Nerve cells (also known as neurons) connect with each other to form complex networks through which signals are carried around the body. Signals are received by branch-like projections called dendrites, pass through the cell body and then pass along a long projection called the axon before being transmitted to the dendrites of neighboring neurons.

In animal embryos, immature neurons in part of the brain called the hippocampus – which is crucial for learning and forming memories – develop into mature neurons through a series of steps. In the early stages of development, an immature neuron sends out multiple projections that extend out in all directions from its cell body. These projections randomly retract and lengthen for a while before a single projection grows into an axon and the others become dendrites.

It is believed that signal proteins inside the neuron that promote the formation of an axon selectively accumulate in a projection as it grows into an axon. These axon-promoting proteins are carried to the axons by a motor protein called kinesin, which moves along fibers called microtubules. In immature neurons, kinesin motors randomly move in and out of different projections, before settling in the projection that will grow into the axon. However, it is not clear what drives these fluctuations.

To address this question, Winans et al. used microscopy to study the transport of axon-promoting proteins in hippocampal neurons. The experiments show that a protein called actin forms a mesh of filaments in a wave-like manner, starting in the cell body and moving outwards into the projections. When a wave of actin reaches a projection, the projection grows for a while and then stops until the next actin wave arrives. Furthermore, the actin waves promote the formation of more microtubule filaments.

This work shows that actin waves make the projections wider to create space for more microtubules to form, which increases the transport of axon-promoting proteins to the projections. Winans et al.’s findings suggest that actin waves direct axon-promoting proteins to axons and promote competition between the projections early on by generating random fluctuations that allow all the projections to grow and retract. This would allow each projection to explore its environment in the search for signals that promote axon growth. The next challenge is to understand how different signals select the “winning axon”.

During development, hippocampal neurons transit through a multi-polar intermediate state in which neurons typically extend 4–5 immature neurites, which are each capable of becoming either an axon or a dendrite (Barnes and Polleux, 2009; Dotti et al., 1988). These neurites stochastically retract and elongate for a period of hours to days before a single neurite is specified as the axon (Figure 1a). This delayed axon specification is typically mediated by extracellular cues such as soluble growth factors, neighboring cells, and the extracellular matrix (Arimura and Kaibuchi, 2007; Barnes and Polleux, 2009) or in vitro by stochastic extension and stabilization of the longest single neurite (Dotti et al., 1988). Previous studies showed that axon specification is based on a competition between “axon-promoting” signals such as Ras, Phosphatidylinositol-4,5-bisphosphate 3-kinase (PI3K), and Protein Kinase A (PKA) and “axon-inhibiting” signals such as Glycogen synthase kinase 3 beta (GSK3β) and Protein Kinase G (PKG) (Barnes and Polleux, 2009; Shelly et al., 2010). It is believed that these signals are controlled by the selective accumulation of axon-promoting proteins in the nascent axon via microtubule-based transport involving one or more self-reinforcing positive feedback loops (Figure 1a) (Cheng et al., 2011; Fivaz et al., 2008; Inagaki et al., 2001; Shi et al., 2003; Toriyama et al., 2006). During the multi-polar state, however, pro-axon components appear to dynamically shuttle collectively to and from different neurites through an unknown mechanism (Figure 1a), a process that has been investigated using a constitutively active version of the microtubule motor Kinesin-1 (a.a. 1–560, CA-KIF5C) (Hammond et al., 2010; Jacobson et al., 2006; Konishi and Setou, 2009; Toriyama et al., 2010). Kinesin-1 carries numerous proteins known to promote axon formation such as CRMP2 (Kimura et al., 2005) and WAVE/Sra (Kawano et al., 2005), and perturbing Kinesin-1 expression or localization inhibits single axon formation (Konishi and Setou, 2009). There is also evidence that the Kinesin-1 adaptor protein c-Jun N-terminal kinase-interacting protein-1 (JIP1) (Dajas-Bailador et al., 2008) and the PI3K interactor Shootin1 (Toriyama et al., 2006, 2010) also relocalizes from one neurite to another before settling in the nascent axon. A similar dynamic collective relocalization of this kinesin motor domain has also been observed in vivo in developing neurons expressing CA-KIF5C (Randlett et al., 2011). What drives these fluctuations is a fundamental open question, as the number, orientation, or age of microtubules may play a role, and conflicting studies suggest that Kinesin-1 may preferentially bind microtubules that are stable (Cai et al., 2009; Hammond et al., 2010; Konishi and Setou, 2009; Reed et al., 2006) or newly polymerized (Nakata et al., 2011; Valesoq et al., 1994). These results regarding microtubule-based transport may also be related to an earlier observation that bulk cytoplasmic flow precedes axon specification (Bradke and Dotti, 1997).

