The elucidation of the principal features of chemical synaptic transmission has been one of the great achievements in the history of neuroscience, yet students have significant difficulties developing a deeper understanding of the underlying concept. This is particularly true for the role that diffusion of neurotransmitters across the synaptic cleft plays in this process. At least part of the learning problem is due to an erroneous view of diffusion as a slow process, and to an inability to apply the concepts of size and scale to the synapse and its structural components. To overcome these difficulties, a structured/guided inquiry activity, combined with quantitative reasoning tasks, is described for teaching chemical synaptic transmission as part of undergraduate biology or neuroscience courses. Through this activity, students familiarize themselves with the absolute and relative dimensions of the structural components of synapses; use data from morphometric and schematic models of synapses to estimate the time it takes a neurotransmitter to diffuse across the synaptic cleft; and evaluate how this process relates to synaptic delay and generation of a sufficiently high concentration of transmitter molecules for activation of postsynaptic receptors.

Introduction: Chemical Synaptic Transmission

Synaptic transmission is the process by which a neuron communicates with a target cell, for example another neuron or a muscle cell, via a specialized structure known as the synapse. Transmission involves either electrical signals or neurotransmitter molecules. The corresponding synapses are referred to as electrical and chemical synapses, respectively.

Chemical synaptic transmission between neuronal cells – the focus of the present article – is a highly complex process (for a review, see Pickel & Segal, 2014). The presynaptic nerve terminal, usually formed by axonal swellings, is separated from the postsynaptic neuron by a synaptic cleft ~20 nm wide (Figure 1A). The presynaptic terminal is distinguished by the presence of synaptic vesicles containing transmitter substances, and of an “active zone” – a small area at the presynaptic membrane facing the synaptic cleft. One function of the active zone is to prime synaptic vesicles into a state of competence for exocytosis, the latter involving formation of a fusion pore between the vesicles and the presynaptic membrane (Figure 1B).

Figure 1.

Morphometric synapse model. (A) The proportions of the axon shaft, presynaptic terminal, and synaptic cleft have been inferred from morphometric data. (B) Boxed area in A shown at higher magnification. The relative sizes of the synaptic vesicle and the synaptic cleft were chosen so as to match the dimensions of these structures in electron micrographs. The sizes of the calcium channels and the postsynaptic transmitter receptor/channel complex are not drawn to scale, but their spatial proximity to the releasing vesicle has been inspired by morphometric findings. Courtesy: Günther K. H. Zupanc.

Figure 1.

Morphometric synapse model. (A) The proportions of the axon shaft, presynaptic terminal, and synaptic cleft have been inferred from morphometric data. (B) Boxed area in A shown at higher magnification. The relative sizes of the synaptic vesicle and the synaptic cleft were chosen so as to match the dimensions of these structures in electron micrographs. The sizes of the calcium channels and the postsynaptic transmitter receptor/channel complex are not drawn to scale, but their spatial proximity to the releasing vesicle has been inspired by morphometric findings. Courtesy: Günther K. H. Zupanc.

Voltage-gated calcium channels (i.e., calcium channels that open in response to depolarization of the cell membrane) are expressed at high concentrations in the presynaptic membrane associated with the active zone. Within the active zone, calcium channels and releasable vesicles are organized in “microdomains” of 30–300 nm (Figure 1B). Arrival of an action potential at the presynaptic terminal activates the voltage-gated calcium channels, and the subsequent influx of Ca2+ ions leads to a transient, localized increase in Ca2+ concentration. Binding of Ca2+ to synaptotagmin (a protein localized to synaptic vesicles, which functions as a calcium sensor) triggers exocytosis of the associated vesicle.

The neurotransmitter molecules released from the vesicles diffuse across the synaptic cleft to the postsynaptic membrane, where they activate postsynaptic receptors and associated channels. Depending on the type of postsynaptic channel, either an excitatory postsynaptic potential (EPSP) or an inhibitory postsynaptic potential (IPSP) will result. The synaptic delay between the arrival of an action potential at the presynaptic terminal and the onset of the postsynaptic potential is ~600 μs. During this delay, the Ca2+ concentration is elevated within ~50 μs; the calcium-triggered release of vesicles takes about 300–400 μs; and the diffusion of the neurotransmitter across the cleft, its binding to the postsynaptic receptor, and the induced conformational change of the channel occur within ~200 μs. Simulations of the diffusion of glutamate – the most commonly found excitatory neurotransmitter in the central nervous system – following release of a single vesicle from a presynaptic terminal has indicated that the peak concentration of glutamate at the postsynaptic receptors occurs ~10 μs after opening of the fusion pore (Ventriglia & Di Maio, 2000). This interval includes the time it takes the transmitter molecules to “escape” by random Brownian motion from the vesicle through the rather narrow fusion pore and the diffusion of the transmitter molecules across the cleft.

