## Abstract

Presynaptic short-term plasticity (STP) dynamically modulates synaptic strength in a reversible manner on a timescale of milliseconds to minutes. For low basal vesicular release probability (prob_{0}), four components of enhancement, *F1* and *F2* facilitation, augmentation (*A*), and potentiation (*P*), increase synaptic strength during repetitive nerve activity. For release rates that exceed the rate of replenishment of the readily releasable pool (RRP) of synaptic vesicles, depression of synaptic strength, observed as a rundown of postsynaptic potential amplitudes, can also develop. To understand the relationship between enhancement and depression at the frog (*Rana pipiens*) neuromuscular synapse, data obtained over a wide range of prob_{0} using patterned stimulation are analyzed with a hybrid model to reveal the components of STP. We find that *F1*, *F2*, *A*, *P*, and depletion of the RRP all contribute to STP during repetitive nerve activity at low prob_{0}. As prob_{0} is increased by raising Ca_{o}^{2+} (extracellular Ca^{2+}), specific components of enhancement no longer contribute, with first *P*, then *A*, and then *F2* becoming undetectable, even though *F1* continues to enhance release. For levels of prob_{0} that lead to appreciable depression, only *F1* and depletion of the RRP contribute to STP during rundown, and for low stimulation rates, *F2* can also contribute. These observations place prob_{0}-dependent limitations on which components of enhancement contribute to STP and suggest some fundamental mechanistic differences among the components. The presented model can serve as a tool to readily characterize the components of STP over wide ranges of prob_{0}.

## Introduction

Chemical synapses are major sites of information transfer between neurons and from neurons to effectors, such as muscle cells. A characteristic property of such synapses is that the amount of transmitter released from nerve terminals by each action potential can change dramatically during a train of impulses (Cowan et al., 2001; Atwood and Karunanithi, 2002; Zucker and Regehr, 2002; Neher and Sakaba, 2008). These changes, referred to as short-term synaptic plasticity (STP), have dramatic reversible effects on synaptic strength (Liley and North, 1953; Zengel et al., 1980; Magleby and Zengel, 1982; Dittman et al., 2000; Wesseling and Lo, 2002; Abbott and Regehr, 2004; Pan and Zucker, 2009; Kandaswamy et al., 2010; Müller et al., 2010).

Components of STP that increase transmitter release (enhancement) include first (*F1*) and second (*F2*) components of facilitation with time constants of 50 and 300 ms (Mallart and Martin, 1967; Magleby, 1973a; Zengel and Magleby, 1982; Goda and Stevens, 1994; Bennett et al., 2007), augmentation (*A*) with a time constant of 4–7 s (Magleby and Zengel, 1976a; Zengel and Magleby, 1982; Stevens and Wesseling, 1999), and potentiation (*P*) with a time constant of tens of seconds to minutes (Liley and North, 1953; Magleby, 1973b). For low basal vesicular release probability, prob_{0}, all four enhancement processes, *F1*, *F2*, *A*, and *P*, make major contributions to STP during repetitive nerve activity (Magleby and Zengel, 1982). In contrast, at normal prob_{0}, depression, typically indicated by a rundown of postsynaptic potential amplitudes during a train of impulses, can develop depending on the specific synapse and the stimulation rate (Liley and North, 1953; Mallart and Martin, 1968; Magleby, 1973b; Wu and Betz, 1998; Dittman et al., 2000; Wesseling and Lo, 2002; Stevens and Williams, 2007). The contributions of *F1*, *F2, A*, and *P* to STP during depression are less clear, as previous studies suggest that some of the components of enhancement may no longer contribute for normal prob_{0} (Dittman et al., 2000; Kandaswamy et al., 2010; Müller et al., 2010).

To explore this question, we examine the interaction of the components of enhancement with depression over a wide range of prob_{0} to change the level of depression. Experiments are performed on the neuromuscular synapse where the components of enhancement and depression were initially characterized (Liley and North, 1953; Takeuchi, 1958; Mallart and Martin, 1967; Magleby and Zengel, 1976a, 1982) and where depletion and recovery of synaptic vesicles is well described (Richards et al., 2003; Rizzoli and Betz, 2005). To reveal the components of STP during repetitive stimulation, a quantitative model that accounts for transmitter release at low quantal content (Magleby and Zengel, 1982) is expanded to incorporate depletion and replenishment of synaptic vesicles, and patterned stimulation is used to facilitate identification of the various components. We find that the specific components of enhancement contributing to STP during repetitive stimulation depend on prob_{0}, with first *P*, then *A*, and then *F2* no longer contributing as prob_{0} is increased from low to normal by increasing extracellular Ca^{2+} (Ca_{o}^{2+}), whereas *F1* always contributes.

## Materials and Methods

#### Animals, solutions, and surface recording of end plate potentials

End plate potential (EPP) amplitude is used to track STP, as under the conditions of our experiments EPP amplitude is proportional to the number of synaptic vesicles releasing their transmitter after each nerve impulse (Zengel and Sosa, 1994; Zengel and Magleby, 1981). EPP amplitudes were recorded from the sartorius nerve–muscle preparation of northern grass frogs (*Rana pipiens*) of either sex with a surface electrode, as described previously (Magleby, 1973a). Animal protocols were approved by the Institutional Animal Care and Use Committee at the University of Miami Miller School of Medicine and are in accordance with National Research Council *Guidelines for the Care and Use of Laboratory Animals*. The preparation was bathed in modified Ringer's solution containing the following (in mm): 115 NaCl, 2 KCl, 2 CaCl_{2}, 1 MgCl_{2}, 5 HEPES, 5 glucose, and 0.03 choline chloride. pH was adjusted to 7.3. Experiments were performed within the physiological temperature range for frogs (18–21°C), as temperature alters STP (Zengel et al., 1980; Klyachko and Stevens, 2006). The extracellular concentration of Ca^{2+} was reduced or raised, as indicated, to decrease or increase prob_{0}, respectively. Tubocurare was added at concentrations of ∼2–5 μm to reduce EPP amplitudes well below threshold for the generation of action potentials in the muscle fibers.