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Here we show that actin waves, growth-cone-like cytoskeletal structures, promote anterograde microtubule and kinesin-based transport during the multi-polar state of symmetry breaking. Previous observations of actin waves showed that they are triggered stochastically, linked to neurite outgrowth and axon specification, more prevalent in early neurons compared to mature neurons, and found in cultured organotypic slices as well as primary hippocampal neurons (Flynn et al., 2009; Katsuno et al., 2015; Ruthel and Banker, 1998, 1999). It has been suggested that they constitute a transport mechanism that brings actin and actin associated proteins towards growth cones (Flynn et al., 2009; Katsuno et al., 2015). Our study shows that actin waves act in concert with microtubules to direct microtubule-based transport and that these discrete transport events are tightly linked to neurite outgrowth during the multi-polar state before an axon is specified.

To investigate the role of actin waves in neuronal polarity, we first characterized actin waves in our in vitro system. Consistent with previous studies of cultured hippocampal neurons extracted from embryonic rat brains (Ruthel and Banker, 1998, 1999; Flynn et al., 2009; Katsuno et al., 2015) actin waves are clearly visible in all neurons and neurites that bear actively growing processes (Video 1), and travel nearly exclusively in an anterograde fashion, from cell body to growth cone (Video 1, 2) during our DIV1 imaging window. Actin waves are generated at a median frequency of 1–2 actin waves per hour (Figure 1—figure supplement 1), move at average speeds of 2–3 µm/min (Figure 1—figure supplement 2), and morphologically resemble growth cones (Figure 1b,c). Structured illumination microscopy (SIM) revealed that actin waves are a mix of lamellipodial and filopodial structures that project outward from the neurite shaft, mainly contained to the x-y plane (Figure 1c). After an actin wave impacts the neurite tip, the neurite undergoes a growth spurt that often lasts until the growth cone shrinks (Figure 1d, e). Afterwards, the neurite often does not grow outwards again until the arrival of an additional actin wave reactivates the growth cone. Kymographs of actin intensity paired with neurite length over time illustrate the tight correlation between neurite outgrowth and actin wave arrival (Figure 1d). In fact, roughly 90% of neurite outgrowth in the DIV1 window is clearly concomitant with actin wave arrival (Video 1). Later stage imaging (DIV2+) displays greater neurite outgrowth in the absence of actin waves (data not shown). We further noted that actin waves entered different neurites at different times in an apparently stochastic fashion without an obvious pattern or frequency (Figure 1f). For the majority of live cell images in this study, fluorescently-tagged F-tractin (Johnson and Schell, 2009) is used as a marker for f-actin, although actin waves can also be observed with only a membrane marker (Video 3) as well. Together with previous findings, our results strongly support the hypothesis that actin waves have a role in promoting the stochastic fluctuations in neurite length observed during the multi-polar phase of symmetry breaking.

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Actin waves are linked to increased microtubule polymerization and increased microtubule based transport

We first hypothesized that actin waves may link to microtubules after observing an increase in neurite volume, or cross-sectional area, in and behind the actin wave (Figure 2a), which was confirmed with averaged line scan analysis (Figure 2b, Figure 2—figure supplement 1). Immunofluorescence experiments staining for neuronal tubulin revealed an increase in microtubule intensity in and behind actin waves (Figure 2c), which was confirmed by structured illumination microscopy (SIM) of single microtubules (Figure 2e) and using averaged line scans of lower-resolution immunofluorescence images (Figure 2d). As a control, we confirmed using lower-resolution IF (Figure 2f) and SIM (Figure 2—figure supplement 2) that the increases in tubulin levels behind versus in front of an actin wave are not the result of a gradual thickening of neurite shafts closer to the cell body (microtubule number ratio in Figure 2—figure supplement 2 is statistically greater than control measurements in Figure 2f).

