Insulin secretion in pancreatic β-cells is tightly regulated and highly heterogeneous. The major stimulator for secretion is glucose, with other nutritional and neuronal signals modulating the response. The prevailing view is that glucose influx results in increased glucose metabolism, higher levels of the cytoplasmic ATP/ADP ratio, and increased levels of metabolite intermediates. The increased ATP/ADP ratio results in the closure of K_ATP channels, β-cell depolarization, and Ca²⁺ influx that triggers vesicular-cell membrane fusion. Metabolite intermediates promote secretion via known (e.g., microtubule [MT]-dependent vesicular biogenesis, movement, and docking) and unknown mechanisms. Intriguingly, β-cells secrete on the order of tens of granules per cell in response to each round of high-glucose stimulus, which last for hours, despite having thousands of available granules (Dean, 1973; Olofsson et al., 2002; Rorsman and Renström, 2003). Glucose-stimulated insulin secretion (GSIS) has characteristic bi-phasic kinetics with a rapid, high peak within minutes after the stimulation (first phase) followed by a sharp decrease and a slow, lower secreting second phase. The mechanisms underlying this timing are believed to be associated with the availability of secretion-ready insulin vesicles, the pool size of which does not depend on changes in Ca²⁺ levels (Gaisano, 2017).

An intriguing property of β-cells is their heterogeneity in morphology, biochemical features, and function (Miranda et al., 2021 and references therein). Accordingly, β-cells have been found to display different metabolic properties (Van De Winkel and Pipeleers, 1983; Kiekens et al., 1992; Van Schravendijk et al., 1992; Giordano et al., 1993), Ca²⁺ influx kinetics (Zhang et al., 2003), proliferation rate (Bader et al., 2016), stress responses (Dorrell et al., 2016; Johnston et al., 2016; Farashi et al., 2018; Lei et al., 2018), expression of some key function- (Jetton and Magnuson, 1992) or marker-genes (Dorrell et al., 2016), and insulin secretion (Giordano et al., 1991; Van Schravendijk et al., 1992; Wojtusciszyn et al., 2008). Such heterogeneous properties are considered important, because different β-cell subsets could contribute to different physiological needs (Hoang Do and Thorn, 2015).

Several mechanisms have been proposed to explain β-cell heterogeneity. For example, it has been proposed that β-cell heterogeneity can result from differences in age, disease state, and location within the islet (Dean and Matthews, 1970; Stefan et al., 1987; Ballian and Brunicardi, 2007; Aguayo-Mazzucato et al., 2017; Gutierrez et al., 2017; Pipeleers et al., 2017). Specifically, β-cell age/disease states can affect gene expression, vesicle maturity, and glucose metabolic flux (Blum et al., 2012; Aguayo-Mazzucato et al., 2017; Zeng et al., 2017; Huang et al., 2018). Specific locations in islets can result in differential cross talk with other islet cell subtypes (Efendić and Luft, 1975; Pipeleers et al., 1982; Wojtusciszyn et al., 2008; van der Meulen et al., 2015) and with vasculature (Ballian and Brunicardi, 2007; Low et al., 2014). However, heterogeneous GSIS is maintained in dissociated single cells (Wojtusciszyn et al., 2008) and in adults when most β-cells are mature (Li et al., 2011; Hoang Do and Thorn, 2015; Dwulet et al., 2021). In this regard, approximately 25% of adult β-cells remain unresponsive regardless of the glucose concentration (Hoang Do and Thorn, 2015). More importantly, islet β-cells show the near-uniform glucose- or depolarization-induced Ca²⁺ influx, despite of the lack of uniform insulin secretion (Li et al., 2011; Dwulet et al., 2021). These findings indicate that the currently proposed mechanisms cannot fully explain β-cell heterogeneity and are consistent with a possibility that different β-cells may have different numbers of Ca²⁺-responsive insulin granules, contributing to their unique GSIS responses.