A surface electrode was used to record the summed response of EPPs from a large number of end plates, each with thousands of active zones, thereby greatly reducing the measured stochastic variation in response. To further reduce variation, EPP amplitudes from three to five trains obtained from the same end plate region of a single muscle were averaged. Such surface recording gives a good measure of average intracellular response (Magleby, 1973a). Under the conditions of our experiments, where EPP amplitudes are typically a few millivolts or less because of low quantal content or the presence of curare, nonlinear summation of EPP amplitudes (McLachlan and Martin, 1981) is minimal and quantal size (miniature EPP amplitude) and postsynaptic sensitivity remain constant during a stimulation train (Magleby and Pallotta, 1981; Zengel and Sosa, 1994). Hence, observed changes in EPP amplitudes (synaptic strength) and STP in our experiments are presynaptic in origin, arising from a change in the number of vesicles whose contents are released by each nerve impulse. Examples of surface recorded EPPs have been presented previously (Magleby, 1973a; Magleby and Zengel, 1976a). The basal (control) EPP amplitude was obtained from the average of five EPPs delivered one every 5 or 10 s before the train. Rest periods between trains of impulses were typically 6 min.

#### Estimating the contributions of *F1*, *F2*, *A*, *P*, and depression to STP

A hybrid model was used to quantify the contributions of *F1*, *F2*, *A*, and *P* during repetitive stimulation. The model is an extension of the quantal hypothesis proposed by del Castillo and Katz (1954) that often serves as a starting point for more extensive models of transmitter release (Varela et al., 1997; Wu and Borst, 1999; Dittman et al., 2000; Zucker and Regehr, 2002; Trommershäuser et al., 2003; Kalkstein and Magleby, 2004; Pan and Zucker, 2009; Kandaswamy et al., 2010) as follows:
where EPP* _{t}* is the number of quanta (vesicles) released by a nerve impulse to generate an EPP at time

*t*during a train, RRP

*is the number of vesicles in the readily releasable pool (RRP) available for release at time*

_{t}*t*, and prob

*is the vesicular release probability given by the fraction of vesicles in the RRP that are released by a nerve impulse at time*

_{t}*t*. EPP

_{0}, prob

_{0}, and RRP

_{0}indicate the values of these parameters in the fully rested state at time 0 before the start of the train. At the frog neuromuscular synapse, RRP

_{0}is ∼10,000 vesicles (Rizzoli and Betz, 2005), and a single action potential in the rested state for conditions of normal quantal content (2 mm Ca

^{2+}) releases ∼200 vesicles from the RRP (Heuser et al., 1979; Van der Kloot and Molgó, 1994), giving a prob

_{0}of ∼0.02. Vesicles released from the RRP are assumed to be replenished from a recycling pool (RP) with a content of ∼75,000 vesicles (Rizzoli and Betz, 2005). There is an additional relatively fixed reserve pool of ∼400,000 vesicles, which is not included in the considered models. With ∼300 active zones and ∼40 vesicles per active zone, ∼12,000 vesicles appear docked at each frog neuromuscular synapse, similar to the size of the RRP (Rizzoli and Betz, 2005).

##### Enhancement.

The model of Magleby and Zengel (1982) is based on the accumulation and decay of release enhancing factors for *F1*, *F2*, *A*, and *P*, and accounts for STP at low quantal content in the absence of apparent depression. Their model is expanded to include depletion of the RRP, as follows:
where EPP* _{t}*/EPP

_{0}is the ratio of the number of vesicles released by a nerve impulse at time

*t*during the train divided by the number of vesicles released by a nerve impulse in the basal condition. Under the recording conditions of our experiments EPP amplitude is proportional to the number of quanta released (see above). EPP

*/EPP*

_{t}_{0}thus gives a normalized measure of the changes in transmitter release during the train.

*F1*,

_{t}*F2*,

_{t}*A*, and

_{t}*P*are the magnitudes of the first and second components of facilitation, augmentation, and potentiation, respectively, at time

_{t}*t*immediately before each nerve impulse. For Equation 2, enhancement arises from increases in

*F1*,

*F2*,

*A*, and

*P*, and depression from the loss of vesicles from the RRP, although depression may be more complex than simple depletion of synaptic vesicles (Zucker and Regehr, 2002; Sippy et al., 2003; Xu et al., 2007; Young and Neher, 2009; Neher, 2010).

The magnitude of each enhancement component is given by the fractional increase in transmitter release when all the other components are zero and there is no depression, *D*. For example, when only *F1* is present, then its magnitude is given by the following:
with similar definitions for *F2*, *A*, and *P*.

The equations describing the buildup and decay of *F1*, *F*2, *A*, and *P* during and after repetitive stimulation under conditions of low quantal content have been presented previously (Magleby and Zengel, 1982; Zengel and Magleby, 1982). Briefly, *F1*, *F2*, *A*, and *P* arise from the underlying factors, *F1**, *F2**, *A**, and *P**. Each nerve impulse adds an increment of these factors, *f*_{1}*, *f*_{2}*, *a**, and *p**, during repetitive stimulation. The growth in the magnitude of *A* can increasingly accelerate during a train of impulses (Magleby and Zengel, 1976a) and has been modeled as an increase in the effective increments of *a** added by each impulse during the train as follows:
where *a**_{0} is the increment of *A** added by the first impulse in the train (in the rested state), *a** is the increment added for impulse number *N* during the train, and *Z* is a parameter with a value ≥1 that determines the rate of increase in *a** with each successive impulse (Zengel and Magleby, 1982). If *Z* = 1, there is no increase in *a**.

*F1**, *F2**, and *A** decay exponentially between nerve impulses with characteristic time constants, τ_{F1}_{*}, τ_{F2}_{*}, and τ_{A}_{*}. For example, the decay of *F1** is given by the following:
where *F1* _{t}* is the magnitude of

*F1** at time

*t*during the train, and

*F1**

_{t}_{+Δt}is the magnitude of

*F1** Δ

*t*after time

*t*. The change in

*F1** during the train is given by the following: where

*f*

_{1}* is the increment of

*F1** added by each nerve impulse,

*k*

_{F1}_{*}is the rate constant (given by 1/τ

_{F1}_{*}) for removal (or deactivation) of

*F1** from its site of action, and

*J*(

*t*) is an impulse function with a value of 1 at the time of each nerve impulse and 0 at all other times. Equations 5 and 6 with appropriate substitutions for the different components also apply for

*F2**,

*A**, and

*P**, with the exception that the decay of

*P*depends on the magnitude of

*P*(Magleby and Zengel, 1975, 1982) as follows: where τ

*is the time constant for the decay of*

_{P0}*P*after the first impulse in the train,

*P*(

*t*) is the magnitude of

*P*at time

*t*during the train, and

*B*is the parameter that sets the increase in τ

*as*

_{P}*P*increases during the train. Mechanisms that could increase the time constant of decay of potentiation have been considered previously (Magleby and Zengel, 1976c; Tank and Zucker, 1997; García-Chacón et al., 2006). Mean estimates of

*B*in this paper were ∼23, which could lead to a 15% increase in τ

*by the end of the trains, depending on the magnitude of*

_{P}*P*.

