system itself oscillates--though the ovaries alone do not oscillate (see Freeman, 1988 for review)--suggested to us that ovarian-cycle synchrony may be another t On the standard definitionof entrainment, two rhythms are entrained if and only if m cycles of one rhythm are locked to n cycles of the other (where m and n are integers and phase is the instantaneous state of a system; see Winfree, t980, 1987; Glass & Mackey, 1988). Synchrony is a special case of entrainment when there is a l-I locking (where re=n) and the cycles have essentiallyno differencein phase (Winfree, 1987). In this paper, we use the term synchronyin a similarsenseexceptthat we distinguish four equal stages or phases of the ovarian cycleand require a I-1 match only between these four phases of ovarian cycles. In this context, the term phase means a stage or interval of a cycle,which is in contrast to phase as the instantaneousstate of a system. We believethat these two uses of the term phase are clear in context.
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example of the mutual entrainment of coupled oscillators, in this case, the mutual entrainment of rat ovarian systems coupled by the exchange of pheromones (McClinrock, 1983b). Moreover, on the basis of experimental evidence described in McClintock (1984a), we believe that coupling among oscillators is mediated by two distinct signals: one advances and the other delays the phase of the ovarian system. In order to test this coupled-oscillator hypothesis, we have built a model for computer simulation. The model proposes that synchrony among rats is produced by the pheromonal coupling of ovarian systems. The model focuses on representing the timing of interactions among the neuroendocrine, the physiological, and the pheromonal systems that interact to produce and entrain ovarian cycles in rats (section 2). Where there are gaps in our knowledge about these interactions, we have proposed auxiliary hypotheses that are biologically reasonable as a basis for developing a workable model (section 3). Data from computer simulation experiments, using this model matched empirical data, and thus allowed us to derive a number of testable theoretical predictions (section 4). Finally, we discuss several functions of the model, both for interpreting ovarian synchrony as well as for guiding future experimental work on its mechanisms and functions (section 5). 2. Ovarian-cycle Synchrony in Rats: An Overview In this section, we describe the empirical basis for our model and computer simulations. The information is presented in considerable detail, because it is important for identifying the key biological events and interactions that should be represented in a biologically realistic model of the rat ovarian system as well as the empirical data relevant to testing the model. We begin by describing the ovarian system: the phases of the ovarian cycle, the biological indicators of these phases, and the key physiological and endocrine events that control the timing of the ovarian cycle (section 2.1). We then describe the characteristics of ovarian-cycle synchrony in groups of female rats and its mediation by pheromones (section 2.2). Finally, we describe the effects of two different pheromones that are produced at different phases of the ovarian cycle: one that lengthens the ovarian cycles of recipient females and another that shortens their cycles (section 2.3). 2.1. T H E O V A R I A N C Y C L E
Ovulation in rats, as well as other mammals, is caused by a surge of luteinizing hormone (LH) from the anterior pituitary; the LH surge luteinizes several follicles in the ovary causing each to rupture and release its egg (see Feder, 1981; Freeman, 1988 for reviews). At the site of rupture, a corpus luteum forms, and although it is technically non-functional in the rat (i.e. it is short lived), it does secrete progesterone that can affect the length of the ovarian cycle (Feder, 1981 ; Freeman, 1988; S~mchezCriado et al., 1988). Just after ovulation, a new set of follicles begins to mature and releases increasing amounts of the ovarian steroid, estrogen, which primes the system for another surge of LH. Typically, the cycle repeats 4 or 5 days later when a new LH surge again triggers ovulation (see Feder, 1981 ; Freeman, 1988 for reviews).