Deficiencies in Understanding the Concepts of Diffusion, Size & Scale as Barriers to Understanding the Concept of Synaptic Transmission

Chemical synaptic transmission is a complex biological process. A deeper understanding of the underlying concept requires the ability to break down the overall process into sub-processes and to analyze the spatiotemporal properties of these sub-processes and link them back to the morphological structure of the synapse and its components. According to my own classroom observations (which are based on teaching of biology and non-biology majors, at both undergraduate and graduate levels, at research universities in Germany, the United Kingdom, and the United States), many students are unable to perform this analysis and the subsequent synthesis – an observation consistent with the results of a survey that has indicated failure, among a large portion of postgraduate and medical students, to even understand the basic physiological function of chemical synapses (Montagna et al., 2010).

Student responses in classroom discussions suggest that at least part of the difficulty in understanding synaptic transmission is due to (1) an incomplete understanding of the phenomenon of diffusion, (2) a widespread lack of familiarity with its microscopic and nanoscopic dimensions, and (3) an insufficient development of a sense of scale. These difficulties are found in general among students of all grades and are well documented in a large number of studies (Westbrook & Marek, 1991; Marek et al., 1994; Odom, 1995; Odom & Barrow, 1995; Tretter et al., 2006; Jones & Taylor, 2009; Jones, 2013).

Most students memorize correctly in their high school or college science classes that diffusion is a passive process (for a definition of diffusion and a demonstration video, see Box 1). However, they incorrectly associate this phenomenon with slow speed of action only, because they have not learned that, although diffusion is indeed very slow over long distances, it is extremely fast over short distances. It is therefore not surprising that, when asked how it is possible that diffusion of transmitters across the synaptic cleft occurs extremely fast, students commonly fail to produce an answer, or they resort to active transport mechanisms or facilitated diffusion as possible explanations.

Box 1.
Diffusion
Diffusion Diffusion is the net movement of molecules from a region of high concentration to a region of low concentration, resulting from random thermal molecular motion. 
Demonstration For a demonstration of diffusion of colored water in gelatin, see the following video: https://commons.wikimedia.org/wiki/File:Diffusion_v2_20101120.ogv
Diffusion Diffusion is the net movement of molecules from a region of high concentration to a region of low concentration, resulting from random thermal molecular motion. 
Demonstration For a demonstration of diffusion of colored water in gelatin, see the following video: https://commons.wikimedia.org/wiki/File:Diffusion_v2_20101120.ogv

This difficulty in applying the concept of diffusion to nanoscale dimensions is closely related to students' frequent failure to correctly apply the concepts of size and scale to dimensions beyond everyday life experience. In the case of chemical synapses, this problem is aggravated by misleading representations of the relative dimensions in a large number of educational models of chemical synapses. This is exemplified by Figure 2, which shows a model of a chemical synapse published on numerous websites, including 50 sites hosted by the Wikimedia Foundation. The model synapse implies that the width of the synaptic cleft is of similar dimension as, for example, the diameter of the axon, without mentioning that the relative dimensions of the various subcellular components are not drawn to scale. This leads to a distorted view of the relative dimensions of the synaptic components, which manifests itself as another widespread deficiency found in numerous publications for teaching synaptic transmission. (In addition to the erroneous relative dimension of the synaptic cleft's width, the model synapse shown in this figure suffers from a second major deficiency – the implication that calcium channels are located distant from the release sites of synaptic vesicles. Such a structural organization would make it impossible to reach the concentration of calcium required for formation of fusion pores at the active zone.)

Figure 2.

Schematic synapse model. This widely published model suffers from two major deficiencies: the erroneous proportion of the width of the synaptic cleft and the location of calcium channel(s) distant to the release site of the synaptic vesicles. Key: (1) mitochondrion; (2) synaptic vesicle with neurotransmitter; (3) autoreceptor; (4) synaptic cleft; (5) neurotransmitter receptor with associated channel; (6) calcium channel; (7) fused vesicle releasing neurotransmitter; (8) neurotransmitter re-uptake pump. Courtesy: Mouagip, licensed under Creative Commons Attribution-Share Alike 3.0 Unported. Source: https://commons.wikimedia.org/wiki/File:Synapse_diag1.svg.

