![[Feedback]](/icons/banner/feedbackACT.gif){kind=icon}
![[For Subscribers]](/icons/banner/subscriberACT.gif){kind=icon}
![[Archive]](/icons/banner/archiveACT.gif){kind=icon}
![[Search]](/icons/banner/searchACT.gif){kind=icon}
![[Contents]](/icons/banner/tocACT.gif){kind=icon}
|
|
|
|
|
||
Vol. 16, Issue 9, 4243-4255, September 2005
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
* Center for Molecular Neurobiology and Department of Neuroscience, The Ohio State University, Columbus, OH 43210;
Developmental Neurobiology Program, The Burnham Institute, La Jolla, CA 92037; and
Department of Physics and Astronomy, Ohio University, Athens, OH 45701
Submitted February 19, 2005;
Revised June 22, 2005;
Accepted June 23, 2005
Monitoring Editor: Erika Holzbaur
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
8% of their time on track and 97% of their time pausing during their journey along the axon. |
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
0.004–0.04 µm/s, several orders of magnitude slower than the rate of fast axonal transport (Lasek et al., 1992
; Nixon, 1998). Numerous studies on neurofilament transport using radioisotopic pulse labeling spanning almost three decades have demonstrated that the pulse of radiolabeled neurofilament proteins moves out along axons in the form of a bell-shaped wave that spreads as it moves distally. These waves have become universally familiar in the field of axonal transport but little is known about how they are generated and what mechanistic significance can be ascribed to their shape.
One early model of slow axonal transport considered that neurofilaments move unidirectionally in a slow and continuous manner (Lasek et al., 1984). In a mathematical description of this model, Blum and Reed (1989) proposed the existence of a hypothetical "engine" that moves at a constant slow velocity of 1 mm/d. Microtubules were considered to interact directly with the engine and neurofilaments were considered to move by piggy-backing on the moving microtubules. According to this model, the average velocity of neurofilament movement was dependent on the equilibrium constants of the interactions between neurofilaments and microtubules and between microtubules and the engine. On the basis of these assumptions, the authors derived a system of partial differential equations to describe slow axonal transport in vivo. By computer simulation of the equations of the model, the authors demonstrated that they could generate transport kinetics similar to those observed in radioisotopic pulse-labeling experiments.
In recent years, considerable progress has been made in the study of neurofilament transport in axons and it is now clear that the motile behavior is quite different from the behavior modeled by Blum and Reed. Specifically, direct observations on neurofilaments in axons of cultured primary neurons using fluorescence microscopy have demonstrated that these polymers actually move at rates of 0.4–0.6 µm/s, approaching the rate of fast axonal transport and that these rapid movements are also intermittent, bidirectional and highly asynchronous (Wang et al., 2000; Roy et al., 2000; Yabe et al., 2001; Wang and Brown, 2001; Ackerley et al., 2003). Based on these observations, it has been proposed that axonal neurofilaments are actually transported by fast motors and that the overall rate of movement is slow because the filaments spend some of their time moving retrogradely and most of their time not moving at all. In other words, the slow rate of movement is an average of rapid bidirectional movements interrupted by prolonged pauses. We refer to this as the stop-and-go hypothesis of slow axonal transport, and we speculate that it may also explain the slow movement of other cytoskeletal and cytosolic proteins that are conveyed by slow axonal transport (Brown, 2000). This hypothesis combines features of two longstanding competing hypotheses, the unitary hypothesis of Ochs (1975) and the structural hypothesis of Lasek (Tytell et al., 1981), and thus it may go some way to reconciling those two apparently disparate perspectives.
A critical test of the stop-and-go hypothesis is whether it can explain the radioisotopic pulse-labeling kinetics in vivo. Specifically, can the rapid infrequent movements of neurofilaments observed in cultured neurons on a time scale of seconds or minutes account for the kinetics of movement of populations of neurofilaments observed in living organisms on a time scale of weeks or months? Because it is presently not possible to examine the behavior of individual neurofilaments in vivo, we have used a computational modeling approach. Here we present a stochastic model of neurofilament transport in axons based on a detailed kinetic analysis of the moving and pausing behavior of individual neurofilaments observed in cultured nerve cells. We propose that neurofilaments move along cytoskeletal tracks, exhibiting short bouts of rapid movement interrupted by short "on-track" pauses and that they can temporarily disengage from their tracks, resulting in more prolonged "off-track" pauses. Our model predicts that axonal neurofilaments spend 8% of their time on track and 97% of their time pausing during their journey along the axon. Thus the bidirectional stop- and-go movements of neurofilaments observed by fluorescence microscopy in cultured neurons can explain the kinetics of neurofilament transport observed by radioisotopic pulse labeling in vivo.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
; Wang and Brown, 2001). For example, most filaments that pause subsequently resume movement in the same direction in which they were moving before pausing. Thus we assume that neurofilaments can switch between two relatively persistent directional states, anterograde or retrograde, and that neurofilaments can move or pause in either state. The net direction is anterograde because neurofilaments spend more time moving anterogradely than retrogradely. As a first approximation, we assume that the transport properties of the neurofilaments do not vary with respect to location along the axon. We also assume that the axon is long so that we can ignore events at the proximal and distal ends.