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2.1.1. Cytological and behavioral indicators of the phase of the ovarian cycle Ovarian cyclicity is associated with cyclic changes in the frequency and intensity of specific sexual behaviors of unmated female rats, termed the estrous cycle (Feder, 1981)t. These behaviors include lordosis (a reflex elicited by flank stimulation) and soliciting the male. These sexual behaviors increase in frequency and intensity on the day of the LH surge, and in general, provide a reliable indicator of ovarian cyclicity in female rats (McClintock, 1984b). Ovarian cyclicity is also associated with cyclic changes in vaginal cytology (e.g. see Feder, 1981 for further discussion). On the basis of changes in behavior and vaginal cytology, it is conventional to distinguish four phases of the estrous cycle: proestrus, estrus, metestrus, and diestrus~. Each phase is 24 hr in length (for the prototypical 4-day cycle), and runs from midnight to midnight. The cyclic changes in behavior and vaginal cytology are dependent on the ovarian cycle, since ovariectomy resulted in the cessation of cycles in both behavior and vaginal cytology (Schwartz, 1969; Feder, 1981; Freeman, 1988). Using the estrous cycle as an indicator of the ovarian cycle, researchers have found that female rats typically have 4-day or 5-day ovarian cycles (Shnchez-Criado et al., 1988; LeFevre & McClintock, 1988). Nonetheless, rats also have a significant number of very prolonged cycles, up to 38 days in length (Long & Evans, 1922; LeFevre & McClintock, 1988). These prolonged cycles appear to be "spontaneous" and share characteristics in common with pseudopregnancies in rats (Long & Evans, 1922; Everett, 1963). In the Sprague-Dawley strain of rats, for which we have data, females typically exhibit 4-day ovarian cycles but with considerable variation in cycle lengths including "spontaneous" prolonged cycles (McClintock, 1978, 1983a; LeFevre & McClintock, 1988). In short, these cytological indicators of the estrous cycle are especially important for three reasons. First, they allowed us to measure increases or decreases in group synchrony (section 2.2). Second, they allowed us to measure the effects of pheromones on ovarian-cycle length (section 2.3)§. Third, they allowed us to generate an empirical cycle-length distribution, which was then used as a template against which to match simulation data (section 4). 2.1.2. Key mechanisms and the timing of ovarian cycle events Ovulation occurs early in the morning of estrus and is triggered by a surge of LH that is released the previous day, during the afternoon of proestrus. An ovulatory surge of LH is released by the pituitary once two conditions have been met. First, the pituitary must be primed by ovarian steroids (especially estrogen during diestrus
t The behavior during this phase of the ovarian cycle is termed estrus (the term "estrus" comes from the Latin term oestrus which means in a frenzy) and the periodic change in behavior is the estrous cycle. :~See footnote on p. 318 for the two senses of the term phase used in this paper. § These four phases of the estrous cycle are also used to describe cycles that are longer than 4 days in length (LeFevre & McClintock, 1988). For example, if a 5-day cycle is observed and there is an extra day with a large proportion of leukocyte cells, then this cycle would be called a 5-day cycle with a prolonged metestrous phase (i.e. 2 days of metestrus were observed).
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and early proestrus). In particu!ar, estrogen may act by increasing pituitary LH content and the number of luteinizing hormone releasing hormone (LHRH) receptors (or by affecting postreceptor mechanisms; see Fink, 1988; Freeman, 1988 for reviews). The pituitary is also primed by LHRH released from hypothalamic neurons into hypophysial-portal blood (during proestrus; Fink, 1988). Second, once the pituitary is fully primed, a surge of LHRH from hypothalamic neurons releases an ovulatory LH surge from the pituitary (Fink, 1988). There are also two conditions that must be met before the LHRH neurons of the hypothalamus release a surge of LHRH. First, these neurons must be primed by ovarian steroids (especially estrogen; see Feder, 1981; Freeman, 1988 for reviews). One effect of estrogen---especially in conjunction with progesterone--may be to increase the capacity of LHRH neurons to respond to depolarizing stimuli, and thereby facilitate the release of LHRH (Kordon & Drouva, 1990; see Freeman, 1988 for review of the priming effects of ovarian steroids on the hypothalamus). It also has been recently reported that estrogen stimulates the synthesis of LHRH mRNA (Rosie et al., 1990). Second, once the LHRH neurons are fully primed, a circadian signal of neural origin (i.e. from the anterior hypothalamus, including the suprachiasmatic nuclei and the medial preoptic areas) causes a cascade of events that triggers the primed LHRH neurons to release a surge of LHRH (see Fink, 1988; Freeman, 1988 for review). The precise timing of the daily neural-signal and of the priming of the pituitary and hypothalamus is known for Sprague-Dawley rats with regular 4-day cycles. The daily