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We then set out to find the source of the increased microtubule number in and behind actin waves and tested the hypothesis that actin waves contain more polymerizing microtubules by imaging neurons that co-express F-tractin and fluorescently-tagged EB1, which binds to the plus ends of growing microtubules. Indeed, live cell imaging of F-tractin and EB1 revealed an increase in the number of EB1 puncta within and behind actin waves, with much lower levels of EB1 puncta in front of the wave (Figure 2g, Figure 9b). This enrichment in the number of polymerizing microtubules progresses down the neurite with the actin wave, creating a dual wave of polymerizing microtubules and polymerizing actin. Control experiments using a maximum intensity projection of time lapse images showed that single EB1 puncta moved in a persistent fashion outward, confirming that they track with anterograde polarized polymerizing microtubules (Figure 2—figure supplement 3), consistent with previous measurements showing that microtubules generally polymerize outward during the multi-polar phase (Stepanova et al., 2003).

This striking co-localization of polymerizing actin and increased microtubule polymerization prompted us to investigate the correlation between actin waves and microtubule-based transport by using the minimal Kinesin 1 motor domain construct (CA-KIF5C-Venus; a.a. 1–560, adapted from Jacobson et al. (2006)). The attachment and movement of this motor domain to microtubules is not regulated by conformational changes and is constitutively active (Friedman and Vale, 1999). The mechanisms controlling the dynamic localization pattern of CA-KIF5C during symmetry breaking have previously been investigated, and the dynamic, stochastic nature of actin wave entry into various neurites struck us as reminiscent of the dynamic localization of CA-KIF5C. We first confirmed that the Kinesin-1 motor, CA-KIF5C, is often enriched at the tip of one or sometimes more neurites (Jacobson et al., 2006) during the multipolar phase (Figure 3a). We also confirmed dynamic switching of the localization of CA-KIF5C back and forth between one or more neurites via the cell body over a period of many hours until most of the construct ultimately localizes to the emerging axon (Video 4).

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Next, we determined whether the stochastic appearance of actin waves in neurites is temporally correlated with that of CA-KIF5C. We marked the time when actin waves entered neurites by visual inspection and averaged the time course of change in total CA-KIF5C intensity in the neurite receiving the actin wave. This analysis showed in the same neurite a marked increase in CA-KIF5C over a period of over 10 min following an actin wave (Figure 3b). Moreover, we found that when CA-KIF5C entered a neurite previously lacking CA-KIF5C, such entry events occurred in parallel with an actin wave (in 34 out of 35 entry events). We then assessed the time lag (if any) between the increases of actin and CA-KIF5C signals during CA-KIF5C entry events and found that the increase in actin intensity preceded the increase in CA-KIF5C intensity by several minutes (Figure 3c). To address the concern that the co-localization of actin waves and CA-KIF5C entry into neurites may be an artifact of a cytoplasmic fraction of CA-KIF5C, we imaged CA-KIF5C moving in and out of neurites in neurons also expressing a cytoplasmic Turquoise fluorescent protein. Taking the ratio of CA-KIF5C over the Turquoise volume marker shows that the movement of CA-KIF5C into and out of neurites is significant over changes in volume; moreover, addition of the microtubule polymerization inhibitor Nocodazole eliminates the movement of CA-KIF5C into and out of neurites relative to a volume marker, confirming that CA-KIF5C movement is dependent on microtubules (Figure 3—figure supplement 1).

In a parallel analysis of the spatial correlation between actin polymerization and CA-KIF5C, we found that CA-KIF5C was transported in pulses, or waves, along the neurite shaft to the growth cone, coincident with actin waves (Figure 3d, Figure 3—figure supplement 2, Video 5). We confirmed this correlation using single cell analysis (Figure 3e), averaged line traces (Figure 3f), and kymographs (Figure 3g). Most of the pulses of CA-KIF5C arriving at growth cones resulted in an increase in CA-KIF5C concentration that persisted for tens of minutes (Figure 3g). Moreover, the arrival of an actin wave can reverse the retrograde movement of CA-KIF5C out of the neurite (Figure 3—figure supplement 3). Taken as a whole, this data shows a strong connection between CA-KIF5C movement and actin waves.

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To further verify an increase in microtubule-based transport in actin waves, we expressed fluorescently-tagged Synaptophysin, a pre-synaptic vesicle marker, in order to image vesicular movement. Similar to CA-KIF5C localization, Synaptophysin-positive vesicles were highly enriched in and behind actin waves (Figure 4a). Averaged line scans of intensity profiles of only moving vesicles (Moving Vesicle Intensity (MVI)) showed the same results (Figure 4b see Materials and methods). Higher frequency imaging showed that Synaptophysin-positive vesicles enriched in the actin waves were not subject to the Brownian motion suggesting that they remain attached to microtubules (Video 6). Taken as a whole, this data suggests a strong correlation between actin waves, increased microtubule polymerization, and increased microtubule based transport.