Figure 2.

Schematic synapse model. This widely published model suffers from two major deficiencies: the erroneous proportion of the width of the synaptic cleft and the location of calcium channel(s) distant to the release site of the synaptic vesicles. Key: (1) mitochondrion; (2) synaptic vesicle with neurotransmitter; (3) autoreceptor; (4) synaptic cleft; (5) neurotransmitter receptor with associated channel; (6) calcium channel; (7) fused vesicle releasing neurotransmitter; (8) neurotransmitter re-uptake pump. Courtesy: Mouagip, licensed under Creative Commons Attribution-Share Alike 3.0 Unported. Source: https://commons.wikimedia.org/wiki/File:Synapse_diag1.svg.

Below, I describe an inquiry activity designed to help students and teachers avoid these difficulties. For the design of this activity, a structured/guided inquiry strategy was chosen because empirical educational psychology research clearly supports the superiority of this instructional model over open inquiry strategies, particularly if students have limited prior knowledge in the area of study (Kirschner et al., 2006). This structured/guided inquiry activity was combined with quantitative reasoning tasks, as it appears unlikely that a deeper conceptual understanding of synaptic transmission involving kinetics aspects, such as diffusion time of transmitters, can be acquired through qualitative treatment only. This instructional strategy is in line with the increasing recognition of quantitative reasoning as a core competency in undergraduate education (Elrod, 2014).

Inquiry-Based Activity

The following inquiry-based activity has been designed primarily for lower-division college courses in biology or neuroscience. However, it might also be a useful exercise for high school students taking AP Biology. Its specific objectives are as follows:

  1. Students will learn how to determine the size of biological structures on microphotographs or drawings using magnification factors. Through this activity, they will develop some basic familiarity with the cellular and subcellular dimensions relevant to synapses.

  2. Students will learn to apply Einstein's approximation equation to estimate the time it takes a neurotransmitter to diffuse across the synaptic cleft of chemical synapses, and they will calculate the rate of diffusion.

  3. Students will learn to discuss how diffusion distance affects both the diffusion time across the synaptic cleft and the concentration of transmitter molecules at the postsynaptic receptors, and thus the overall synaptic transmission process.

Materials & Resources Needed

For each group of two students, the following materials are needed:

Part 1: Estimation of the Dimensions of the Model Synapse

Procedure

In the first part of the guided inquiry activity, the students will estimate the width of the synaptic cleft of the synapses shown in Figures 1A and 2. In the following, I refer to the two models shown in these figures as “Morphometric Synapse Model” and “Schematic Synapse Model,” respectively.

By the time the students start Part 1, they should be familiar with the relevant metric prefixes and the corresponding values shown in Table 1. The students should also be able to relate the results obtained through the inquiry activity to some fundamental dimensions of nerve cells in the central nervous system, such as the range of soma sizes (granule cells in the cerebellum: ~4 μm; Betz cells of the motor cortex: 100 μm) and the range of diameters of axons (0.1–10 μm) among cells.

Table 1.
Metric prefixes.a
PrefixSymbolMultiplication FactorPower
(no prefix)  100 
centi 0.01 10−2 
milli 0.001 10−3 
micro μ 0.000001 10−6 
nano 0.000000001 10−9 
PrefixSymbolMultiplication FactorPower
(no prefix)  100 
centi 0.01 10−2 
milli 0.001 10−3 
micro μ 0.000001 10−6 
nano 0.000000001 10−9 
a

The metric prefix is a modification of the basic unit of measure to indicate the value of the unit. Examples: 1 μm (micrometer) = 1·10−6 m; 5 ms (millisecond) = 5·10−3s.

For the estimation of the synaptic dimensions, the students are provided with printouts of the model synapses shown in Figures 1A and 2, including a description of the labeled components. The only other information they receive is that the diameter of the presynaptic axon is 0.5 μm. Based on this information, the students are asked to estimate the dimensions of the following two components of the two model synapses: (1) length of the presynaptic terminal (defined as the dimension perpendicular to the axon shaft) and (2) width of the synaptic cleft. To estimate these dimensions, they should follow these steps:

  1. Measure (in millimeters) the diameter of the axonal shaft on each of the two printouts.

  2. Assuming that the diameter of the axonal shaft is 0.5 μm, use the results obtained in step 1 to calculate the magnification factor of the drawings shown in each of the two figures. This is done by dividing the diameter measured on the drawing by 0.5 μm. Remember to use identical units of measure for your calculations.