The observed potentiation *P* is not directly proportional to the underlying factor *P**, but appears to saturate, as follows:
where *G* sets the level of saturation (Magleby and Zengel, 1982).

##### Depression.

In addition to enhancement of transmitter release, reflected as an increase in the probability of release caused by increases in one or more of the components *F1*, *F2*, *A*, and *P*, repetitive stimulation can also lead to a depression of transmitter release. In the model we use to study STP, depression arises from a depletion of vesicles from the RRP during stimulation. The RRP is then replenished from a recycling pool (RP). The formulation used for depletion is similar to previous studies (Schikorski and Stevens, 1997, 2001; Wu and Betz, 1998; Richards et al., 2003; Kalkstein and Magleby, 2004; Rizzoli and Betz, 2005; Neher and Sakaba, 2008; Pan and Zucker, 2009; Kandaswamy et al., 2010). Depletion occurs because vesicles are released from the RRP faster than they are replaced as follows:
where *d*(RRP* _{t}*)/

*dt*is the rate of change in the number of vesicles in the RRP,

*J*EPP

_{t}_{0}(EPP

*/EPP*

_{t}_{0}) is the number of vesicles released by a nerve impulse at time

*t*, where

*J*equals 1 at the time of each nerve impulse and zero at all other times, EPP

_{t}_{0}is the quantal content of the first EPP in the train, EPP

*/EPP*

_{t}_{0}is given by Equation 2, RRP

_{0}− RRP

*is the number of vesicles in the RRP that are depleted, RP*

_{t}*/RP*

_{t}_{0}is the fractional fullness of the RP, and 1/τ

_{RRP}is the rate constant for replenishment of the RRP from the RP. Movement of vesicles from the RRP to the RP is not included, as this process is slow (Murthy and Stevens, 1999) compared with the durations of the stimulation trains.

In a similar manner, the change in the number of vesicles in the RP with time, *d*(RP)*/dt*, is given by the following:
where 1/τ_{RP} is the rate constant for refilling the RP.

The predicted EPP amplitudes during a train are calculated from the numerical solution of Equations 2–8 for enhancement together with Equations 9 and 10 for synaptic vesicle turnover and depression. Estimates of the parameters in this study are those that give the least-squares error [i.e., the least sum of ((predicted − observed)/predicted)^{2}) for each EPP amplitude during the train, determined using an iterative approach to search for the parameter values that minimized the error using a program written in the laboratory (EPP37S54)]. If the search routine reduced the magnitude of a component of enhancement or depression to negligible values, then the component no longer contributed to STP, becoming undetected. RRP_{0} was fixed at 10,000 synaptic vesicles (Rizzoli and Betz, 2005). For data obtained at low prob_{0}, depletion of the RP was small so that the RP_{0} and τ_{RP} were poorly defined, with their values having little effect on the goodness of fit as long as RP_{0} > 20,000 and τ_{RP} > 10 s.

The key to revealing the faster components of STP during repetitive stimulation and the interaction between these components and depression was to apply step changes in stimulation rate throughout the train (Magleby, 1973a; Magleby and Zengel, 1982; Wesseling and Lo, 2002; Müller et al., 2010). Whereas application of natural stimulation patterns serves the same purpose while allowing the critical decoding of natural synaptic input (Dittman et al., 2000; Hermann et al., 2009; Kandaswamy et al., 2010), such irregular stimulation does not readily allow direct visual observation of the components and their time course, as is the case when step changes in stimulation rate are applied systematically.

##### Testing additional mechanisms.

The data and analysis presented in this paper are for replenishment of the RP from unspecified sources, as described by Equation 10. We also examined a model in which the number of vesicles available to refill the RP depends on the number of vesicles incorporated into the presynaptic membrane that have not yet been retrieved and are available for recycling, such that Equation 10 is replaced by the following: We found that the ability to describe the data was essentially the same assuming either replenishment versus strict recycling for the examined stimulation patterns. As an additional test, the data were fitted with various models with three compartments for vesicle recycling instead of two. If a component of enhancement was found to be negligible with the two-compartment model, its contribution with the three-compartment models was also negligible (data not shown).

In addition to Equation 2, we also examined the ability of Equation 12 to describe STP. This equation is consistent with the idea that the mechanisms of the components of enhancement are fully independent of the other components: We found that Equation 12 gave descriptions of STP almost identical with those of Equation 2.

We left *n* a free parameter in Equations 2 and 12 to maximize the possibility of finding the facilitation components, as there is typically a power relationship for facilitation (Zengel and Magleby, 1982; Zucker and Regehr, 2002). As will be shown in the results, estimates of *n* were ∼1.5 for low and intermediate prob_{0}, and ∼0.8 for normal to elevated prob_{0}, indicating possible cooperativity for lower prob_{0} and possible saturation for higher prob_{0}. Nevertheless, STP could be described about equally well using a linear relationship by setting *n* = 1.0, consistent with previous observations of difficulty in distinguishing the power for facilitation models (Zengel and Magleby, 1982; Dittman et al., 2000; Kandaswamy et al., 2010).

Kandaswamy et al. (2010) described *F1* and *F2* and *A* with a saturation formulation such that for *F1* (in our terminology) is given as follows:
where *F1* is the observed facilitation, *F1** is an exponentially decaying factor that gives rise to *F1*, and η is a saturation factor that relates *F1** to *F1*. The same form of saturation applied to *F2* and *A* in their study. Kandaswamy et al. (2010) set θ = 1.0, as higher values led to no significant improvement, and found η = 1.2 for *F1** and *F2** and 0.59 for *A*. To test whether their formulation for saturating facilitation could be applied to the neuromuscular synapse, we substituted Equation 13 for *F1* and *F2* with θ = 1.0 into Equation 12, and set *n* = 1.0 in Equation 12, and fit the data. Estimated values of η in Equation 13 ranged from 0.02 to 0.13, consistent with limited saturation at the neuromuscular synapse (see above). The description of STP with the Kandaswamy et al. (2010) formulation for saturation of facilitation was little changed from the description with our formulation of facilitation. We did not examine a saturating *A* because in our formulation of STP the increment of *A** added by each impulse was found to increase during the trains (Eq. 4), consistent with previous studies (Zengel and Magleby, 1982). *P* in our formulation was saturating (Eq. 8), also consistent with previous studies (Magleby and Zengel, 1982).