In addition to secretory heterogeneity in the β-cell population, uneven distribution of secretion has been also observed at subcellular levels. Designation of insulin secretion to specialized loci at the cell membrane has been shown to be essential for the pathophysiology of type 2 diabetes (Fu et al., 2019). The sites of preferential insulin secretion depend on the cellular location of L-type voltage-dependent Ca²⁺ channels (VDCCs) in combination with molecular tethers and other exocytotic proteins (Bokvist et al., 1995; Ohara-Imaizumi et al., 2019a). This molecular machinery resembles the composition of ‘active zones’ or areas of high exocytosis in neurons (Garner et al., 2000) and is thought to underlie the hot spots of secretion at the plasma membrane (Landis et al., 1988). Interestingly, some major components of the hot spot machinery (e.g., ELKS) are assembled at the membrane in response to integrin activation by vascular extracellular matrix (ECM) proteins such as laminin (Hotta et al., 2010; Nishimune, 2012), and in islets they are preferentially found at sites of β-cell contact with the vasculature (Ohara-Imaizumi et al., 2005; Low et al., 2014). However, as most β-cells in an in-situ islet have discrete points of contact with the capillaries (Low et al., 2014), it is clear that positioning and ECM-dependent activation of secretion hot spots is insufficient for the differences in secretion activity of individual cells. Thus, despite a significant progress toward the understanding of β-cell heterogeneity, some key cellular mechanisms underling their functional differences in islets are still unknown.

Previously, we have shown that the secretion capacity of β-cells is regulated by the MT cytoskeleton, which is uniquely structured to help tune β-cell function (Zhu et al., 2015). Unlike in many other cell types, MTs in β-cells do not radiate from a central point in the cell, and instead form a dense mesh-like network (Zhu et al., 2015; Trogden et al., 2019; Bracey et al., 2020). This network configuration is, to a large extent, due to the fact that most MTs in β-cells originate at the Golgi apparatus (Zhu et al., 2015; Trogden et al., 2019). The large surface area of the Golgi acts as an MT organizing center (MTOC), leading to an unusual non-radial MT network appearance. Intriguingly, optimal β-cell function depends on a finely tuned balance of MT assembly and disassembly, which can both promote and restrict secretion capacity of a cell. On the one hand, Golgi-derived MTs function aids the budding of new insulin granules from the Golgi (Trogden et al., 2019). High glucose stimuli lead to an increase in Golgi-derived MT nucleation, which is necessary to replenish insulin granule content after a secretion pulse (Zhu et al., 2015; Trogden et al., 2019). Long-term loss of this MT subpopulation causes degranulation of the β-cell as vesicle budding is less efficient (Trogden et al., 2019). Thus, glucose-dependent MT nucleation is a critical factor supporting the capacity of β-cells to secrete. On the other hand, MTs act to prevent over-secretion in functional β-cells, which contain excessive amounts of insulin granules (Zhu et al., 2015). This function relies on the configuration of MT networks in β-cells, where the non-radial mesh in the cell interior prevents directional granule movement, and the extremely stable MT bundles extending along the plasma membrane serve as tracks for granule withdrawal from docking sites (Bracey et al., 2020). Upon glucose stimulation, these pre-existing MTs are destabilized and partially depolymerized (Ho et al., 2020), allowing for release of a subset of granules. This regulated dynamicity of the MT network is vital for the dosage of GSIS at each stimulus: loss of all MTs acutely leads to over-secretion, while hyper-stabilization of MTs greatly suppresses it (Lacy et al., 1972; Howell et al., 1982; Hill and Rhoten, 1983; Zhu et al., 2015). These effects are only seen after GSIS stimulation but not at basal glucose conditions, indicating the leading role for other mechanisms in secretion triggering (Zhu et al., 2015; Trogden et al., 2019). In functional β-cells, which are able to secrete in response to a glucose stimulus, the effects of MT destabilization are finely tuned because simultaneous increase in MT nucleation promptly replaces depolymerizing MTs (Zhu et al., 2015). The intriguing combination of positive (long-term) and negative (short-term) MT regulation of secretion may be responsible for the early controversy on the role of MTs in insulin secretion (Lacy et al., 1968; Lacy et al., 1972; Malaisse et al., 1974; Howell et al., 1982; Hill and Rhoten, 1983; Mourad et al., 2011). It also makes the MT cytoskeleton a candidate for differential control of secretory activity, which acts in concert with other regulatory mechanisms to underlie functional β-cell heterogeneity.