  3. Measure (in millimeters) the length of the presynaptic terminal (defined as the dimension perpendicular to the axon shaft) on each of the two printouts.

  4. Use the magnification factors calculated in step 2 and the corresponding results obtained in step 3 to estimate the actual lengths of the presynaptic terminals shown in the two drawings.

  5. Measure (in millimeters) the width of the synaptic cleft on each of the two printouts.

  6. Use the magnification factors calculated in step 2 and the corresponding results obtained in step 5 to estimate the actual width of the synaptic clefts shown in the two drawings.

Results

Let us assume that, on the printout of the Schematic Synapse Model, the diameter of the axonal shaft is 40 mm (please note that this value may vary among different printouts) – that is, this structure is 80,000 times enlarged, compared to the actual dimensions of a typical axon, here assumed to be 0.5 μm. The length of the presynaptic terminal (determined on the same printout to be 85 mm or 0.085 m) is, therefore, 8.5·10−2 m ÷ 80,000 = 1.06·10−6 m or 1.06 μm or ≈1 μm. Applying the same procedure, the width of the synaptic cleft is estimated to be 475 nm (≈0.5 μm).

Similarly, application of the above procedure to the Morphometric Synapse Model yields ≈1 μm for the length of the presynaptic terminal and ≈20 nm for the width of the synaptic cleft.

Evaluation of the Results

Educational models of chemical synapses, like the one shown in Figure 2, generally provide a good indication of the relative proportions of the presynaptic terminal and the axon from which this terminal emerges. For example, in the adult visual cortex, terminal lengths between 0.5 μm and 2.2 μm, with a mean of 1.2 μm, have been measured (Stettler et al., 2006). Axon diameters in the central nervous system typically range between 0.1 μm and 10 μm, but thinner axons are the most abundant (Perge et al., 2012). Thus, a ratio of roughly 2:1 of the length of the presynaptic terminal to the diameter of the axon shaft, as depicted in Figure 2, is well within the range of the proportions of axons and terminals found in the central nervous system.

On the other hand, a width of 0.5 μm of the synaptic cleft, as indicated by the Schematic Synapse Model, is far off – roughly by a factor of 25. Electron microscopy studies have shown that the distance between the apposed synaptic membranes typically ranges between 15 nm and 25 nm (Peters et al., 1991; Zuber et al., 2005). As will be demonstrated in Part 2, this severe distortion of the actual dimension of the synaptic cleft in many educational models of chemical synapses, without mentioning that the dimensions of the synaptic components are not drawn to scale, has serious consequences for the predicted impact on neurotransmitter diffusion time and concentration of transmitter molecules in the synaptic cleft, and thus for the functioning of the synapse.

By contrast, the Morphometric Synapse Model presented in Figure 1A depicts realistically the relative dimensions of axon diameter versus presynaptic terminal length and synaptic cleft width. If the diameter of the axon is 0.5 μm, then the presynaptic terminal will be ~1 μm long and the synaptic cleft will be ~20 nm wide. Furthermore, the synaptic vesicle shown in Figure 1B will then have a diameter of ~40 nm, a value that falls well within the size range of synaptic vesicles containing classical transmitters such as glutamate (Zhang et al., 1998).

Part 2: Calculation of the Time Required for Diffusion of Neurotransmitter across the Synaptic Cleft

Procedure

  1. In this part, the students will estimate (a) the time it takes glutamate to diffuse from its release sites on the presynaptic membrane across the synaptic cleft to the postsynaptic membrane and (b) the rate of diffusion. For these estimations, follow steps 2–4 below.

  2. In case of the Morphometric Synapse Model, the distance between the apposed membranes is assumed to be 20 nm. The diffusion coefficient of glutamate in the synaptic cleft has been determined to be 330 μm2/s (Nielsen et al., 2004). For the calculation, use Einstein's approximation equation. This equation approximates the average time t it takes a molecule with the diffusion coefficient D to diffuse in solution over the distance x in one dimension: 
    tx22D
  3. Repeat the calculation performed in step 1, now for the Schematic Synapse Model, by assuming the distance between the apposed membranes to be 500 nm.