In our experimental studies, the neurofilaments that we tracked spent 70% of their time pausing (Wang et al., 2000; Wang and Brown, 2001). However, we have noted previously that these studies underestimated the true overall pausing behavior (Wang et al., 2000). The reason for this is that our measurements relied on the observation of short gaps in the neurofilament array and we were only able to track neurofilaments that moved into these gaps during the period of observation. The fact that the edges of the gaps remained fixed throughout most of our movies indicates that many filaments flanking the gaps paused throughout the observation period, yet we were unable to track these filaments because they could not be resolved from their neighbors. To explain these observations, we propose that in each directional state (anterograde or retrograde), axonal neurofilaments can switch between two additional states: a state in which neurofilaments alternate between bouts of rapid movement interrupted by short pauses, corresponding to the motile behavior observed in our live cell imaging studies, and a state in which neurofilaments pause for more prolonged periods without any movement. For the purposes of this model, we refer to these states as on track and off track.
Assignment of Rate Constants and Probabilities
Assuming that neurofilaments can be either anterograde or retrograde and either on track or off track, we can define four distinct kinetic states: on track in the anterograde state, off track in the anterograde state, on track in the retrograde state and off track in the retrograde state (Figure 1). To determine whether neurofilaments are in the anterograde or retrograde state, we define a reversal rate constant kAR, which represents the average number of times per second that an anterograde filament becomes retrograde, and a reversal rate constant kRA, which represents the average number of times per second that a retrograde filament becomes anterograde. We also define an overall reversal rate, kREV = kAR + kRA. To determine whether the neurofilaments are on or off track, we define a rate constant kOFF, which represents the average number of times per second that an on-track filament moves off track, and a rate constant kON, which represents the average number of times per second that an off-track filament moves on track. As a first approximation, we assume that these rate constants are the same for both anterograde and retrograde filaments. Because the simulations in the present study were all performed using a fixed time interval, we express the rate constants as events per time interval rather than per second.
|
|
), the proportion of filaments that are on track (i.e., the probability of being on track) is given by the ratio pON = kON/(kON + kOFF) and the proportion that are off track (i.e., the probability of being off track) is given by the ratio pOFF = kOFF/(kON + kOFF). Similarly, the proportion of filaments in the retrograde state (i.e., the probability of being in the retrograde state) is given by the ratio pR = kAR/(kAR + kRA) and the proportion in the anterograde state (i.e., the probability of being in the anterograde state) is given by the ratio pA = kRA/(kAR + kRA).
Calculation of Transition Probabilities for the Moving and Pausing Behavior
An important feature of neurofilament movement that we have noted in our live cell imaging studies is that there is a persistence to their motile behavior. Rather than switching randomly between moving and pausing states without memory, the filaments tend to alternate between bouts of sustained movement and bouts of sustained pausing. This can be seen by visual inspection of the traces for individual neurofilaments, such as those shown in Figure 4, F–J. Thus the probability of a filament moving in any given time interval is greater if it was moving in the previous time interval than if it was pausing in the previous time interval. Conversely, the probability of a filament pausing in any given time interval is greater if it was pausing in the previous time interval than if it was moving in the previous time interval. Depending on the probabilities of switching between the moving and pausing states, this kind of behavior can be described as a Markovian process, i.e., one in which the behavior in any one time interval is dependent on the behavior in the preceding time interval.