neural-signal that triggers the LHRH surge occurs during a very narrow critical period: every afternoon from 1400-1600 hr (Everett et al., 1949; Everett & Sawyer, 1950, 1953; Everett, 1956; Everett & Tejasen, 1967)t. In addition, priming of both the pituitary and hypothalamus is complete by 1200 hr of proestrus (Feder, 1981). Thus, if a neural signal is received by 1600 hr, and if the hypothalamus and pituitary have been fully primed by ovarian steroids, then an LHRH surge is triggered, rapidly causing the release of an LH surge from the pituitary in the late afternoon of proestrus, which in turn triggers ovulation early the following morning, on estrus. We are aware of the many other neuroendocrine events and mechanisms involved in this axis, e.g. the pulsatile release of LH (Levine & Ramirez, 1982; Fox & Smith, 1985), inhibin (Steinberger & Ward, 1988) and FSH (Schwartz, 1969). Our initial goal, however, was to select just those events and mechanisms directly responsible for the timing of the preovulatory LH surge, in a time frame of hours and days. Future elaborations of the model could incorporate the neuroendocrine mechanisms regulating the rate of ovarian development, i.e. follicular maturation and the life
t The timing of this critical period is relative to a constant light--dark cycle and entrained to the particular light-dark cycle under which rats are maintained (it is the same for 14 hr of light and 10 hr of dark or 12 hr of light and 12 hr of dark; (Everett et al., 1949; Everett & Sawyer, 1950, 1953; Everett & Tejasen, 1967). Finally, Everett & Tejasen (1967) emphasized differences in the critical period between Sprague-Dawley and Osborne-Mendel rats, but after examining the data they present in Everett & Tejasen (1967: fig. I, p. 791), it is clear that this difference is minimal and that Sprague-Dawley rats should be characterized as having a critical period between 1400 and 1600 hr.
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span of the corpus luteum, if needed to develop a better model (e.g. see Lacker, 1981; Lacker & Peskin 1981; Lacker et al., 1987a, b for mathematical models of follicular maturation in mammals).
2.2. O V A R I A N - C Y C L E
SYNCHRONY
When female rats are placed in small groups, there is an increase in the synchrony of their ovarian cycles. Synchrony is manifested by an increase in the number of females in a group that are in the same phase of the cycle on the same day (e.g. in proestrus as indicated by sexual behavior and vaginal cytology; McClintock, 1978). Synchrony, in Sprague-Dawley rats, is also associated with a characteristic distribution of cycle lengths, including "spontaneous" prolonged ovarian-cycles (McClintock, 1983a). It takes about three cycles for synchrony to develop and it is maintained for at least 12 cycles (McClintock, 1978, 1983b). Complete synchrony is rare, however. In groups of five females, there are usually one or two females that are not synchronized with the others, which may reflect a balance of different reproductive strategies (see section 5.3.2; McClintock, 1978, 1983b). Ovarian-cycle synchrony is mediated by pheromones (airborne chemosignals), since females that share a recirculated air supply, but are otherwise physically isolated from each other, synchronize their cycles as rapidly, and to the same level, as females that are caged together (McClintock, 1978). This suggested to us that there are pheromones released during specific phases of the ovarian cycle that synchronize ovarian cycles within a group. If so, then ovarian-cycle synchrony can be conceptualized as the result of the mutual entrainment of ovarian cycles in a pheromonallycoupled system of oscillators (McClintock, 1983a, b, 1984a).
2.3. T H E
EFFECT
OF OVARIAN
PHEROMONES
ON THE
OVARIAN
CYCLE
In many coupled-oscillator systems, synchrony is caused by the interaction of two types of signals: one that phase delays the cycle and another that phase advances it (e.g. Aschoff, 1960; Buck & Buck, 1968; von Hoist, 1969; McClintock, 1983b, c). Given that pheromones mediate ovarian-cycle synchrony in rats, we hypothesized that there are two different pheromones released during specific phases of the ovarian cycle that have opposing effects on the recipient's ovarian cycle: one pheromone that phase-delays and therefore lengthens the cycle, and a second, released during a different phase, that phase advances and therefore shortens the cycle. In order to test this hypothesis, we identified three phases of the ovarian cycle that have distinct hormonal patterns and thus could produce different pheromones with different effects: ovulatory, luteal, and preovulatory phases. The ovulatory phase is characterized by high levels of estrogen, progesterone, and LH (Fig. 1). The luteal phase is characterized by high levels of progesterone, but low levels of estrogen and LH (Fig. 1). In contrast, the preovulatory phase is characterized by high levels of estrogen, but low levels of progesterone and LH (Fig. 1). We collected pheromones during a 24-hr period in each of these three phases (0500-0500 h) and continuously
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Estrogen Time of pheromone sampling
Luteal
,,
(
[]
..---..