  4. For both the Morphometric Synapse and the Schematic Synapse models, determine the rate of diffusion by dividing the distance (in meters) over which glutamate diffuses by the diffusion time (in seconds).

  5. To express the rate by a more familiar measure of speed, kilometers per hour (km/h) or miles per hour (mi/h), multiply the rate determined in step 3 by a factor of 3.6 or 2.24, respectively.

Results

Einstein's approximation equation predicts that a 25-fold increase in cleft width, from 20 nm to 500 nm, results in a 625-fold increase in diffusion time, from ~0.606 μs to ~378.788 μs. These diffusion times translate into mean rates of diffusion of 0.033 m/s or 0.12 km/h or 0.074 mi/h (at an assumed cleft width of 20 nm) and 0.0013 m/s or 0.0048 km/h or 0.0030 mi/h (at an assumed cleft width of 500 nm). For comparison, continuous tracking of nocturnal activity of garden snails has indicated that these animals travel at average speeds of up to 1 m/h (http://www.exeter.ac.uk/news/featurednews/title_315519_en.html); they are, thus, 30 or 300 times faster than glutamate diffusing across a synaptic cleft of 20 nm or 500 nm width, respectively.

Evaluation of the Results

The above calculations provide some important perspectives. As expected from diffusion as a passive process, the rate at which glutamate diffuses across the synaptic gap is low, particularly when expressed by measures used in everyday life. However, the seemingly paradoxical situation that the glutamate molecules, nevertheless, diffuse from the presynaptic membrane to the postsynaptic membrane within an extremely short period of time can be readily resolved by taking the width of the synaptic cleft into account, which is just a few nanometers.

The calculations also help overcome a frequent misunderstanding: that the total delay time of 200 μs between the opening of the fusion pore on the presynaptic membrane and the opening of the channels associated with the glutamate receptors is due to the time it takes the transmitter molecules to diffuse across the synaptic cleft. In fact, the latter is just ~1 μs and, thus, contributes rather insignificantly to the total delay time.

However, it is important for students to appreciate the fact that diffusion time increases with the square of diffusion distance. Synapses with disproportionately wide clefts, as they are depicted in the Schematic Synapse Model and in many other models used for educational purposes (without mentioning that the width of these clefts is not drawn to scale), would, if they existed, increase diffusion dramatically and delay the generation of postsynaptic potentials severely. Despite the extremely short diffusion time of glutamate at the synaptic cleft, the rate of diffusion is rather sobering – 0.074 mi/h or only 1/30th the average speed of a garden snail during nocturnal activity. At an assumed cleft width of 500 nm, it would be even more disillusioning – just 0.0030 mi/h!

In addition, the width of the synaptic cleft impacts not only neurotransmitter diffusion time but also local glutamate concentration at the postsynaptic receptor site. The latter has an important consequence. Studies have shown that high levels of glutamate are required to induce opening of the channels associated with the receptors (for reviews, see Meinrenken et al., 2003; Südhof, 2004; Lisman et al., 2007). Such high concentrations of glutamate exist in the synaptic cleft only near (within ~100 nm) the site of vesicle release. Synapses with cleft widths of several hundred nanometers would, therefore, be unable to accommodate the transient, local increases in transmitter concentration required for receptor activation.

Assessment of Student Learning

Learning of the concept of chemical synaptic transmission is challenged by at least two major deficiencies commonly found among students across all grade levels. The first deficiency is their limited skill set for conceptualizing size and scale in the micro- and nano-ranges (Tretter et al., 2006; Jones, 2013). The second is the widespread lack of a conceptual understanding of diffusion (Westbrook & Marek, 1991; Odom, 1995). The guided inquiry activity presented here is aimed at helping students overcome these deficiencies, at least in the context of chemical synaptic transmission. This is achieved by having students (1) determine absolute and relative sizes of structural components of synapses, based on drawings of synapses that depict different schematic representations of synapses; and (2) relate the estimated differences in synaptic cleft width to differences in calculated diffusion times of a transmitter substance across the synaptic cleft.