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Actin waves may spatially de-restrict microtubule polymerization to increase microtubule-based transport

We next examined whether the striking connection between actin waves, microtubule polymerization and microtubule-based transport are causal. We first probed the potential role of actin waves in promoting microtubule polymerization and microtubule-based transport by examining both microtubule polymerization and microtubule-based transport after the addition of Jasplakinolide, an actin-stabilizing agent that stalls the progression of actin waves. We found that stalling actin waves halted the progression of CA-KIF5C (Figure 5a,b) as well as the progression of the wave of polymerizing microtubules (Figure 5c,d), suggesting that progression of actin waves was necessary in order to continue the forward progression of the other two components. Notably, EB1 comets were still observed in the stalled actin wave, suggesting that although microtubules were still polymerizing in the actin waves, they were unable to polymerize beyond the structural bottleneck present at the front of the actin wave. This observation suggests that a mechanical mechanism may, at least partially, drive the increase in microtubule polymerization observed in the actin wave, and may explain the conundrum presented by the discrepant speeds of the components moving along with actin waves. More precisely, vesicular transport and Kinesin motors both advance at a speed of ~50 μm/min along microtubules while actin waves only advance at a speed of ~ 2 μm/min (Figure 1—figure supplement 2). This raises important mechanistic questions of why Kinesin motors and vesicles have a net progression that is much slower than their molecular transport rate, why motors and vesicles appear to be restrained behind the leading edge of actin waves, and why vesicular transport stays elevated in and behind an actin wave (Figure 4a).

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To answer these discrepancies, we speculated that the bottleneck at the front of the actin wave restrains the movement of polymerizing microtubules and microtubule-based transport, and that the dilation of the neurite shaft caused by the actin wave may spatially de-restrict microtubules and allow more room for microtubules to polymerize towards the growth cone. In this hypothesis, the increase in the number of microtubules could enhance the flux of microtubule-based transport through the neurite. Another motivation for this hypothesis was that the speed of microtubule polymerization is ~10x faster than the speed of actin waves (in neurite: 20.4 +/- 5.4 um/min (39 measurements) in wave: 16.8 +/- 5.4 (23 measurements)), which is consistent with previously measured microtubule polymerization rates (Stepanova et al., 2003). Thus, in order for the wave of EB1 puncta to advance at the same speed as the actin wave, individual EB1 puncta must stall and disappear at the leading edge of the actin wave, similar to what we see when a polymerizing microtubule hits the membrane of the neurite tip (Figure 6a, left). Indeed, kymograph analysis of EB1 comets moving through the bottleneck of the actin wave revealed that EB1 comets disappear at the bottleneck (Figure 6a, right). As a separate experiment, we quantifiedthe flow of EB1 puncta through two windows placed right before and right after the bottleneck (but within 6 μm of each other) at time points 100 s apart which showed the same marked difference consistent with a loss of EB1 comets in between. In control experiments, we observed that the flow through each window does not significantly change over the time window measured, suggesting that microtubule polymerization is at a steady state over short time periods (Figure 6b). Also, the difference between the flow of EB1 puncta through the two windows does not change over time (Figure 6—figure supplement 1). Thus, the larger flow of polymerizing microtubules through the window closer to the cell body does not reach the second window ahead of the actin wave, suggesting EB1 puncta disappear between the two windows. To understand this result, it is helpful to again consider that processive EB1 puncta should move 25–30 μm in approximately 100 s, much faster than the actin waves. We also measured EB1 puncta flow versus neurite width in a smooth neurite or within an actin wave which reveals a correlation between neurite width and the number of EB1 puncta (Figure 6c). The lack of a pronounced higher number of EB1 puncta per unit area in actin waves relative to smooth neurites suggests that the mechanism by which actin waves promote microtubule polymerization is mainly steric, although this does not rule out other signaling cross-talks between the two cytoskeletal components. Furthermore, as for microtubule polymerization, the number of microtubules present also correlates with neurite width, as shown by SIM (Figure 6d).