|
). Implicitly, we assume that the movements and pauses of those filaments were all on track. The filaments were tracked for an average of 2.26 min at 4- or 5-s time intervals (average = 4.73 s), and the total number of time intervals for all 72 filaments was 2061. For each time interval we calculated an interval speed, which we define as the distance moved in one time interval divided by the duration of one time interval. Because we found no evidence for a relationship between the speed or pausing behavior and the direction of movement (Wang et al., 2000; Wang and Brown, 2001), we pooled the data for anterograde and retrograde movements. Movements of 
0.065 µm/s (1 camera pixel per second), which we estimated to be the limit of the precision of our measurements, were defined as pauses. Using this approach, we obtained a total of 1989 interval speeds. To simplify the computation, we assigned each interval speed to one of seven speed bins: v0: v = 0 (i.e., pausing); v1: 0 < v 0.5 µm/s; v2: 0.5 < v 1.0 µm/s; v3: 1.0 < v 1.5 µm/s; v4: 1.5 < v 2.0 µm/s; v5: 2.0 < v 2.5 µm/s; and v6: 2.5 < v 3.0 µm/s.
|
The Algorithm
To simulate the movement of neurofilaments, we start with a specified number of neurofilaments distributed along the axon in a specified manner and then determine their position and velocity iteratively for a specified number of time intervals (Figure 3). We use a time interval of 4.73 s, which represents the average time interval used in our experimental studies (see above). We consider the location of each neurofilament to be a single point in space that might be considered the middle of the filament. This is a reasonable assumption given that the average length of neurofilament polymers is small relative to the segment length (3 mm) and axon length (several centimeters) in the radioisotopic pulse-labeling experiments (see below). For simplicity, we assume that neurofilaments can switch on and off track and between anterograde and retrograde states only when they are pausing. If the filament is moving, we generate a pseudorandom number within the range 0–1 and compare it to the probabilities in the matrix of transition probabilities in Table 1 to determine whether the filament remains in the same speed bin or switches to a new speed bin. Then we use the new speed to calculate a new location for the filament. If the filament is pausing, we generate a pseudorandom number to determine its directional state (governed by the probabilities pA and pR) and a second pseudorandom number to determine whether the filament is on or off track (governed by the probabilities pON and pOFF). For filaments that are on track, we then determine a new location for the filament based on the new direction and speed as described above. Pseudorandom numbers are generated using the ran2 algorithm (Press et al., 1992).
|
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
), so we assume that pR = 0.31 and pA = 0.69. The rates kREV, kON, and kOFF are unknown, so we initially estimated the values of these parameters and subsequently optimized them as described below. In two separate studies on neurofilament movement in cultured neurons, we observed a total of 141 filaments for a total observation time of 5.4 h (4111 time intervals), yet we observed no sustained reversals (Wang et al., 2000; Wang and Brown, 2001). In another study, Roy et al. (2000) reported 5 of 73 neurofilaments reversed direction, but some of those neurofilaments exhibited unusually erratic behavior, reversing multiple times within the short period of time that they were tracked. Thus the magnitude of kREV is low. As a starting point for our simulations, we assume kREV = 0.001 (kAR = 0.00031 and kRA = 0.00069). Because the existence of distinct on-track and off-track populations of neurofilaments is hypothetical, we have no experimental data to guide our selection of values for kON and kOFF. However, we expect that filaments must spend most of their time off track to account for the overall slow rate of movement. As a starting point for our simulations, we assume kON = 0.01 and kOFF = 0.1 (9% of neurofilaments on track).
Simulation of the Movement of a Single Neurofilament
To test the model, we first simulated the movement of a single neurofilament (Figure 4). At the start of the simulation, we consider the filament to be off track in the anterograde state. Figure 4, A–E, shows representative excerpts of the simulated behavior of a single neurofilament, including both anterograde and retrograde phases of its movement, assuming kON = 0.01, kOFF = 0.1, and kREV = 0.001. The filament exhibited brief bouts of rapid movement interrupted by pauses of varying duration. Consistent with our experimental data, the transitions between movements and pauses were abrupt and reversals were rare; in a 24-h simulation the filament reversed direction eight times, which represents a frequency of 0.00044 per time interval, consistent with the theoretical prediction pAkAR + pRkRA. Figure 4, F–J, shows representative plots of actual neurofilament behavior observed by time-lapse fluorescence microscopy in cultured neurons (data from the study of Wang and Brown, 2001). It can be seen that the model generates a motile behavior very similar to the experimental data, except that some of the pauses in the simulation are much longer. This is expected because our model assumes that filaments can enter an off-track state in which they pause for prolonged periods (as explained in Materials and Methods, our experimental studies were biased toward the detection of moving filaments; filaments that did not move during the time that we observed them could not be tracked and therefore were excluded from our analyses).