In this study, we investigate the role of the MT cytoskeleton in β-cells as a factor in the differential secretory response of β-cells to glucose stimulation. Our computational analysis of insulin secretion toward the vascular ECM at the single-cell level in whole islets shows that this regulation occurs via secretion hot spot activity. Our findings indicate that the presence of stable MTs attenuates initiation of secretion hot spots in both otherwise dormant and already active β-cells, thus contributing to functional heterogeneity of insulin secretion. We also show that MTs regulate the timing of insulin secretion by restricting hot spot activity to the first phase of GSIS.

It has been known for over six decades that islet β-cells, from both rodent models and human donar islets, can be divided into different subpopulations with different gene expression, morphology, and GSIS activities (Miranda et al., 2021). The functional β-cell heterogeneity, established via hemolytic plaque assays (Salomon and Meda, 1986; Bosco et al., 1995; Katsuta et al., 2012) or real-time secretion assays (Li et al., 2011; Hoang Do and Thorn, 2015) is particularly intriguing because it was proposed to be important for an adaptable, efficient response to various changes in physiological conditions and is one of the parameters that dramatically changes in diabetes (Aguayo-Mazzucato et al., 2017; Gutierrez et al., 2017). Mechanism-wise, it has been proposed that β-cell heterogeneity can result from differences in β-cell age, disease state, β-cell maturity, and location within the islet or association with other islet cell types (Dean and Matthews, 1970; Efendić and Luft, 1975; Pipeleers et al., 1982; Stefan et al., 1987; Ballian and Brunicardi, 2007; Wojtusciszyn et al., 2008; van der Meulen et al., 2015; Aguayo-Mazzucato et al., 2017; Gutierrez et al., 2017; Pipeleers et al., 2017) and to vasculature (Ballian and Brunicardi, 2007; Low et al., 2014). Yet, these studies do not fully explain why similar levels of Ca²⁺ influx cannot induce similar insulin secretion from different β-cells.

In this study, we have evaluated the role of the MT cytoskeleton in influencing the spatial distribution and heterogeneity of insulin secretion events both at the level of pancreatic β-cell populations and sub-plasma membrane regions. Our data indicate that MT stability in the β-cell population is heterogeneous and that this heterogeneity is a contributing factor to the previously established heterogeneity of insulin response. We also show that the loss of MTs causes initiation of additional insulin secretion: (1) activation of hot spots in a higher fraction of cells, (2) increase in the number of hot spots in active cells, and (3) broadens the timing of secretion from the hot spots in the first phase of GSIS. Stabilizing MTs prevents GSIS so that all parameters are indistinguishable from basal secretion levels. Importantly, MT-dependent regulation of hot spots acts in parallel to glucose-induced Ca²⁺ influx, rather than in the same pathway.

There are a number of advantages to the approach utilized in this paper. It is important to measure the spatiotemporal distribution of secretion from individual β-cells in its natural environment in the whole islet with intact cell-to-cell contacts and a proper basement membrane. High-resolution detection of secretion event distribution over the surface of the plasma membrane is a challenging task. While secretion detection in whole islets has been successfully achieved by two-photon microscopy (Takahashi et al., 2002; Low et al., 2014), this method does not allow for high time resolution and for registration of secretion hot spots over the plasma membrane due to its complex topography. Furthermore, it is very labor-intensive and the number of examined samples is very limited. In contrast, TIRF microscopy with β-cells secreting toward the glass coverslip (Nagamatsu and Ohara-Imaizumi, 2008; Loder et al., 2013) allows for rapid imaging in the plasma membrane focal plane. The major challenge is the rapidly compromised responsiveness to glucose characteristic for whole-mount islets plated on glass. To our advantage, it has become clear that ECM signaling through integrin-dependent Ca²⁺ channel activity is critical for the preservation of correctly patterned secretion (Gan et al., 2018; Ohara-Imaizumi et al., 2019b). Our approach of culturing whole-mount islets on vascular ECM preserves the functionality of β-cells (Patterson et al., 2000; Zhu et al., 2015), supporting the idea that the signals downstream of integrins are vital to preserving β-cell identity (Gan et al., 2018). TIRF microscopy in this system allows us to register single secretion events associated with their physiological organizer—the vascular ECM. Thus, this experimental model allows for the evaluation of the secretion patterning arranged by vascular cues, and at the same time, analysis of individual β-cell responses as they maintain their connections with each other and other islet cell types. An additional advantage of our approach is that utilization of FluoZin-3 dye provides direct information of precise insulin secretion time and location without the need for genetically encoded markers of insulin.