## Results

### STP is highly dependent on prob_{0}

To examine the relationship between the components of enhancement and depression, STP was studied over a wide range of prob_{0}, obtained by changing external Ca^{2+}. Prob_{0} is the probability that a synaptic vesicle in the RRP releases its contents into the synaptic cleft after a nerve impulse is delivered under basal (resting) conditions when the components of STP are at their baseline values (i.e., the probability of vesicular release for the first impulse in a train of impulses). The nerve leading to the presynaptic nerve endings was stimulated at 33/s, with a dropped or added impulse every 20 stimuli to test for facilitation. Figures 1*B*, 2*B*, and 3*B*, which plot normalized EPP amplitudes during the trains, show that STP is profoundly different for low prob_{0} (Fig. 1, 0.2 mm Ca^{2+}), intermediate prob_{0} (Fig. 2, 1.0 mm Ca^{2+}), and normal prob_{0} (Fig. 3, 2.0 mm Ca^{2+}).

During the 12 s train of patterned stimulation at low prob_{0}, EPP mean amplitudes increased 24-fold above the first (control) EPP in the train (Fig. 1*B*), reflecting the buildup of *F1*, *F2*, *A*, and *P* during the train (Magleby and Zengel, 1982). At the low prob_{0} used for this experiment, the stepwise increase in EPP amplitudes after each added impulse and rapid decay back to the mean response (Fig. 1*A*) mainly reflects *F1* and *F2* facilitation added by the extra impulse (Magleby, 1973a; Magleby and Zengel, 1982; Zengel and Magleby, 1982). Similarly, the step decrease in EPP amplitudes after each dropped impulse and return to the mean response mainly reflects the absence of the increments of *F1* and *F2* that would have been added by the dropped impulse. It is the faster time constants of decay of *F1* (∼50 ms) and *F2* (∼300 ms) compared with the slower time constants of decay of *A* (∼6 s) and *P* (tens of seconds to minutes) and the larger increments of *F1* (∼0.8) and *F2* (∼0.15) added by each impulse when compared with the smaller increments of *A* (∼0.005) and *P* (∼0.01) that enables the detection of *F1* and *F2* with dropped and added impulses when these components are superimposed on *A* and *P* during repetitive stimulation at low prob_{0} (Magleby, 1973a; Magleby and Zengel, 1982).

In contrast to the 24-fold increase in mean EPP amplitude at low prob_{0} (Fig. 1*B*), at intermediate release probability mean EPP amplitudes increase 3.6-fold during the train (Fig. 2*B*), and at normal release probability EPP amplitudes increase 1.5-fold during the first few impulses and then run down to 30% of the control level by the end of the 12 s train (Fig. 3*B*). Despite the marked differences in the mean responses during the trains, two consistent features are present at all release probabilities: EPP amplitudes increase rapidly at the very start of the trains and there are step changes in EPP amplitudes with rapid return after the dropped and added impulses (Figs. 1*A*,*B*, 2*A*,*B*, 3*A*,*B*). At low prob_{0}, these rapid changes in STP arise predominantly from *F1* and *F2*, as discussed above. The presence of similar features at intermediate and normal prob_{0} suggests that *F1* and possibly also *F2* also contribute to STP at intermediate and normal prob_{0}. In the following sections, the contributions of *F1*, *F2*, *A*, and *P*, and the depletion of the RRP to STP during repetitive stimulation are determined by fitting the data with the model presented in Materials and Methods. Dissecting out the components of STP during repetitive stimulation requires a model because of the complex relationship between the various components and transmitter release (see Materials and Methods).

*F1*, *F2*, *A*, *P*, and partial depletion of the RRP all contribute to STP at low prob_{0}

Estimates of *F1*, *F2*, *A*, *P*, RRP, and RP during the train at low prob_{0} are shown in Figure 1*E–G. F1* and *F2* rapidly increase at the start of the train to near steady-state levels after the first 5 and 30 impulses, respectively, and then undergo step decreases and increases (with rapid return) from these levels after each dropped and added impulse during the train (Fig. 1*F*). The components of *A* and *P* increase throughout the train (Fig. 1*G*), and the RRP and RP decrease during the train, becoming depleted by 37 and 23%, respectively, because of depletion of vesicles from each pool (Fig. 1*E*). The product of RRP_{t} and prob* _{t}* (Eq. 1) predicts the observed STP during the train (Fig. 1

*A*,

*B*,

*D*). Hence,

*F1*,

*F2*,

*A*,

*P*, and partial depletion of the RRP all contribute to STP at low quantal content. The partial depletion of the RRP did not give rise to observable depression during the train because the increases in

*F1*and

*F2*at the start of the train and the continuing increase in

*A*and

*P*during the train more than compensated for the decreasing RRP during the train. Thus, even though obvious depression is not observed during repetitive stimulation at low prob

_{0}, partial depletion of the RRP contributes to STP by making the transmitter release less than what would be expected from enhancement processes alone. Mean parameters for three experiments like that in Figure 1 are presented in Table 1.

Figure 1*C* shows why a partial depletion of the RRP develops during repetitive stimulation at low prob_{0} even though prob_{0} in this experiment is <1% of prob_{0} at normal release probability. Although the first EPP in the train at low prob_{0} releases only 1.5 vesicles on average, after 400 impulses the release per impulse has increased to >36 vesicles, so that the cumulative release during the train sums to ∼9000 vesicles, which is sufficient to partially deplete the RRP even though vesicles are being mobilized from the RP to the RRP.

The model used to describe STP in the present study is the same as the one used by Magleby and Zengel (1982) to describe STP at low release probability, but with the added feature that depletion of the RRP can occur. Magleby and Zengel (1982) did not include depletion in their studies, assuming that there would be little depletion at the low quantal contents used in their study. We fit the two sets of data in the study by Magleby and Zengel (1982), their Figure 6, with the expanded model to allow possible depletion and found a small (8%) depletion of the RRP at the end of their 200 impulse trains and also a small increase in enhancement to compensate for the depletion (results not shown), consistent with both the assumption in Magleby and Zengel (1982) of limited depletion and the findings in Figure 1 that a small partial depletion of the RRP contributes to STP at low prob_{0}.