Analysis of the Pause Durations
In a stochastic system characterized by alternating movements and pauses, we can gain insight into the mechanism of movement by analyzing the frequency distribution of the pause durations. Specifically, if we consider that there is no off-track state and we define the rate at which neurofilaments transition from the pausing state to a moving state as kPM, then a histogram of the pause durations will be exponentially distributed proportional to exp(-kPMt), and the exponential will decrease with a time constant 1/kPM (Van Kampen, 1981). If we now consider distinct on-track and off-track states, with transitions between them dictated by kON and kOFF, then we expect to observe the superimposition of two exponentials with time constants of 1/kPM and 1/kON. Figure 5A shows the pause duration frequency distribution generated by our model, assuming kON = 0.01, kOFF = 0.1, and kREV = 0.001. As expected, the distribution is biphasic and matches a double exponential relationship due to the existence of distinct on-track and off-track states for the neurofilaments. The initial (rapidly declining) phase of these plots is due primarily to on-track pauses (shorter duration) and the later (slowly declining) phase is due primarily to off-track pauses (longer duration). Figure 5, B and C, shows the frequency distribution of the actual pause durations for neurofilaments in cultured neurons (previously unpublished data from the study of Wang and Brown, 2001). Note that the shape of the predicted distribution is similar to that of the experimental data (compare Figure 5, B and C). However, we consider that the experimental data in Figure 5C is only reliable for short pauses because our experimental observations underestimate the number and duration of long pauses (see Materials and Methods). Because the frequency distribution for short pause durations can be characterized by its initial slope, we define the initial slope of the histogram in Figure 5C as the benchmark for optimization of the pause distributions in our model (see below).
|
Simulation of the Movement of a Population of Neurofilaments
To investigate the behavior of the model in a radioisotopic pulse-labeling experiment, we first simulated the movement of a population of radiolabeled neurofilaments distributed uniformly along a 3-mm length of axon (i.e., in the form of a 3-mm-wide square wave; Figure 6 and Supplementary Video, QuickTime Movie 1). At the start of each simulation, we considered all filaments to be off track and 31% to be in the retrograde state. Note, however, that these starting conditions have no significant effect on the end result because of the long duration of the simulations (several weeks) relative to the short duration of the time intervals. We found that the square wave spreads rapidly to form a Gaussian wave that continues to spread as it propagates distally, as generally expected for a stochastic process (for the specific conditions under which this applies, see Jung et al., 1996). Notably, the shape and spreading of this wave is similar to the behavior described for neurofilaments in vivo (e.g., Hoffman et al., 1985; Jung and Shea, 1999; Xu and Tung, 2000).
|
|
In summary, the only parameter that affects the average rate of movement is the ratio kON/kOFF (Figure 7A). Both the ratio kON/kOFF and the magnitudes of kON and kOFF affect the pause duration distribution (Figure 7, C and F), but the only parameters that affect the initial slope are the magnitudes of kON and kOFF. (Figure 7F). All three parameters affect the spreading of the wave, but only kREV does so without affecting the pause duration frequency distribution (Figure 7I). Thus, any given combination of average rate, spreading, and pause duration frequency distribution in this model corresponds to a single unique combination of values for the parameters kON, kOFF, and kREV.
|
) for neurofilament protein L in ventral root and sciatic nerve motor axons of wild-type mice because this is one of the few published data sets for which the statistical error has been calculated for each data point (Figure 8). In the Xu and Tung study, the average velocity of neurofilament transport was found to be approximately constant during the first 3 wk and then slowed at later times, indicating that the velocity of neurofilament transport varies along the length of these axons (see Discussion). For the purposes of this study, we chose to focus on the initial 3-wk period when the velocity is constant. Because the exact length, duration, and shape of the starting pulse in the pulse-labeling experiments is not known, we started our simulations with a distribution of neurofilaments that matches the day 7 data (Figure 8A), at which time most of the filaments had entered the ventral root, and then attempted to match the distribution of neurofilaments at day 21, 2 wk later (Figure 8B).