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Consistent with an expected role for Rac-regulated actin polymerization in generating actin waves, we used a Raichu FRET reporter (Komatsu et al., 2011) and found high Rac activity in and around actin waves. Interestingly, we also used a Cdc42 Raichu FRET reporter and observed that only Cdc42 exhibited a relatively higher activity in front of the actin wave, suggesting that the consistent anterograde direction of actin waves propagation may in part be directed by Cdc42 (Figure 7a,b). To directly investigate the dependence of microtubule polymerization on actin waves, we used a photo-activatable Rac1 construct designed by the Hahn laboratory to test whether Rac activity is sufficient to generate actin waves (Wu et al., 2009). This approach led to the successful generation of either fully processive (5 times) or partially processive (5 times) actin waves during successful Rac1 activations (18 times) using selective photo-excitation at the base of a neurite on a scanning confocal microscope (example in Figure 7c). The generated waves caused neurite widening (Figure 7—figure supplement 1) and increased numbers EB1 puncta (Figure 7d), consist with naturally-generated waves. This suggests that Rac1 activity is sufficient to initiate actin waves and to generate the enrichment of microtubule polymerization observed in actin wave.

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Positive feedback links actin waves and microtubules

Our data thus far has shown that the increases in microtubule polymerization is dependent on actin waves. We next investigated the corollary question of whether microtubules may also have a role in the advancement of actin waves. Indeed, consistent with a previous study (Ruthel and Banker, 1998), we found that the addition of Nocodazole caused actin waves to dissolve (Figure 8a, b). We also found that the addition of a high dose of Taxol (50 nM), a small molecule that stabilizes microtubules, leads to non-processive bursts of actin polymerization, interfering with normal actin wave formation (Figure 8c). 50 nM Taxol also appears to affect microtubule polymerization (Figure 8—figure supplement 1), indicating that microtubule stabilization and/or an effect on microtubule polymerization may be affecting actin wave production. These drug studies argue for a co-dependence between actin waves and microtubules – one is needed to advance the other.

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Changes in microtubule polymerization and microtubule-based transport are transient

Finally, we measured how long the effect of enhanced microtubule polymerization and microtubule-based transport lasts. If such changes were long-lasting, we would expect that neurites would steadily thicken over time, which has not been previously observed. Also, our analysis of neurite growth over 10 hr time periods suggest that the growth promoting effect of an incoming actin waves is lost after tens of minutes (Figure 1d). To determine whether the induced microtubule polymerization persists after an actin wave, we imaged the number of EB1 puncta in a neurite segment before, during, and after actin waves (Figure 9a, top). Markedly, the EB1 puncta number increased along with an actin wave and persisted after the wave passed (Figure 9a, bottom; Figure 9b), in agreement with our analysis of the persistence of the spatial profiles of Synaptophysin, volume, and microtubule enrichment. We then generated kymographs of actin intensity, EB1 intensity, and neurite width in a single section of neurite with multiple actin waves (Figure 9c). The kymographs reveal simultaneous increases in EB1 intensity and neurite width that remained past the passage of the actin wave, but gradually decayed with variable timescales (Figure 9c, Video 7). The transient nature of the increases in microtubule polymerization and microtubule-based transport was confirmed using a kymograph analysis of Synaptophysin vesicles in a neurite containing actin waves (Figure 9d, Video 8). Thus, our data as a whole suggests that each actin wave, by creating a transient increase in neurite width, creates a burst of microtubule polymerization and microtubule-based transport that will eventually decay after approximately 30 min and neurites will start to retract (Figure 1d, Figure 10a). The transient characteristic of the increase in transport explains the frequent neurite retractions and the necessity of frequent actin waves to continually deliver cargo to a single growth cone to maintain and elongate the neurite and ultimately allow one of the neurites to dominate and become the axon.

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Our study argues that developing neurons employ an interlinked cytoskeletal system whereby actin waves cross-talk with microtubules to direct microtubule-based transport and drive neurite extension. More broadly, our study suggests that the stochastic nature of actin waves leads to the stochastic increase of microtubule-based transport paired with growth cone extension in different neurites thereby creating the dynamic multi-polar state that allows a search for external cues and ultimately enables single axon formation. In particular, we show that the fluctuating actin waves control the previously observed pulsatile anterograde Kinesin transport generated during the multi-polar phase of symmetry breaking. We discovered that the link from actin wave to Kinesin-mediated transport appears to be based on a mechanical control mechanism whereby actin waves widen the neurite shaft and create the space needed for more microtubules to polymerize. The increase in microtubule polymerization in turn increases microtubule number and vesicular microtubule-based transport. In addition, these morphological changes and consequent changes in microtubule-based transport are transient, resulting in the pulsatile delivery of cargo to the growth cone and necessitating the generation of frequent actin waves in order to continue to deliver axon-promoting factors into the neurite. Finally, the results of our pharmacological perturbation of microtubules suggest that, in fact, actin waves and microtubules co-regulate each other through a positive feedback mechanism, potentially mediated by cross-talk mechanisms that have been identified in other systems (Akhshi et al., 2014).