### Components of STP during repetitive stimulation at intermediate prob_{0}

For the experiment shown in Figure 2 at intermediate prob_{0}, *F1*, *F2*, *A*, *P*, and depletion of the RRP contribute to STP (Fig. 2*E–G*), and the product of the RRP_{t} and prob* _{t}* predicts the observed STP during the train (Fig. 2

*A*,

*B*,

*D*). The 53% depletion of the RRP and 25% depletion of the RP during the train at intermediate prob

_{0}(Fig. 2

*E*) is greater than at low release prob

_{0}(Fig. 1

*E*), and the buildup of

*A*and

*P*during the train is considerably less at intermediate prob

_{0}(Fig. 2

*G*, note change in scale) than at low prob

_{0}(Fig. 1

*G*). It is the increased depletion of the RRP and the decreased buildup of

*A*and

*P*that limits the mean increase in EPP amplitudes during the train to 3.6-fold at intermediate prob

_{0}(Fig. 2

*B*) compared with 24-fold (Fig. 1

*B*) at low prob

_{0}(Fig. 1). No obvious depression is observed at intermediate prob

_{0}(Fig. 2

*B*) because the increases in

*F1*and

*F2*(Fig. 2

*F*) and the smaller but continuing increase in

*A*and

*P*during the train (Fig. 2

*G*) are still sufficient to compensate for the larger depletion of the RRP. Mean parameters for six experiments like that in Figure 2 are summarized in Table 1.

In experiments of this type, differences in prob_{0} among different frogs for the same 1.0 mm Ca_{o}^{2+} could lead to differences in the contribution of *P* during the train. As will be shown in a later section, when EPP_{0} for the first EPP in the train was <40 vesicles, as was the case for Figure 2, *P* was present during the train, and when it was >40 vesicles, *P* was typically absent. Hence, at intermediate prob_{0}, *F1*, *F2*, *A*, and partial depletion of the RRP contribute to STP, and in some experiments at the lower range of intermediate prob_{0}, *P* also contributes.

As indicated by the changes in EPP amplitudes in Figure 2, *A* and *B*, there is a period of time after a dropped impulse when fewer vesicles are released. This is the case because the dropped impulse itself does not release vesicles and the decreased facilitation after the dropped impulse leads to fewer vesicles released for the next seven to eight impulses. Inversely, more vesicles are released for a period of time when an impulse is added because the added impulse itself releases additional vesicles and because facilitation from the added impulse leads to more vesicles released for the next seven to eight impulses. These decreases and increases in vesicles released during the train lead to increases and decreases in the size of the RRP during the train (Fig. 2*E*), which then lead to small increases and decreases in mean EPP amplitudes during the train after facilitation approaches steady-state levels (marginally visible in Fig. 2*A*,*B*,*D*, but will be more apparent in later figures with different stimulation patterns). Such changes in EPP amplitudes after changes in stimulation rate have been exploited to estimate the fullness of the RRP (Wesseling and Lo, 2002).

*F1* and marked depletion of the RRP can account for STP during rundown at normal prob_{0}

At normal prob_{0} with associated rundown of EPP amplitudes during the train (Fig. 3*B*), only *F1* and marked depletion of the RRP contribute to STP (Fig. 3*E*,*F*). *F2*, *A*, and *P* were not detected (Fig. 3*F*,*G*), so that the product of RRP_{t} and prob* _{t}*, where prob

*included only*

_{t}*F1*, was sufficient to predict the observed STP during the train (Fig. 3

*A*,

*B*,

*D*). The 85% depletion of the RRP and 60% depletion of the RP during the rundown at normal prob

_{0}(Fig. 3

*E*) can be compared with the 53 and 25% depletion at intermediate prob

_{0}(Fig. 2

*E*) and the 37 and 23% depletion at low prob

_{0}(Fig. 1

*E*). After the 1.5-fold increase in EPP amplitudes at the start of the train in Figure 3

*B*, the rundown of the EPP amplitudes tracked the depletion of the RRP (Fig. 3

*E*) because there was no buildup of

*F2*,

*A*, and

*P*during the train to counter the decrease in the RRP. That

*F1*still contributes during the train can be seen by the response to the dropped and added impulses. Mean parameters for eight experiments like that in Figure 3 with marked depression are presented in Table 1 (listed under normal to elevated prob

_{0}). Consistent with the absence of

*F2*at normal prob

_{0}, Mallart and Martin (1968) did not observe

*F2*after five impulses of high frequency stimulation.

### Imposing *F2*, *A*, and *P* at normal prob_{0} gives a response inconsistent with the data, indicating that these processes do not contribute to STP during rundown

The question arises as to whether *F2*, *A*, and *P* were not detected during rundown because they were missing or because the fitting program could not find them. If *F2*, *A*, and *P* were contributing to STP but not detected, then it should be possible to describe the data by imposing *F2*, *A*, and *P* and refitting. When this was done, the mean response during the rundown was approximated (Fig. 4*B*,*D*), but the predicted responses after dropped and added impulses were incorrect, being opposite to what was observed (Fig. 4*A*,*B*,*D*). Imposing *F2*, *A*, and *P* in various combinations and with various magnitudes also did not describe the data (data not shown), and when *F2*, *A*, and *P* were given initial values and then allowed to freely change during fitting, their values went to zero (Fig. 3*F*,*G*). Hence, *F1* and depletion of the RRP were sufficient to account for STP during the rundown in Figure 3, with no evidence that *F2*, *A*, and *P* contribute.

As additional support for why *F2*, *A*, and *P* do not contribute to STP during the rundown, it is worthwhile to consider why imposing these components and refitting gave such a poor description of the response after dropped and added impulses. Imposing *F2*, *A*, and *P* led to large progressive increases in prob* _{t}* during the train. Therefore, to describe the rundown with this large imposed increase in prob

*, the program optimized the parameters to severely deplete the RRP (Fig. 4*

_{t}*E*) so that the product of prob

*× RRP*

_{t}*during the rundown would remain the same as in the absence of imposed*

_{t}*F2*,

*A*, and

*P*. The responses after dropped and added impulses were not predicted when the RRP was severely depleted in the presence of imposed

*F2*,

*A*, and

*P*for the following reason. During the slow phase of the rundown, most of the vesicles released by each nerve impulse are replaced from the RP during the interval before the next impulse. When an impulse is dropped, the transmitter that would have been released by the dropped impulse is not released so that the RRP is increased by that amount of transmitter, compared with if the impulse were not dropped. For example, when

*F2*,

*A*, and

*P*were imposed, the RRP was 94% depleted at 5.4 s so that the dropped impulse led to a large ∼16% fractional increase in the RRP (Fig. 4

*E*, determined from numerical data). The consequence of such a large fractional increase in the RRP is that the predicted EPP amplitudes increase after the dropped impulse (Fig. 4

*A*, red circles, ∼5.4 s) in contrast to the experimentally observed decrease (Fig. 4

*A*, black circles), even though facilitation decreases because of the dropped impulse.