One important conclusion from our study is that MT stability varies in the β-cell population. The mechanistic basis of the differences in MT stability between β-cells is yet unclear. For example, since MTs are sensitive to Ca²⁺ (Hepler, 2016), MT stability might be modified by the Ca²⁺ influx wave, which is thought to contribute to spatial and temporal differences in β-cell response to stimulation (Benninger et al., 2014). However, we have recently shown that blocking Ca²⁺ influx by verapamil does not prevent glucose-induced changes in MT dynamics (Ho et al., 2020). Keeping also in mind the evidence that Ca²⁺ influx is insufficient to provide for secretion heterogeneity (Li et al., 2011), we suggest that MT differences are likely triggered by another mechanism. MT heterogeneity might be promoted by such factors involved in β-cell variability as cell maturity (Aguayo-Mazzucato et al., 2017; Gutierrez et al., 2017; Pipeleers et al., 2017), islet microenvironment (Trimble and Renold, 1981; Trimble et al., 1982; Brereton et al., 2015), and/or paracrine signaling from other islet cell types (Efendić and Luft, 1975; Pipeleers et al., 1982; Wojtusciszyn et al., 2008; van der Meulen et al., 2015). Interestingly, we have shown that glucokinase, an enzyme, which expression/activity is involved in promoting β-cell variability (Jetton and Magnuson, 1992, Heimberg et al., 1993), is important for MT network remodeling downstream of glucose (Ho et al., 2020). Thus, glucokinase variability could lead to heterogeneous MT stability in β-cells.

One possible important molecular player in this pathway could be the MT stabilizer tau, which we have recently found to be a critical component of glucose- and glucokinase-dependent MT remodeling, leading to efficient insulin release from β-cells (Ho et al., 2020). Other MT-stabilizing proteins found in β-cells, such as MAP2 and doublecortin, may also be involved (Krueger et al., 1997; Jiang et al., 2013). It is clear from our data that regardless of the source of MT heterogeneity, it is functioning to enhance the variability of β-cell secretion activity: pushing MTs toward uniform stability or uniform depolymerization makes β-cell secretion response more uniform in opposite directions. This role of MT heterogeneity in the regulation of variable β-cell response to stimulation is not entirely unexpected. The effect of heterogeneity of MT stability in cell populations has been described in other cell types and is implicated in the variability of cell function. For example, motile cells that have directionally stable MT arrays have an increased ability for migration in wound healing assays (Sugioka and Sawa, 2012). Heterogeneity of MT dynamics in neurons has been found to underlie the distinction between the axon and dendrites (Conde and Cáceres, 2009), neurite capacity for cargo movement (Franker and Hoogenraad, 2013), and modulation of local signaling and rearrangements in neuronal connectivity (Hoogenraad and Bradke, 2009). Now, our data add β-cells to the list of cell types where the differential MT stability plays an important role in cell physiology.

How do differential MT dynamics promote differential secretion? The first possibility is the direct MT regulation of insulin secretion, when differently organized MT networks differentially transport insulin granules within individual cells. This aligns well with the model supported by our previous findings (Zhu et al., 2015; Bracey et al., 2020), where stable MTs act as tracks for the withdrawal of insulin granules from the plasma membrane, restricting secretion. Lack of this regulated withdrawal should allow for the increased secretion at random locations. Indeed, this is what we observed: the increase of glucose-stimulated non-clustered events when MTs are absent (nocodazole treatment). However, we found that MTs most prominently regulate heterogeneity of β-cells responsiveness to glucose specifically via activation of secretion clusters, or hot spots. Such specific restriction of clustered secretion would be achieved by MT-dependent withdrawal if secretion-competent granules are specifically accumulated near the hot spots prior to the secretion stimulus by an additional mechanism. Alternatively, specific MT withdrawal from the secretion hot spots could result from local molecular motor activation and/or local organization of MT tracks at these cellular locations. In this regard, it is interesting that ELKS, a tether molecule involved in MT anchoring at the cell cortex in some cell types (Lansbergen et al., 2006), is specifically concentrated at secretion hot spots. While ELKS is likely involved in the regulation of insulin exocytosis (Ohara-Imaizumi et al., 2005; Ohara-Imaizumi et al., 2019b), it might also be a regulator of local MT anchoring at those sites.