°,atory o m ............... ....... -........
\
)
Progesterone ( ................... ) LH (....... )
i\
.
i
i
i
i
....,°..-""*°°
................................... 0-25 E
0.5 M
)'i 0.75 D
.................
0"0 P
0.25 E
Phase of ovarian cycle in days and phase scale [0,1] F1G. 1. A schematic representation of hormone levels during the rat's ovarian cycle: luteinizing hormone (LH) and the ovarian steroids, estrogen and progesterone. The horizontal axis represents both the
four phases of the ovarian cycle in days, estrus (E), metestrus (M), diestrus (D), and proestrus (P), as well as the phase scale [0, I] used in the model described below. The shaded bars indicate the times when different pheromones were sampled during McClintock's phase-resetting experiments (1984). Ovulatory odors were sampled when estrogen levels were high, progesterone was rising sharply and there was a surge of LH. Preovulatory odors were sampled when estrogen was rising, progesterone was decreasing, and LH was at baseline levels. Luteal odors were sampled when estrogen was low, progesterone was rising and LH was at baseline levels.
exposed female rats to them (see Fig. I for results and McClintock, 1983a, b, 1984a for experimental methods)t. Preovulatory pheromones shorten and regularize the ovarian cycles of recipient rats, in comparison to cycles of control rats exposed only to background odors; in fact all cycles are four days in length [Fig. 2 (a) and (b); see section 5.1 for an interpretation of this result]J;. Ovulatory pheromones have the opposite effect, they lengthen ovarian cycles and make them more irregular [Fig. 2(c)]. Luteal pheromones have no significant effect [Fig. 2(d)]. These experimental results clearly support the hypothesis that there are two signals mediating synchrony. Moreover, since these t The period from 0500 hr of estrus to 0500 hr of metestrus is part of the luteal phase but was not sampled in the experiment described below in order to control for duration of pheromone production (McClintock, 1984a). :[:The cycle-length data presented in Fig. 2(a)-(d) differs from the cycle-length data presented in McClintack (1984) in our reinterpretation of 2- and 3-day cyclic changes in vaginal cytology. Based on the literature and new hormonal data, we now interpret them as being part of the previous cycle rather than an extremely short cycle. For example, if a 5-day cycle was followed by a 3-day cycle, this was reinterpreted as a prolonged 8-day cycle. This reinterpretation affected less than 5% of the cycles.
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Preovulotory
Control I00
(a)
I
,o)
80 60 40 20
~
o Ovulatory
t.)
Luteal
(c)
(d)
8O 6O 4O
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8+
I
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.5
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8+
Cycle length (days)
FIG. 2. The effectsof four different odor conditions on the cycle-lengthdistributions of female rats. In the control condition, femaleswere exposed to background colony odors (a). In the experimentalconditions, three kinds of odors were presented continuously (the sampling times for these three ovarian-cycle odors are indicated in Fig. 1). Preovulatory odors shortened and regularized ovarian cycles (b), while ovulatory odors lengthened ovarian cycles and made them more irregular (c). Luteal odors had no significant effect (d).
results precisely established the times when pheromones with opposing effects on ovarian-cycle length are released, they allowed us to incorporate the timing o f these opposing effects into the model described below.
3. The Model and Simulation Design We used the empirical information just described to design the coupled-oscillator model and computer simulations o f ovarian cycle synchrony proposed in this section. But, this empirical information is not by itself sufficient to design even a simple workable model of ovarian-cycle synchrony in groups of rats; it does not provide sufficient biological detail of neuroendocrine and pheromonal systems required to build a formal model. Therefore, we have also proposed auxiliary hypotheses, which are nevertheless biologically plausible, aimed at filling in the gaps in our knowledge about key features o f these systems (see Kauffman, 1971 for a classic account o f this kind o f exploratory modeling strategy, and Barinaga, 1990 for a brief discussion o f the use o f this strategy in neuroscierfce).
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A successful match between computer simulation and empirical data will support the empirical plausibility of the model; that is, it will confirm the main hypotheses, such as the pheromonal coupling of oscillating-ovarian systems, as well as lending empirical plausibility to the auxiliary hypotheses that we have proposed about specific neuroendocrine and pheromonal systems. In particular, because these auxiliary hypotheses are an essential part of this model, a match would also be a directive for future empirical work aimed at testing the predictions made by these auxiliary hypotheses.