Conversely, with imposed *F2*, *A*, and *P*, the fractional decrease in the size of the RRP for an added impulse was much greater (∼18%) than without imposed *F2*, *A*, and *P* (∼3%), so that the predicted EPP amplitudes decreased (Fig. 4*A*, red circles, ∼6 s) in contrast to the experimentally observed increase (Fig. 4*A*, black circles), even though facilitation increased because of the added impulse. Hence, *F2*, *A*, and *P* do not contribute to STP during rundown at normal prob_{0}, because if they did, the response to patterned stimulation would be opposite to what was observed.

### Absence of *F2*, *A*, and *P* during rundown at normal prob_{0} using a stimulation pattern that amplifies the contributions of these components

As an additional test for *F2*, *A*, and *P* during rundown at normal prob_{0}, we applied stimulation that amplifies the contributions of the components of enhancement by applying 40 impulses at 40/s alternating with 20 impulses at 20/s (Fig. 5). With such a pattern, the changes in *F2*, *A*, and *P* should be approximately twice as great at the higher than the lower stimulation rate. With this amplifying stimulation pattern, *F1* and depletion of the RRP were still sufficient to account for STP during the train, as *F2*, *A*, and *P* were not detected (Fig. 5). As was the case for Figure 4, imposing *F2*, *A*, and *P* gave far worse descriptions of the data (Fig. 6).

### For low stimulation rates at normal prob_{0}, *F2*, in addition to *F1* and depletion of the RRP, can also contribute to STP

Because of the large fractional release of transmitter at normal prob_{0}, it is possible that the limited time for refilling release sites between nerve impulses might contribute in some way to the loss of *F2*, *A*, and *P* at normal prob_{0} for the high average stimulation rates (≥30/s) used in Figures 3 and 5. To explore this possibility, we applied stimulation patterns with a low average stimulation rate of 5/s to increase the average time between nerve impulses (Fig. 7*A*,*B*, black open circles). For these slow stimulation rates at normal prob_{0}, *F1* (blue) and now also *F2* (green) contributed to enhancement during the rundown (Fig. 7*F*), compared with no contribution from *F2* at higher stimulation rates (Figs. 3*F*, 5*F*). As was the case at higher stimulation rates for normal prob_{0}, there was no contribution from *A* and *P* at the slower stimulation rates at normal prob_{0} (data not shown). Hence, for low stimulation rates at normal prob_{0}, *F1*, *F2*, and depletion of the RRP are sufficient to account for STP (Fig. 7*A*,*B*,*D*,*F*).

As an additional test of the contribution of *F2* to STP at the low stimulation rates during rundown, *F2* was fixed to zero and the data refitted. The responses to the step changes in stimulation rate were no longer predicted (Fig. 7*A*, blue stars; compare *G* with *B*, *D*), consistent with *F2* contributing to STP during rundown for slower stimulation rates at normal prob_{0}. Transmitter output for low-frequency simulation is maintained by recycling rather than mobilization from the reserve pool (Richards et al., 2003), which might contribute to differences in *F2* at different stimulation rates. This variable contribution of *F2* to STP at normal prob_{0}, depending on the stimulation rate, adds another complexity to STP.

### Solving for EPP_{0} and RRP_{0}

When solving for the components of STP, fixing the size of RPP_{0} to values in the literature gave a calculated value for EPP_{0} in Equation 1. For example, setting RRP_{0} to 10,000 vesicles (Rizzoli and Betz, 2005) for the experiments in Figures 1⇑–3 for low, intermediate, and normal prob_{0} gave calculated values for EPP_{0} of 1.5, 38, and 176 vesicles, respectively (and see Table 1), consistent with expected experimental values for the levels of extracellular Ca^{2+} used in these experiments (Dodge and Rahamimoff, 1967; Magleby and Pallotta, 1981; Rizzoli and Betz, 2005). Prob_{0} for these same experiments would then be 0.00015, 0.0038, and 0.018, given by EPP_{0}/RRP_{0}. Alternatively, fixing the value of EPP_{0} in normal Ca^{2+} to the previously calculated value of 176 vesicles (found in Fig. 3), setting new starting parameters, and refitting with RRP_{0} as a free parameter gave estimates of RRP_{0} within 0.5% of 10,000 synaptic vesicles. Hence, given either EPP_{0} or RRP_{0}, the unspecified parameter can be determined together with EPP amplitudes during a train expressed as the number of released vesicles. In the absence of a specified value for either EPP_{0} or RRP_{0}, RRP_{0} can be set to 1.0 and the equations then give normalized EPP amplitude (normalized synaptic strength) with the fitted value of EPP_{0} giving prob_{0}. In terms of the equations, it is the ratio of EPP_{0}/RRP_{0} that determines STP by setting prob_{0}. Prob_{0} then determines the depletion rate of the RRP and the components of enhancement that contribute during the train, as shown in the next section.

### The components of enhancement contributing to STP during repetitive stimulation depend on prob_{0}

Twenty-three additional experiments for a variety of stimulation patterns over a wide range of prob_{0}, including three experiments with 4 mm Ca_{o}^{2+}, were performed to estimate the components of STP during repetitive stimulation. The observations in these additional experiments are consistent with those presented in previous sections. RRP_{0} was fixed at 10,000 vesicles (Rizzoli and Betz, 2005) and EPP_{0} was determined by fitting the trains. Prob_{0} was then calculated from EPP_{0}/RRP_{0}. Figure 8 summarizes the results. The increments of *F1* and *F2* added by each impulse, *f*_{1}* and *f*_{2}*, are plotted against prob_{0} in Figures 8, *A* and *B*. The magnitudes of *A* and *P* and the percentage of the RRP remaining just before impulse 400 in the train are also plotted against prob_{0} in Figure 8*C–E*, respectively. EPP_{0} is also plotted in Figure 8*D* and applies to all parts of the figure.