It is important to integrate our understanding of MT function with prior accumulated knowledge on secretion hot spots regulation. Existing evidence indicates that loci of repeated clustered secretion involve membrane accumulation of K⁺ channels (Fu et al., 2019), VDCCs (Bokvist et al., 1995), as well as tethering and membrane fusion machinery (Ohara-Imaizumi et al., 2004; Ohara-Imaizumi et al., 2007). Accordingly, it is thought that the functioning of a hot spot includes insulin granule docking in preparation for secretion, ion channels to promote Ca²⁺ influx, and Ca²⁺-dependent membrane fusion. Our data indicate that MT depolymerization does not affect Ca²⁺ influx, and that acute Ca²⁺ influx stimulates secretion of readily releasable granules at hot spots regardless of MT presence, consistent with previous data (Mourad et al., 2011). Thus, Ca²⁺-dependent steps of secretion are not MT-dependent. In contrast, our previous findings show that insulin granule docking at the plasma membrane is regulated by MTs, because MT-dependent transport withdraws granules from the docking sites (Bracey et al., 2020). We propose a model (Figure 9A) where glucose signaling stimulates both insulin granule docking and Ca²⁺ influx, which are thought to be triggered via independent pathways (Gaisano, 2017). MT-dependent transport negatively regulates the process of docking, restricting the number of readily-releasable granules. Ca²⁺ influx, in turn, promotes secretion of docked granules, in an MT-independent manner. In the experimental setup, when secretion is stimulated by KCl, only pre-docked granules are released, and MT disruption does not have a significant effect (Figure 9B).

Figure 9

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An additional potential scenario is that dynamic MTs facilitate secretion at hot spots by coupling insulin exocytosis with compensatory endocytic events, as was shown for ELKS/LL5β patches in cultured Ins-1 cells (Yuan et al., 2015a). Another possibility is that MTs act indirectly by modulating one of the prominent mechanisms involved in β-cell heterogeneity regulation. Interestingly, such master regulators of heterogeneous β-cell response as gap junctions and ion channels have been shown to be modulated by MTs in other cell types (Shaw et al., 2007; Joseph et al., 2014).

Regardless of the mechanism, the important conclusion from our data is that it is the activation of hot spots in additional cells that makes the β-cell population response more uniform in the absence of MTs. Since Ca²⁺ is essential but likely insufficient for β-cell heterogeneity (Benninger and Hodson, 2018), it is possible that suppression of hot spot activity by stable MTs provides a required layer of control restricting secretion in a subpopulation of cells in the presence of Ca²⁺ influx. Furthermore, our finding that larger clusters secrete insulin at higher rates suggests a potential enhancement of secretion via a chemical (e.g., insulin signaling or ATP signals) or mechanical (e.g., in terms of membrane tension) feedback mechanism (Rodríguez-Iturbe et al., 2002; Saltiel and Pessin, 2003).

Another important take-home message from our analyses is that MTs regulate the timing of the first phase of GSIS via control of clustered secretion. We show that initiation of secretion hot spots that is normally rapidly triggered by the metabolic signal is dysregulated when MTs are lost, possibly due to the presence of excessive, unregulated readily-releasable granules. In the absence of MT regulation, new secretion sites continue to appear even at the time points when the first phase of secretion should normally be fading. This suggests a potential role for MTs in the decay of the first phase of GSIS, which could be a significant part of prevention of over secretion under physiological conditions. At the same time, MT-dependent regulation of random secretion applies to both stages of the bi-phasic GSIS. An extended first phase of secretion and enhanced secretion levels in both phases are consistent with our previous findings (Zhu et al., 2015).