3.1. A U X I L I A R Y H Y P O T H E S E S
3.1.1. Production of pheromones Although we do know that pheromones produced during the 24-hr period of the follicular, or preovulatory, phase (0500-0500 hr) have effects opposite to those of pheromones produced during the 24-hr period of the ovulatory phase (also 05000500 hr), we do not know exactly how either of these effects change within these 24hr periods. In the absence of this information, we have hypothesized that the effects of both pheromones wax and then wane, rather than dichotomously turning on and then off. Given that the phase-advance pheromone directly precedes the phase-delay pheromone, we decided to use a sinusoidal curve that spans half of an ovarian cycle" to representthe change in the effect of pheromones (i.e. spanning 0500 hr of diestrus to 0500 hr of estrus; see Fig. 4 below). It is also biologically reasonable to hypothesize that the effects of these pheromones dissipate quickly (i.e. over minutes or hours and not days), since otherwise the effects of these two pheromones would tend to "cancel" each other out during an ovarian cycle. This is in agreement with what we know about the chemical volatility of many pheromones in mammals (Albone, 1984). Thus the sinusoidal curve that we use combines both the waxing and waning of pheromone production with the dissipation of these pheromones. 3.1.2. Pheromone sensitivity: timing and duration If there are two pheromones that cause synchrony, sensitivity to pheromones must also wax and then wane. This is because mutual synchronization within a group requires that: (1) an oscillator that is just lagging behind the rest of the oscillators in a group receive a phase-advancing signal and (2) an oscillator that is just ahead of the group receive a phase-delaying signal (Winfree, 1980). If sensitivity to pheromones does not wax and then wane, this condition for synchronization cannot be met because the entrainment effects of the two opposing pheromones would cancel each other out over an entire cycle (see section 5.1 for further discussion). It is biologically reasonable to hypothesize that sensitivity to pheromones involves the olfactory system, and that cyclic variation in olfactory sensitivity of female rats could indicate when they are sensitive to ovarian-cycle pheromones. Pietras & Moulton (1974) systematically documented changes in olfactory sensitivity during the ovarian cycle of female Sprague-Dawley rats. Olfactory sensitivity increases from
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the early afternoon of proestrus (i.e. 1400 hr) and remains high until late in the evening ofestrus (i.e. 2200 hr). This places the center of olfactory sensitivity to odors at 0600 hr o f estrus. The increases and decreases in sensitivity to odors are sharp transitions, which have the form o f a square wave. Thus, we hypothesized that Sprague-Dawley rats are sensitive to pheromones only when their olfactory sensitivity is high: a 32-hr period centered at 0600 o f estrus, adequately approximated by a square wave (see Fig. 4 below).
3. 1.3. Indioidual differences in pheromone sensitioity There are individual differences in the distribution of ovarian-cycle lengths among young female Sprague-Dawley rats (ages 3-6 months; LeFevre & McClintock, 1991 ; see also Long & Evans, 1922: table 37). Some females exhibit nearly all 4-day cycles. Other females exhibit a mix o f 4- and 5-day cycles. Still fewer females exhibit predominantly 5-day cycles or a mix of 4- and 6-day cycles with an occasional prolonged cycle or spontaneous pseudopregnancies. Long & Evans (1922) hypothesized that the 4-day cycle is normal for female rats and that any deviation indicates poor health of the animal. But, contrary to Long & Evans (1922), the young animals in our laboratory colony were in excellent health (McClintock, 1978, 1984a). Thus, individual variation in our cycle-length data is not likely due to individual differences in the health of animals. Indeed, any factor that affects the rate o f follicular development could account for the individual differences observed in ovarian-cycle length in female rats. As a first approximation, we can begin by distinguishing between intrinsic and extrinsic factors affecting cycle length. An example o f an intrinsic factor would be individual differences in the initial state o f maturity of follicles recruited to start a new ovarian cycle, which has been shown theoretically to lead to differences in ovarian-cycle length in mammals (Lacker, 1981 ; Lacker & Peskin, 1981). An example of an extrinsic factor would be ovarian-cycle pheromones, which presumably act in some manner to alter the rate o f follicular development. In our model, we are particularly interested in the effects o f pheromones on ovarian-cycle length and therefore we have made the idealizing assumption that in healthy young female rats, pheromones are the only source o f individual differences in ovarian-cycle lengtht. Although this assumption is an idealization, we will show below that it does a remarkably good job o f explaining our empirical data, which strongly suggests that individual differences in cycle lengths-measured in days in female rats--has its main source in the exchange o f ovariancycle pheromones (also see section 5.1 for further discussion o f this hypothesis)~. t Another extrinsic factor that is likely to be important for determining the individual differencesin the sequence of cycles of different length is the specificconfiguration of ovarian-cyclephases within the group. This configuration is important because the ovarian-cyclephases of these other rats will determine what type of pheromones a female rat is exposed to when she is sensitive to pheromones. :l:The circadian regulation of the timing of ovulation in rats tends to support this idealization. Small intrinsic individual differencesin rates of follicular development or timing of LH surges, which are measured on a time scale of minutes or hours, are truncated to a time scale of days via circadian modulation. Thus, even though there may be intrinsic individual differencesamong females in rates of follicular development or timing of LH surges, in the absence of extrinsic factors such as pheromones, cycle lengths in female rats will typically be 4 days in length.