Figure 8 shows that *F1* is a major contributor to STP for all examined levels of prob_{0}. In contrast, the contributions of *F2*, *A*, and, *P* decrease as prob_{0} increases, with the contributions of *P*, *A*, and *F2* becoming negligible when prob_{0} is greater than ∼0.005, 0.01, and 0.015, respectively, or when EPP_{0} is greater than ∼50, 100, and 150 vesicles, respectively. Hence, as prob_{0} is increased, the three slower components of enhancement disappear in order of longer to shorter time constants of decay. (The information in Fig. 8 and Table 1 could be used to set parameters to estimate STP for a given prob_{0} using Eqs. 2–10.)

Whereas changes in Ca_{o}^{2+} were used to change synapses from highly facilitating to highly depressing in the experiments reported in this paper, the data have been presented in terms of prob_{0} for the following reasons: (1) consistent with the findings in Figures 1⇑⇑⇑⇑⇑⇑–8, synaptic strength (which is related to prob_{0}) has been associated with determining whether synapses are facilitating or depressing (Mallart and Martin, 1968; Magleby, 1973b; Atwood and Karunanithi, 2002; Zucker and Regehr, 2002); (2) the STP response is not always strictly tied to Ca_{o}^{2+}, as the STP responses for neuromuscular synapses from different frogs can differ somewhat for the same Ca_{o}^{2+}; and (3) neuromuscular synapses can become more facilitating during extended durations of experimentation, even though Ca_{o}^{2+} is kept constant (Magleby and Zengel, 1976b). Variability in STP properties at the same Ca_{o}^{2+} for calyx synapses from different rats has previously been observed (Weis et al., 1999; Hennig et al., 2008).

Presenting the data in terms of prob_{0} rather than Ca_{o}^{2+} removed much of the synaptic variability and has the advantage that, in terms of the examined models, prob_{0} is a major determinant of the initial rate of depletion of the RRP, giving immediate insight into the expected type of response. Nevertheless, it was Ca_{o}^{2+} that was altered to change the type of synaptic response. Thus, the results in Figures 1⇑–3 are the same for low (0.2 mm), intermediate (1.0 mm), and normal (2.0 mm) Ca^{2+} as for low (0.00015), intermediate (0.00384), and normal (0.0176) prob_{0}. When the data from multiple experiments were grouped in terms of low (0.14–0.2 mm), intermediate (1.0 mm), and normal to high (2–4 mm) Ca_{o}^{2+}, the parameter values and trends were very similar to those in Table 1 for low, intermediate, and normal to elevated prob_{0}, but with more variability in some of the parameters (data not shown). Thus, our findings in terms of the components contributing to enhancement are essentially the same for changes in either Ca_{o}^{2+} or prob_{0}. This is not surprising, as changing Ca_{o}^{2+} would change both Ca^{2+} entry and residual Ca^{2+}, which has been associated with the components of enhancement (see Discussion).

Whereas Figure 8 describes the relationships between prob_{0} and the various enhancement components of STP, such a relationship is unlikely to apply to all synapses or for all experimental conditions, because prob_{0} can be uncoupled from STP. For example, Young and Neher (2009) have shown that overexpressing mutated synaptotagmin leaves intrinsic Ca^{2+} sensitivity intact while loosening the tight coupling between Ca^{2+} influx, release, and STP, most likely by interfering with the positioning of vesicles with respect to Ca^{2+} channels. Additional support for possible uncoupling comes from the observations of Sippy et al. (2003), who found that a depressing synapse can be converted into a facilitating synapse without changing basal synaptic strength by increasing the level of neuronal calcium sensor-1, effectively uncoupling prob_{0} from STP. Changes in Ca^{2+} currents or changes in increments in intracellular Ca^{2+} with each nerve impulse during trains (Borst and Sakmann, 1998; Narita et al., 2000; von Gersdorff and Borst, 2002; Xu et al., 2007) might also be expected to partially uncouple prob_{0} from STP.

## Discussion

### Summary of findings

Presynaptic STP encompasses a broad range of responses, from highly facilitating synapses to deeply depressing synapses (Cowan et al., 2001; Zucker and Regehr, 2002). Whereas all four components of enhancement, *F1*, *F2*, *A*, and *P*, contribute to STP at a highly facilitating neuromuscular synapse induced by low Ca_{o}^{2+} (Magleby and Zengel, 1982), the contributions of these components to STP is less clear for moderately facilitating to strongly depressing synapses. To address this question, we explored which components contribute to STP at the neuromuscular synapse as it was progressively transformed from a highly facilitating synapse to a deeply depressing synapse by changing prob_{0} over a 280-fold range, from very low (0.00015) to above normal (0.043), by changing Ca_{o}^{2+} in the range of 0.14–4.0 mm.

We found that *F1*, *F2*, *A*, *P*, and partial depletion of the RRP all contribute to STP during repetitive nerve activity at low prob_{0} (Figs. 1, 8). Interestingly, significant depletion of the RRP can occur at low prob_{0} because the robust buildup of enhancement during the trains greatly increases release (Fig. 1). As prob_{0} was increased by raising Ca_{o}^{2+}, the contributions of the slower components of enhancement to STP progressively decreased to negligible levels, with first *P*, then *A*, and then *F2* no longer contributing (Figs. 2⇑⇑⇑–6, 8). For levels of prob_{0} that led to appreciable rundown during repetitive stimulation, only *F1* and depletion of the RRP were needed to account for STP (Figs. 3⇑⇑–6, 8), with *F2* also contributing during rundown for low stimulation rates ≤5/s (Fig. 7). Despite the essentially unconstrained parameters during the fitting, the properties of the detected components were consistent with those in the literature obtained by other methods, lending support to the approach and analysis.

Our expectation when starting this study was that the kinetic model combined with step changes in stimulation rate would reveal all four components of enhancement for the explored levels of depression, provided that the RRP contained excess synaptic vesicles. The presence of *F1* throughout the rundowns indicates that excess vesicles were immediately available for release. Indirect support for excess vesicles also comes from the observation that the calculated RRP contained vesicles in large excess over the number released by any individual nerve impulse during the rundown. Thus, the absence of *F2*, *A*, and *P* during rundown at normal prob_{0} did not arise from a lack of vesicles available for release.

Imposing slower enhancement components for those experiments where the slower components were undetected and then refitting gave predictions of STP that were inconsistent with the experimental data (Figs. 4, 6). Hence, slow components that were not detected were not contributing to STP, because if they were, it would not have been possible to describe STP (Figs. 4, 6).