At the same time, we do not find a significant role of MTs in the secretion dynamics within individual clusters. Our data clearly indicate that MTs do not affect the frequency of secretion events within clusters, which is at odds with a previous finding in KCl-stimulated Ins-1 cells plated on glass, where a decreased frequency of events within a cluster was observed in the absence of MTs (Yuan et al., 2015b). It is unclear at this point whether this discrepancy is due to the dramatic differences in the experimental models used in the two studies, but it is not surprising that the fine regulation detected here was not observed in the absence of islet cell interactions and vascular ECM signals.

To conclude, this study highlights a novel role of MT network in promoting β-cell heterogeneity in islets by restricting secretion hot spot activity.

All numerical data generated during this study are included in the manuscript and supporting files. Source data files have been provided for all figures. Code is provided for computational data.

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Author details

1. Kathryn P Trogden

   Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

   Contribution

   Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Validation, Visualization, Writing - original draft, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0003-3288-3859

2. Justin Lee

   Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

   Contribution

   Formal analysis, Investigation

   Contributed equally with

   Kai M Bracey, Kung-Hsien Ho and Hudson McKinney

   Competing interests

   No competing interests declared

3. Kai M Bracey

   Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

   Contribution

   Formal analysis, Investigation

   Contributed equally with

   Justin Lee, Kung-Hsien Ho and Hudson McKinney

   Competing interests

   No competing interests declared

4. Kung-Hsien Ho

   Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

   Contribution

   Formal analysis, Investigation

   Contributed equally with

   Justin Lee, Kai M Bracey and Hudson McKinney

   Competing interests

   No competing interests declared

5. Hudson McKinney

   Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

   Contribution

   Formal analysis, Software, Writing – review and editing

   Contributed equally with

   Justin Lee, Kai M Bracey and Kung-Hsien Ho

   Competing interests

   No competing interests declared

6. Xiaodong Zhu

   1. Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States
   2. Department of Medicine, Vanderbilt University, Nashville, United States

   Contribution

   Conceptualization, Methodology, Validation, Writing – review and editing

   Competing interests

   No competing interests declared

7. Goker Arpag

   Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

   Contribution

   Methodology, Software, Writing – review and editing

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6893-2678

8. Thomas G Folland

   Department of Mechanical Engineering, Vanderbilt University, Nashville, United States

   Contribution

   Methodology, Software, Writing – review and editing

   Competing interests

   No competing interests declared

9. Anna B Osipovich

   1. Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, United States
   2. Center for Stem Cell Biology, Vanderbilt University, Nashville, United States

   Contribution

   Resources

   Competing interests

   No competing interests declared

10. Mark A Magnuson

    1. Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States
    2. Department of Molecular Physiology and Biophysics, Vanderbilt University, Nashville, United States
    3. Center for Stem Cell Biology, Vanderbilt University, Nashville, United States

    Contribution

    Resources, Writing – review and editing

    Competing interests

    No competing interests declared

11. Marija Zanic

    1. Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States
    2. Department of Chemical and Biomolecular Engineering, Vanderbilt University, Nashville, United States
    3. Department of Biochemistry, Vanderbilt University, Nashville, United States

    Contribution

    Formal analysis, Software, Writing – review and editing

    Competing interests

    No competing interests declared

    "This ORCID iD identifies the author of this article:" 0000-0002-5127-5819

12. Guoqiang Gu

    Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

    Contribution

    Conceptualization, Funding acquisition, Methodology, Project administration, Supervision, Validation, Writing - original draft, Writing – review and editing

    Competing interests

    No competing interests declared

13. William R Holmes

    1. Department of Physics and Astronomy, Vanderbilt University, Nashville, United States
    2. Department of Mathematics, Vanderbilt University, Nashville, United States
    3. Quantitative Systems Biology Center, Vanderbilt University, Nashville, United States

    Contribution

    Methodology, Software, Validation, Writing - original draft, Writing – review and editing

    Competing interests

    No competing interests declared

14. Irina Kaverina

    Department of Cell and Developmental Biology and Program in Developmental Biology, Vanderbilt University, Nashville, United States

    Contribution

    Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Supervision, Validation, Writing - original draft, Writing – review and editing

    For correspondence

    irina.kaverina@vanderbilt.edu

    Competing interests

    No competing interests declared

    "This ORCID iD identifies the author of this article:" 0000-0002-4002-8599

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