Figure 9 shows the results of our simulations of the Xu and Tung data. For ease of computation, we fit the day 7 data using a Gaussian function and used this Gaussian curve as the starting distribution for our simulations (Figure 9A). Note that the Gaussian curve matches the experimental data closely, though there is a slight discrepancy at the leading edge. Using our initial "best guess" values for the model parameters (kON = 0.01, kOFF = 0.1, kREV = 0.001), we found that the simulated neurofilament population moved too fast and did not spread enough compared with the experimental data (Figure 9B). In addition, the initial slope of the pause duration frequency distribution did not match the experimental data (Figure 9G). We have shown above that the only parameter or combination of parameters that affects average velocity in our model is the ratio kON/kOFF (Figure 7). By decreasing kON/kOFF to 0.0083, we were able to match the average velocity of the experimental data (Figure 9C). This had little effect on width of the wave because the ratio kON/kOFF has little effect on spreading at low ratios (Figure 7B). As expected, based our earlier findings (Figure 7C), changing kON/kOFF had no effect on the initial slope of the pause duration frequency histogram (Figure 9H).
|
Because the existence of distinct on-track and off-track populations of neurofilaments is hypothetical, we examined whether we could match the experimental data if we assumed that all neurofilaments are on track (this is the equivalent of assuming kOFF = 0 in our model). As expected, we found that the pulse of radiolabeled neurofilaments moved too fast and the wave spread too little (data not shown). The spreading could be increased by decreasing kREV, but this had no effect on the velocity because the only way to affect average velocity in our model is to alter the ratio kON/kOFF (Figure 7G). We also examined whether we could match the experimental data if we assumed that neurofilaments can only move anterogradely (this is the equivalent of assuming kAR = 0 and kRA = 1 in our model). Under this condition, the wave moved too fast and spread too little, and there was no combination of kON and kOFF that could match the experimental data (data not shown). Thus our model cannot match the in vivo experimental data unless we assume that there are distinct on-track and off-track populations of neurofilaments in vivo and that neurofilament transport is bidirectional in vivo.
Figure 10 and Supplementary Video QuickTime Movie 2 show a simulated radioisotopic pulse-labeling experiment using the final optimized parameters obtained above, and Figure 11 shows the average velocity, spreading, and pause duration frequency distribution for this simulation. Supplementary Video QuickTime Movie 3 is a graphic representation of the simulated behavior for 22 neurofilaments in a 200-µm segment of axon over a period of 1 h. Because the plots in Figure 11 represent the result of our optimized simulation, they can be considered to be predictions of neurofilament behavior in vivo. The average distance moved was linear with respect to time, with an average velocity of 0.56 mm/d (Figure 11A). The spreading of the wave increased in a nonlinear manner (Figure 11B) and was proportional to t1/2 when the simulation was extended to longer times (data not shown). Based on the optimized values of the parameters kON and kOFF, the average proportion of the neurofilaments that was on track at any point in time was 8.0%. This number is slightly larger than kON/(kON + kOFF) = 0.077 (i.e., 7.7% on track) because we assume that a filament cannot switch off track while it is moving. The average duration of continuous uninterrupted pausing was 430 s, but the range was large. For example, 38% of the pauses were 1 min or less in duration and 16% of the pauses were 15 min or more in duration (Figure 11C). Moreover, the average duration of sustained uninterrupted movement was only 14 s. Thus movements were brief and pauses were prolonged. On average, the filaments spent 97% of their time pausing.
|
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
8% of their time on track; and fourth, that neurofilaments spend 97% of the time pausing during their journey along these axons. These predictions are discussed in more detail below.
Neurofilament Transport Is Bidirectional In Vivo
The idea that slow axonal transport may be a bidirectional process was first proposed more than a decade ago by Griffin and colleagues, based on their analysis of the distribution of cytoskeletal proteins in transected peripheral nerves in Ola mice, which exhibit delayed Wallerian degeneration. These authors reported that neurofilament and other cytoskeletal proteins accumulated proximally as well as distally in the isolated nerve segments, implying that a proportion of cytoskeletal proteins move retrogradely in vivo (Watson et al., 1993; Glass and Griffin, 1994). This conclusion is supported by studies on transgenic mice over-expressing the p50/dynamitin subunit of dynactin. These mice develop a motor neuron disease characterized by accumulations of neurofilaments in axons, which implies that the activity of a retrograde microtubule motor is important for neurofilament transport along axons in vivo (LaMonte et al., 2002). Our computational modeling studies lend further support to this notion. Specifically, we were unable to match the kinetics of neurofilament transport in mouse spinal motor neurons unless we assumed that neurofilaments move bidirectionally and that the frequency of reversals is low. In fact, these bidirectional excursions appear to be a significant contributor to the spreading of the wave.