To assess students' learning outcomes, I routinely include multiple-choice questions like those in Box 2 in quizzes or exams. The scores that the students obtain in response to these two questions are most commonly similar to the average score obtained in the respective test. This is encouraging given that, at the beginning of each course, the vast majority of students typically express significant difficulties in applying microscopic and nanoscopic scales to cellular and subcellular structures, and in correctly using the concept of diffusion to explain the process of synaptic transmission. Although, as in any single-group design involving pre- and post-intervention testing, the causality of the effectiveness of the inquiry activity on the student learning cannot be determined (for a methodological discussion of this issue, see Spurlock, 2018), it is plausible to assume a benefit of the employed exploratory approach that allows students to link their observations to the ideas of size, scale, and diffusion in the context of the synaptic transmission concept. Similar benefits of such instructional approaches for learning at the nanoscale, or for remediating students' misconceptions regarding diffusion, have been reported by other authors (Marek et al., 1994; Jones et al., 2003).

Box 2.
Sample exam questions

The following multiple-choice questions have been designed to assess students' familiarity with both absolute and relative dimensions of synaptic components (question 1) and their ability to identify the correct mechanism underlying the crossing of neurotransmitter molecules from the vesicle release sites at the presynaptic membrane to the receptor binding sites at the postsynaptic membrane of chemical synapses (question 2). The correct answers are in bold.

Question 1 
Which of the following four combinations describes realistic dimensions/proportions of a neuron found in the human brain? (Remember: 1 μm = 10−6 m; 1 nm = 10−9 m)
  • Size of soma = 200 μm; diameter of axon = 10 μm; width of synaptic cleft = 1 μm

  • Size of soma = 6 μm; diameter of axon = 0.02 μm; width of synaptic cleft = 1 μm

  • Size of soma = 6 μm; diameter of axon = 1 μm; width of synaptic cleft = 0.02 μm

  • Size of soma = 1 μm; diameter of axon = 0.05 μm; width of synaptic cleft = 0.001 μm

 
Question 2 
During synaptic transmission, neurotransmitter molecules are released into the synaptic cleft by exocytosis. They cross the gap between the presynaptic membrane and the postsynaptic membrane extremely fast because movement of the transmitter molecules is mediated by
  • active transport

  • facilitated diffusion

  • diffusion over extremely short diffusion distances

 
Question 1 
Which of the following four combinations describes realistic dimensions/proportions of a neuron found in the human brain? (Remember: 1 μm = 10−6 m; 1 nm = 10−9 m)
  • Size of soma = 200 μm; diameter of axon = 10 μm; width of synaptic cleft = 1 μm

  • Size of soma = 6 μm; diameter of axon = 0.02 μm; width of synaptic cleft = 1 μm

  • Size of soma = 6 μm; diameter of axon = 1 μm; width of synaptic cleft = 0.02 μm

  • Size of soma = 1 μm; diameter of axon = 0.05 μm; width of synaptic cleft = 0.001 μm

 
Question 2 
During synaptic transmission, neurotransmitter molecules are released into the synaptic cleft by exocytosis. They cross the gap between the presynaptic membrane and the postsynaptic membrane extremely fast because movement of the transmitter molecules is mediated by
  • active transport

  • facilitated diffusion

  • diffusion over extremely short diffusion distances

 

Conclusions

The difficulty many students have in developing a deeper understanding of the chemical synaptic transmission underscores the need for a comprehensive instructional strategy for teaching this important concept, which clearly ranks among the greatest achievements in the history of neurobiology. As part of this strategy, I suggest replacing educational models of chemical synapses that depict misleadingly the relative dimensions of the key components of synapses (as demonstrated by the model in Figure 2) with more realistic morphometric models (exemplified by Figure 1). The other important step of this strategy is to move from teaching of diffusion as a slow process to a differential teaching approach – conveying clearly the message that diffusion is an extremely fast process over nanoscopic distances, but a slow process over microscopic and macroscopic ranges. Combined with inquiry activities and quantitative reasoning tasks, like the ones presented here, this approach has significant potential to catalyze in students a deeper understanding of one of the core concepts of biology.

I thank Marianne M. Zupanc for helpful comments on the manuscript.