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3.1.4. Priming the pituitary and the hypothalamus: a mechanism for variation in cycle length Although ovarian cycles in rats are typically 4 days long, there is considerable variation in cycle length, including cycles of up to 38 days or longer (Long & Evans, 1922; LeFevre & McClintock, 1991). Cycles that are 5-7 days long typically appear as extended 4-day cycles, that is, with extended metestrus and/or diestrus-estrus phases (Nequin et al., 1979; LeFevre & McClintock, 1988). There is another class of long cycles, 8 days or more in length, that we term prolonged ovarian cycles. These prolonged cycles are often described as occurring "spontaneously" and are sometimes referred to as "spontaneous" pseudopregnancies (e.g. Long & Evans, 1922; Everett, 1963). Close examination of changes in vaginal cytology during these "spontaneous" prolonged cycles has revealed subliminal cycles, in the proportion of cell types, that are 4-7 days in length (McClintock, unpublished data)t. Since the length of "spontaneous" prolonged cycles can be interpreted as multiples of shorter, more typical cycles (i.e. 4-, 5-, 6-, and 7-day cycles), this suggested to us a possible mechanism for their "spontaneous" occurrence. That is, a mechanism that would enable the ovarian system to "reset" without also triggering the full ovulation that normally begins a new cycle. Such a mechanism could produce subliminal anovulatory cycles that together would comprise a prolonged cycle with a length that is a multiple of shorter-cycle lengths. Our proposed mechanism has two thresholds: one for full and the other for partial steroid priming of the pituitary and hypothalamus. When ovarian steroid levels reach the full-priming threshold, the daily neural signal triggers a full LH surge and ovulation, which begins a new cycle (see section 2). When ovarian steroid levels reach only the partial-priming threshold, which is slightly lower than the full-priming threshold, the neural signal will only trigger a partial LH surge. A partial LH surge can reset the ovarian cycle but cannot cause ovulation (i.e. there is some luteal activity and folliculogenisis, but not complete follicular rupture). These anovulatory cycles should be 4-7 days in length, as are short ovulatory cycles bounded by full LH surges. A sequence of one or more anovulatory cycles will be observed as a prolonged cycle (i.e. a prolonged cycle is bounded by full LH surges, but contains one or more subliminal cycles, each indicated by a partial LH surge). If ovarian steroids do not reach either of the two thresholds by the time of the daily neural signal, then ovarian development continues until the next daily signal and the cycle is lengthened by only 1 or more days. For these short cycles, the cycle length is directly proportional to the rate of ovarian development. This is in contrast to prolonged cycles, which are longer than would result simply from delayed ovarian development.
t More specifically, subliminal cycling in vaginal cytology means that there are 4- to 5-day cyclic patterns of increase and decrease of nucleated and cornified epithelial cells in the daily smears within prolonged cycles. The subliminal variation in the percentage of leukocytes in these prolonged cycles does not reach the criterion of >80% in the smear, which indicates proestrus, ovulation, and a new cycle onset (McClintock, 1978).