Neurofilaments Can Pause for Prolonged Periods
Our model assumes that neurofilaments can exist in two states that differ in their pausing behavior. We refer to these states as on track and off track. Neurofilaments that are on track exhibit short bouts of rapid movement interrupted by short pauses, whereas neurofilaments that are off track are stationary for prolonged periods. In mouse lumbar spinal motor axons, we predict that neurofilaments spend 92% of their time pausing off track as they move along the axon. The idea that axonal neurofilaments spend a significant proportion of their time in a stationary state was originally proposed by Nixon and Logvinenko (1986) based on their analysis of the axonal transport of radiolabeled neurofilament proteins in mouse optic nerve. The data in that study were subsequently disputed on technical grounds (Lasek et al., 1992), sparking a vigorous debate. In essence, the principal issue has been whether the data in the original Nixon and Logvinenko study represent pure neurofilament transport kinetics or whether the kinetics were contaminated with cytosolic proteins that comigrate with neurofilament proteins when subjected to one-dimensional SDS-PAGE. Although this controversy remains unresolved, our modeling indicates that the basic idea that neurofilaments may be stationary for prolonged periods during their transit along axons does appear to be correct. In fact, our modeling predicts that neurofilaments in mouse lumbar spinal motor axons spend only 3% of the time moving.
Mechanistically, we consider that on track and off track neurofilaments could differ in some way that influences their capability for movement. One factor that may regulate the frequency of neurofilament movement is phosphorylation of neurofilament protein H (Ackerley et al., 2003). The molecular mechanism of this effect is not known, though it is attractive to speculate that neurofilament phosphorylation might act by affecting the activity of neurofilament motors or their affinity for the neurofilament cargo. Although our model does not assume the identity of the tracks along which neurofilaments move, it is likely that they are microtubules. For example, neurofilaments have been shown to move along microtubule polymers in vitro (Shah et al., 2000) and there is evidence that neurofilaments are transported by microtubule motors (see below). Neurofilaments have been shown to interact with myosin Va, which suggests that they may also be capable of moving along microfilaments, but a recent study in cultured neurons has shown that neurofilament movement can be abolished by depolymerizing microtubules but not by depolymerizing microfilaments (Francis et al., 2005), which suggests that microtubules are the principal substrate. Assuming that microtubules are the tracks, it is interesting to note that in myelinated axons, which contribute more than 95% of the slowly transported radioactivity in the radioisotopic pulse-labeling studies (Wujek et al., 1986), neurofilaments generally outnumber microtubules. For example, in the sciatic nerve of 14-wk-old mice, neurofilaments outnumber microtubules by 7:1 in small axons (<1.5 µm internodal diameter) and by 16:1 in large axons (>3.5 µm internodal diameter; Reles and Friede, 1991). In occulomotor nerve of 4-wk-old chickens, neurofilaments outnumber microtubules by 69:1 in somatic motor axons and 97:1 in parasympathetic axons (Price et al., 1988). A consequence of this high axonal neurofilament:microtubule ratio is that at any given point in time many neurofilaments may not be adjacent to a microtubule. Thus one factor that may contribute to the distinct pausing behavior of neurofilaments in the on track and/or off track states is their proximity to the tracks along which they move.
The Significance of the Bell-shaped Waves
The bell-shaped waves characteristic of radioisotopic pulse-labeling studies on slow axonal transport were first described more than 25 years ago, yet remarkably little is known about how they are generated. In the present study, we show that the bell-shaped waves obtained for neurofilaments in mouse ventral root and sciatic nerve are approximately Gaussian and can be considered to represent the movement of a population of filaments at a broad range of rates, dictated largely by stochastic variation in the direction and frequency of movement. At any point in time those neurofilaments at the leading edge of the wave happened to have moved more frequently than others, or more consistently in an anterograde direction, whereas those at the trailing edge of the wave happened to have moved less frequently, or more frequently in a retrograde direction. Over time, the population spreads apart but the net direction is anterograde because on average the filaments spend more time moving anterogradely than retrogradely. According to this perspective, individual filaments can sustain rapid rates of movement for short periods of time, but all filaments eventually pause or reverse direction and thus the average velocity is slow. However, it should be noted that spreading Gaussian waves can be generated by a variety of different mechanisms, and thus they are certainly not unique to our model. In fact, similar kinetics were observed by Blum and Reed (1989) based on the assumption that neurofilament transport is a slow unidirectional movement. Thus the significance of our modeling is not so much that we can match the experimental data in vivo, but that we can do so with a model based actual experimental measurements of the stop- and-go motile behavior of neurofilaments in living cells.