References

References
Elrod, S. (
2014
).
Quantitative reasoning: the next ‘across the curriculum' movement
.
Peer Review
,
16
,
4
8
.
Jones, M.G. (
2013
). Conceptualizing size and scale. In R. Mayes & L. Hatfield (Eds.),
Quantitative Reasoning in Mathematics and Science Education: Papers from an International STEM Research Symposium
.
WISDOMe Monograph Series
, vol.
3
.
University of Wyoming
,
Laramie
.
Jones, M.G., Andre, T., Superfine, R. & Taylor, R. (
2003
).
Learning at the nanoscale: the impact of students' use of remote microscopy on concepts of viruses, scale, and microscopy
.
Journal of Research in Science Teaching
,
40
,
303
322
.
Jones, M.G. & Taylor, A.R. (
2009
).
Developing a sense of scale: looking backward
.
Journal of Research in Science Teaching
,
46
,
460
475
.
Kirschner, P.A., Sweller, J. & Clark, R.E. (
2006
).
Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching
.
Educational Psychologist
,
41
,
75
86
.
Lisman, J.E., Raghavachari, S. & Tsien, R.W. (
2007
).
The sequence of events that underlie quantal transmission at central glutamatergic synapses
.
Nature Reviews Neuroscience
,
8
,
597
609
.
Marek, E.A., Cowan, C.C. & Cavallo, A.M.L. (
1994
).
Students' misconceptions about diffusion: how can they be eliminated?
American Biology Teacher
,
56
,
74
77
.
Meinrenken, C.J., Borst, J.G. & Sakmann, B. (
2003
).
Local routes revisited: the space and time dependence of the Ca2+ signal for phasic transmitter release at the rat calyx of Held
.
Journal of Physiology
,
547
,
665
689
.
Montagna, E., de Azevedo, A.M.S., Romano, C. & Ranvaud, R. (
2010
).
What is transmitted in “synaptic transmission”?
Advances in Physiology Education
,
34
,
115
116
.
Nielsen, T.A., DiGregorio, D.A. & Silver, R.A. (
2004
).
Modulation of glutamate mobility reveals the mechanism underlying slow-rising AMPAR EPSCs and the diffusion coefficient in the synaptic cleft
.
Neuron
,
42
,
757
771
.
Odom, A.L. (
1995
).
Secondary & college biology students' misconceptions about diffusion & osmosis
.
American Biology Teacher
,
57
,
409
415
.
Odom, A.L. & Barrow, L.H. (
1995
).
Development and application of a two-tier diagnostic test measuring college biology students' understanding of diffusion and osmosis after a course of instruction
.
Journal of Research in Science Teaching
,
32
,
45
61
.
Perge, J.A., Niven, J.E., Mugnaini, E., Balasubramanian, V. & Sterling, P. (
2012
).
Why do axons differ in caliber?
Journal of Neuroscience
,
32
,
626
638
.
Peters, A., Palay, S.L. & Webster, H.D.F. (
1991
).
The Fine Structure of the Nervous System
.
New York, NY
:
Oxford University Press
.
Pickel, V. & Segal, M. (Eds.) (
2014
).
The Synapse: Structure and Function
.
Oxford, UK
:
Academic Press
.
Spurlock, D.R. (
2018
).
The single-group, pre- and posttest design in nursing education research: it's time to move on
.
Journal of Nursing Education
,
57
,
69
71
.
Stettler, D.D., Yamahachi, H., Li, W., Denk, W. & Gilbert, C.D. (
2006
).
Axons and synaptic boutons are highly dynamic in adult visual cortex
.
Neuron
,
49
,
877
887
.
Südhof, T.C. (
2004
).
The synaptic vesicle cycle
.
Annual Review of Neuroscience
,
27
,
509
547
.
Tretter, T.R., Jones, M.G. & Minogue, J. (
2006
).
Accuracy of scale conceptions in science: mental maneuverings across many orders of spatial magnitude
.
Journal of Research in Science Teaching
,
43
,
1061
1085
.
Ventriglia, F. & Di Maio, V. (
2000
).
A Brownian model of glutamate diffusion in excitatory synapses of hippocampus
.
BioSystems
,
58
,
67
74
.
Westbrook, S.L. & Marek, E.A. (
1991
).
A cross-age study of student understanding of the concept of diffusion
.
Journal of Research in Science Teaching
,
28
,
649
660
.
Zhang, B., Koh, Y.H., Beckstead, R.B., Budnik, V., Ganetzky, B. & Bellen, H.J. (
1998
).
Synaptic vesicle size and number are regulated by a clathrin adaptor protein required for endocytosis
.
Neuron
,
21
,
1465
1475
.
Zuber, B., Nikonenko, I., Klauser, P., Muller, D. & Dubochet, J. (
2005
).
The mammalian central nervous synaptic cleft contains a high density of periodically organized complexes
.
Proceedings of the National Academy of Sciences USA
,
102
,
19192
19197
.