In combination with studies in other systems, our results suggest that mechanical regulation is a major avenue of crosstalk from the actin cytoskeleton to microtubule growth during neurite outgrowth. Consistent with this finding, it has also been shown that depolymerizing actin in growth cones spatially de-restricts microtubule polymerization, thus promoting neurite growth (Bradke and Dotti, 1999). A later study further found that ADF/cofilin, an actin severing enzyme, promotes neuritogenesis by disassembling the actin meshwork at the cortex, allowing for microtubule polymerization to promote a new protrusion (Flynn et al., 2012). In conjunction with these previous studies, our results argue that the actin cortex structurally inhibits microtubule extension, and that a stent-like broadening of the neurite shaft or other mechanisms to “loosen” the actin cortex, by actin waves or other processes, relieves this inhibition to enable more microtubules to extend forward.

In the context of neuron polarization, the stochastic nature of actin waves allows each neurite to repeatedly grow and retract thereby allowing the growth cone of each neurite to spatially explore its local environment to find external axon-promoting inputs (e.g. Arimura and Kaibuchi, 2007). When receiving sufficient input, signaling in one of the neurites is expected to be strengthened and the neurite is marked as the future axon. Such a specification of one neurite as the axon is known to subsequently inhibit axonal maturation of the other neurites and convert them to dendrites (Esch et al., 1999; Ménager et al., 2004; Shelly et al., 2010). Together with these previous considerations, our study argues that actin waves have a dual function. First, they are the drivers for neurite outgrowth by directing microtubule-based transport to deliver axon-promoting factors to the growth cones at the neurite tip. Second, they promote competition between neurites by generating large stochastic fluctuations that allow each neurite to sample “winning” and “losing” states as they explore their surroundings for the cues that will ultimately determine axon specification.

Our study does not directly address the role of actin waves in in vivo symmetry breaking and single axon formation. However, imaging of later stage polarized neurons in culture showed that actin waves still move through the nascent dendrites and the axon, but their effect on neurite outgrowth appears to be smaller (Video 9). This suggests that actin waves may become less important after polarization. With respect to their in vivo relevance, actin waves have been observed in hippocampal and cortical neurons in slice cultures (Flynn et al., 2009; Katsuno et al., 2015), although whether they promote microtubule polymerization and transport is more difficult to explore in this setting. Nevertheless, the results of our study suggest that actin waves could play an equally important role in neurite extension in vivo, to allow neurites to properly sense the polarized growth cues provided by the developing brain.

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Together, our study provides a key missing link in our understanding of the axonal symmetry breaking process by demonstrating that the multi-polar state is characterized by actin waves driving microtubule-based transport, a link that we show is likely generated by an actin wave-triggered stent-like dilation of the neurite shaft. Our study further argues that the stochastic nature of actin waves creates the previously described stochastically fluctuating microtubule-based transport events during the multi-polar state. Thus actin waves may play a critical role in a stochastic search mechanism that allows a set of neurites to explore the surrounding space, integrate external signaling cues, and measure relative input differences to select the a “winning” axon.

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Author details

1. Amy M Winans

   1. Biophysics Program, Stanford University, Stanford, United States
   2. Department of Chemical and Systems Biology, Stanford University, Stanford, United States
   3. Center for Systems Biology, Stanford University, Stanford, United States

   Contribution

   AMW, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

2. Sean R Collins

   1. Department of Chemical and Systems Biology, Stanford University, Stanford, United States
   2. Center for Systems Biology, Stanford University, Stanford, United States

   Present address

   Department of Microbiology and Molecular Genetics, University of California, Davis, Davis, United States

   Contribution

   SRC, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   Competing interests

   The authors declare that no competing interests exist.

3. Tobias Meyer

   1. Department of Chemical and Systems Biology, Stanford University, Stanford, United States
   2. Center for Systems Biology, Stanford University, Stanford, United States

   Contribution

   TM, Conception and design, Analysis and interpretation of data, Drafting or revising the article

   For correspondence

   tobias1@stanford.edu

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0003-4339-3804

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