Temporal and Spatial Variations in Neurofilament Transport Behavior
In this study, we showed that our model can match the kinetics of neurofilament transport in vivo when the average velocity of movement is constant. However, there are examples in the literature in which the average rate of neurofilament transport varies both spatially and temporally. For example, Xu and Tung (2000, 2001) have shown that rate of neurofilament transport in mouse lumbar ventral root and sciatic nerve decreases abruptly 12–15 mm from the spinal cord, which corresponds to the point at which the motor axons emerge from the vertebral foramen. In addition, Hoffman and colleagues have reported a slowing of neurofilament transport with both developmental age and distance along the axons in lumbar ventral root and sciatic nerve of rats (Hoffman et al., 1983, 1985). In our model of neurofilament transport, the average velocity of the wave of radiolabeled proteins is determined by the ratio kON/kOFF, i.e., the proportion of time that the neurofilaments spend in the on track state, and the ratio kA/kR, i.e., the proportion of the time that the neurofilaments spend in the anterograde state (see Figure 7). Thus we hypothesize that the decrease in transport velocity observed along lumbar spinal motor axons in mice and rats could be due to a decrease in the proportion of time that the filaments spend on track or an increase in the proportion of time that the filaments spend in the retrograde state. This could arise, for example, by spatial or temporal regulation of the binding or activity of the neurofilament motors. In future we plan to extend our modeling to address specifically the mechanisms that could account for temporal and spatial variations in transport velocity, because it is likely that such mechanisms are critical for regulating the steady state distribution of neurofilaments along axons. However, to test these hypotheses experimentally it will be necessary to develop new approaches that are capable of analyzing neurofilament pausing and directionality in vivo, which is a significant challenge.
The Relationship between Fast and Slow Axonal Transport
The average velocity of neurofilament transport excluding pauses is 0.5 µm/s (Wang and Brown, 2001), which approaches the average velocity of membranous organelles in axons (Hill et al., 2004). Thus it is possible that the cargoes of fast and slow axonal transport share similar or identical motors. In fact, there is now good evidence that dynein is the retrograde motor for neurofilaments (Shah et al., 2000; Helfand et al., 2003; Wagner et al., 2004; He et al., 2005) and dynein is also a known retrograde motor for membranous organelles (Vallee et al., 2004). Likewise, conventional kinesin or its KIF5A isoform have been proposed to be the anterograde motor for neurofilaments (Yabe et al., 1999; Helfand et al., 2003; Xia et al., 2003 and at least one of the KIF5 isoforms, KIF5B, is a known anterograde motor for some membranous organelles (Hirokawa and Takemura, 2005). In fact, the similarities between fast and slow axonal transport also extend to the pattern of movement itself. Direct observations on the movement of membranous organelles indicate that they can exhibit stop-and-go movements reminiscent of the behavior of neurofilaments (Zhou et al., 2001; Zahn et al., 2004) and the similarity is particularly striking for mitochondria, which move in a very intermittent manner (Hollenbeck, 1996; Ligon and Steward, 2000).
The fact that cargoes of fast and slow axonal transport are both conveyed by fast motors and can both exhibit stop- and-go movements might cause one to question whether there is really any difference between fast and slow axonal transport. In answer to this question, it is important to note that even though these distinct cargoes move at similar rates on a time scale of seconds or minutes, they clearly move at very different rates on a time scale of hours or days. However, this difference in overall rate is due primarily to differences in the amount of time spent pausing rather than to differences in the rate of movement. Thus the principal difference between fast and slow axonal transport is not the mechanism of movement per se but rather the mechanism by which the movement is regulated. Cytoskeletal and cytosolic protein complexes, including cytoskeletal polymers, form the slow components of axonal transport because they spend only a small fraction of their time moving. In contrast, membranous organelles such as Golgi-derived vesicles form the fast components of axonal transport because they spend a much higher proportion of their time moving. Thus the regulation of motor protein activity or motor-cargo interactions may be key to understanding the differences between fast and slow axonal transport (Brown, 2003).
|
ACKNOWLEDGMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
|
Footnotes |
|---|
The online version of this article contains supplemental material at MBC Online (http://www.molbiolcell.org). 
Address correspondence to: Anthony Brown (brown.2302{at}osu.edu).
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
|---|
Blum, J. J., and Reed, M. C. ((1989). ). A model for slow axonal transport and its application to neurofilamentous neuropathies. Cell Motil. Cytoskelet. 12, , 53-65.[CrossRef][Medline]
Brown, A. ((2000). ). Slow axonal transport: stop and go traffic in the axon. Nat. Rev. Mol. Cell Biol. 1, , 153-156.[CrossRef][Medline]
Brown, A. ((2003). ). Axonal transport of membranous and nonmembranous cargoes: a unified perspective. J. Cell Biol. 160, , 817-821.