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This idea--that there is a second threshold for partial steroid priming of the hypothalamus and pituitary and that partial LH surges can lead to anovulatory resetting of the ovarian cycle--is a novel hypothesis. Nonetheless, it is supported by the literature in several respects. A few studies of the full LH surge also report anecdotally very small or partial surges of LH (e.g. less than 20% of full surge levels; Carrillo & Sawyer, 1978; Allen & Kalra, 1986). These partial LH surges, however, are typically dismissed as anomalies or measurement errors with no functional significance. There is, however, in vitro evidence that small amounts of LH (i.e. as small as 5% of the normal LH surge) can cause luteal steroidogeisus without ovulation (Peluso, 1990). If confirmed in vivo, this mechanism would explain how partial LH surges reset the ovarian system without causing full ovulation, producing an anovulatory cycle. Finally, evidence also comes from a classic series of elegant studies by Everett and colleagues (Everett et al., 1949; Everett & Sawyer, 1950, 1953; Everett & Tejasen, 1967) which showed that by partially blocking a full LH surge during the circadian critical period, partial ovulation or anovulation often results. In the model, we have specified that: (1) Full steroid priming, in both the pituitary and hypothalamus, is reached by 1200 hr of proestrus in regular 4-day cycling rats (Feder, 1981 ; Wise et al., 1981). (2) Partial priming is hypothesized to have a lower threshold, which is achieved 3 hr earlier, at 0900 hr. We based this hypothesis on experimental evidence, which has established that this is the time when LHRH concentrations in the hypothalamus increase significantly in Sprague-Dawley rats (Wise et al., 1981). An increase in the hypothalamic concentration of LHRH indicates steroid priming in both the hypothalamus and the pituitary, and in turn, triggers the release of LH from the pituitary. (3) Prior to 0900 hr of proestrus LHRH concentrations are not significantly above baseline (Wise et al., 1981), and thus we hypothesized that neither the hypothalamus nor pituitary are primed prior to 0900 hr of proestrus during a regular 4-day cycle. In short, if full priming is achieved by the end of the critical period for the neuralcircadian signal (1600 hr), then a full LH surge will be triggered, causing ovulation and resetting of the ovarian cycle. If, however, only partial priming is achieved by the end of the critical period, then there will only be a partial LH surge and the ovarian cycle will reset without ovulation, ceasing an anovulatory cycle. If neither threshold is reached by the end of the critical period, then the cycle will be prolonged by at least another day--until the time of the neural signal on the next day. 3.1.5. Summary o f the main auxiliary hypotheses The principle auxiliary hypotheses described above are worth emphasizing again: (H 1) Sensitivity to pheromones starts at 1400 hr of proestrus and ends at 2200 hr of estrus. (H2) There are individual differences among female rats in their sensitivity to pheromones. (H3) If ovarian steroids reach only the partial-priming threshold by the end of the critical period for the daily neural signal, then the neural signal will trigger only a partial LH surge.
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(H4) Partial LH surges cause anovulatory cycles, which are part of prolonged ovulatory cycles. (H5) Ovarian-cycle pheromones (specifically, ovulatory pheromones) increase the likelihood of partial LH surges by delaying ovarian-cycle development, which, in turn, delays the priming of the hypothalamus and pituitary. (H6) Individual differences among female rats in pheromone sensitivity are primarily responsible for individual differences in ovarian-cycle length.
3.2. T H E M O D E L
The interactions among the components of this multi-level model are presented schematically in Fig. 3. These include interactions among: the neuroendocrine components of the ovarian system, ovarian and pheromonal systems, and rats living in groups. A simple mathematical model of this multi-level system is presented below in terms of finite difference equationst. In this model, the ovaries can cycle only if there is hormonal input from the pituitary; thus the ovaries are not modeled as simple clocks. Full or partial LH surges from the pituitary reset the ovaries (ovarian phase, Oi, resets from 1, the maximum value for ovarian phase, to 0). If there is a full LH surge from the pituitary, P~(t) = 2, the ovaries reset to onset and ovulation is assumed to occur. If there is only a partial LH surge, P,(t) = 1, the ovaries also reset to onset but no ovulation (or only partial ovulation) is assumed to occur. With each change in time, At, the phase of the ovarian system changes by a constant proportion, AO, which is modulated by the state of the pheromonal-sensitivity system, PSi(t). The current ovarian phase, O~(t), is changed by AO[1 + PSi(t)], if the result is less than l, the maximum value for ovarian phase. Once it reaches its maximum value, ovarian phase does not change further until it is triggered to onset by an LH surge from the pituitary. 010
O,(t+ l) = 0
,(t)+AO[I+PS~(t)]
if Pi(t) = 2 if Pt(t) = l if O,{t)+AO[l+PSi(t)]