### Limitations of analysis

The models described by Equations 1–12 were suitable to test for the components of STP during repetitive stimulation under the conditions of our experiments, and provided excellent descriptions of the dynamics of STP over wide ranges of prob_{0}. Nevertheless, the equations are not meant as a comprehensive description of transmitter release, because the long-term recovery processes of some of the component parameters are not known and, consequently, not included. Related to this limitation, the models would not be able to predict the delayed onset of *P* after extensive stimulation at normal prob_{0} (Magleby, 1973b) that gives rise to posttetanic potentiation, because a recovery process for undetected *P* is not incorporated. Furthermore, the recycling of synaptic vesicles is more complicated than included in the model (Stevens and Wesseling, 1998; Wang and Kaczmarek, 1998; Wesseling and Lo, 2002; Richards et al., 2003; Sudhöf, 2004; Schweizer and Ryan, 2006; Denker and Rizzoli, 2010), and additional factors that can contribute to STP are not included (Zucker and Regehr, 2002; Neher and Sakaba, 2008; Todd et al., 2010).

The mechanism of the Ca^{2+}-dependent release process is not part of the model, but replaced by an impulse function that places few restrictions on fundamental release mechanisms. Such mechanisms have been considered by others (Bennett et al., 2004; Neher and Sakaba, 2008; Pan and Zucker, 2009; Parnas and Parnas, 2010). To fully understand STP, it will be necessary to extend physical models based on underlying cellular physiology and structure, such as those by Bennett et al. (2007) and Pan and Zucker (2009) to account for all observed STP phenomena. Descriptive models such as Equations 2–13 are useful in that they provide dynamic descriptions of STP and provide a tool to study underlying physical processes.

### Comparison with previous work

Our observations that *F1*, *F2*, *A*, and *P* components of enhancement all contribute to STP for a low prob_{0} highly facilitating amphibian synapse are consistent with highly facilitating invertebrate synapses (Kamiya and Zucker, 1994) and mammalian ganglion synapses (Zengel et al., 1980). In addition, our studies suggest that some depletion of the RRP is also likely to contribute to STP even at highly facilitating synapses (Fig. 1).

For intermediate prob_{0} leading to moderately facilitating synapses, release increases severalfold at the start of a train and then changes by only limited amounts during the train (Fig. 2). Our observations that *F1*, *F2*, and *A* (and also *P* for the lower range of intermediate prob_{0}) together with a sequential two pool depletion and replacement of vesicles can account for STP at such moderately facilitating synapses (Fig. 2) are consistent with previous descriptions of STP at moderately facilitating excitatory hippocampal synapses (Kandaswamy et al., 2010) and also at moderately facilitating cutaneous pectorus neuromuscular synapses (Kalkstein and Magleby, 2004).

Our observations that *F1* and depression, but not *F2*, *A*, and *P*, contribute to STP for highly depressing synapses with marked rundown because of normal or elevated prob_{0} (Figs. 3⇑⇑–6) are consistent with previous observations from depressing calyx synapses (Müller et al., 2010) and visual cortex layer 2/3 synapses (Varela et al., 1997), where STP arises mainly from a fast component of facilitation and one or two components of depression. Calyx synapses can also exhibit fast and slow phases of rundown (Hennig et al., 2008), as is the case for the neuromuscular synapse (Fig. 3). Hence, the model we present for STP has major features in common with STP at calyx and visual cortex layer 2/3 synapses. Nevertheless, depending on the stimulation pattern, STP at calyx may be simpler (Hermann et al., 2009) or more complicated (Hennig et al., 2008) than a fast component of facilitation and one or two components of depression.

Dittman et al. (2000) accounted for STP at three different CNS synapses ranging from highly facilitating to depressing with a general model that included depression and a fast component of facilitation, with Ca^{2+}-dependent refilling of empty release sites. Whereas our findings are consistent with theirs for depressing synapses, their model had fewer components of enhancement for highly facilitating and moderately facilitating synapses than either our model or the model of Kandaswamy et al. (2010). This difference may reflect that their trains were generally brief so that the slower components of enhancement, if present, would have made only small contributions.

That *F1*, *F2*, *A*, and *P* components of miniature EPP frequency (Zengel and Magleby, 1981) are still observed in the presence of depression (Zengel and Sosa, 1994) suggests that the presumed Ca^{2+}-dependent driving processes for the enhancement components (Kamiya and Zucker, 1994; Tank and Zucker, 1997; Suzuki et al., 2000; Zucker and Regehr, 2002; Kalkstein and Magleby, 2004; García-Chacón et al., 2006) are still present during marked rundown, but uncoupled from evoked release so that *F2*, *A*, and *P* of evoked release are not detected. The reason for this uncoupling during marked depression is not known but may be related to the fact that spontaneous and evoked release may have differences in location and/or molecular components (Washbourne et al., 2002; Zucker and Regehr, 2002; Maximov and Südhof, 2005; Wadel et al., 2007; Young and Neher, 2009; Yoshihara et al., 2010). Our observations that *F1* contributes to STP under conditions where *F2*, *A*, and *P* are undetected (Figs. 3⇑⇑⇑⇑–8) supports previous studies suggesting that the mechanism for *F1* has some differences from *F2*, *A*, and *P* (Delaney and Tank, 1994; Kamiya and Zucker, 1994; Neher and Sakaba, 2008).

### Significance

Facilitating synapses typically have lower prob_{0} than depressing synapses (Zucker and Regehr, 2002) and Figures 1⇑⇑⇑⇑⇑⇑–8. Our systematic study characterizes yet another mechanistic difference. At low prob_{0}, the four enhancement processes *F1*, *F2*, *A*, and *P* are robust, overcoming the partial depletion of the RRP, leading to a facilitating synapse. In contrast, as prob_{0} increases, the contributions of the three slower enhancement components *F2*, *A*, and *P* progressively decrease so there is little enhancement (except from *F1*) to compensate for the increased depletion of the RRP, leading to rundown. Thus, prob_{0}-dependent enhancement adds additional complexity to STP that will need to be taken into account. On this basis, experimental procedures that alter prob_{0} might also be expected to alter *F2*, *A*, and *P*, even if they do not directly act on these components.

## Footnotes

This work was supported in part by a grant from the Muscular Dystrophy Association (K.L.M.) and an American Heart Association fellowship (A.M.H.).

The authors declare no competing financial interests.

- Correspondence should be addressed to either of the following: Alice M. Holohean, Research 151, Miami Veterans Affairs Hospital, 1201 NW 16th Street, Miami, FL 33125, aholohean{at}med.miami.edu; or Karl L. Magleby, Department of Physiology and Biophysics, R430, University of Miami Miller School of Medicine, Miami, FL 33136, kmagleby{at}med.miami.edu