Francis, F., Roy, S., Brady, S. T., and Black, M. M. ((2005). ). Transport of neurofilaments in growing axons requires microtubules but not actin filaments. J. Neurosci. Res. 79, , 442-450.[CrossRef][Medline]
Glass, J. D., and Griffin, J. W. ((1994). ). Retrograde transport of radiolabeled cytoskeletal proteins in transected nerves. J. Neurosci. 14, , 3915-3921.[Abstract]
He, Y., Francis, F., Myers, K. A., Yu, W., Black, M. M., and Baas, P. W. ((2005). ). Role of cytoplasmic dynein in the axonal transport of microtubules and neurofilaments. J. Cell Biol. 168, , 697-703.
Helfand, B. T., Loomis, P., Yoon, M., and Goldman, R. D. ((2003). ). Rapid transport of neural intermediate filament protein. J. Cell Sci. 116, , 2345-2359.
Hill, D. B., Plaza, M. J., Bonin, K., and Holzwarth, G. ((2004). ). Fast vesicle transport in PC12 neurites: velocities and forces. Eur. Biophys. J. 33, , 623-632.[CrossRef][Medline]
Hirokawa, N., and Takemura, R. ((2005). ). Molecular motors and mechanisms of directional transport in neurons. Nat. Rev. Neurosci. 6, , 201-214.[CrossRef][Medline]
Hoffman, P. N., Griffin, J. W., Gold, B. G., and Price, D. L. ((1985). ). Slowing of neurofilament transport and the radial growth of developing nerve fibers. J. Neurosci. 5, , 2920-2929.[Abstract]
Hoffman, P. N., Lasek, R. J., Griffin, J. W., and Price, D. L. ((1983). ). Slowing of the axonal transport of neurofilament proteins during development. J. Neurosci. 3, , 1694-1700.[Abstract]
Hollenbeck, P. J. ((1996). ). The pattern and mechanism of mitochondrial transport in axons. Front. Biosci. 1, , d91-d102.[Medline]
Jung, C., and Shea, T. B. ((1999). ). Regulation of neurofilament axonal transport by phosphorylation in optic axons in situ. Cell Motil. Cytoskelet. 42, , 230-240.[CrossRef][Medline]
Jung, P., Kissner, J. G., and Hanggi, P. ((1996). ). Regular and chaotic transport in asymmetric periodic potentials: inertia ratchets. Phys. Rev. Lett. 76, , 3436-3439.[CrossRef][Medline]
LaMonte, B. H., Wallace, K. E., Holloway, B. A., Shelly, S. S., Ascano, J., Tokito, M., Van Winkle, T., Howland, D. S., and Holzbaur, E. L. ((2002). ). Disruption of dynein/dynactin inhibits axonal transport in motor neurons causing late-onset progressive degeneration. Neuron 34, , 715-727.[CrossRef][Medline]
Lasek, R. J., Garner, J. A., and Brady, S. T. ((1984). ). Axonal transport of the cytoplasmic matrix. J. Cell Biol. 99, , 212s-221s.
Lasek, R. J., Paggi, P., and Katz, M. J. ((1992). ). Slow axonal transport mechanisms move neurofilaments relentlessly in mouse optic axons. J. Cell Biol. 117, , 607-616.
Ligon, L. A., and Steward, O. ((2000). ). Movement of mitochondria in the axons and dendrites of cultured hippocampal neurons. J. Comp. Neurol. 427, , 340-350.[CrossRef][Medline]
Nixon, R. A. ((1998). ). The slow axonal transport of cytoskeletal proteins. Curr. Opin. Cell Biol. 10, , 87-92.[CrossRef][Medline]
Nixon, R. A., and Logvinenko, K. B. ((1986). ). Multiple fates of newly synthesized neurofilament proteins: evidence for a stationary neurofilament network distributed non-uniformly along axons of retinal ganglion cells. J. Cell Biol. 102, , 647-659.
Ochs, S. ((1975). ). A unitary concept of axoplasmic transport based on the transport filament hypothesis. In: Recent Advances in Myology: Proceedings of the Third International Congress on Muscle Diseases, ed. W. G. Bradley, D. Gardner-Medwin, and J. N. Walton, Amsterdam: Excerpta Medica, 189-194.
Press, W. H., Flannery, B. P., Teukolsky, S. A., and Vetterling, W. T. ((1992). ). Numerical Recipes in Fortran, New York: Cambridge University Press.
