ORIGINAL RESEARCH article
Volume 10 - 2022 | https://doi.org/10.3389/fphy.2022.875687
A Pili-Driven Bacterial Turbine
- 1Department of Physiology, Development and Neuroscience, University of Cambridge, Cambridge, United Kingdom
- 2Department of Biology, Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany
- 3Max Planck Zentrum für Physik und Medizin, Erlangen, Germany
Work generated by self-propelled bacteria can be harnessed with the help of microdevices. Such nanofabricated microdevices, immersed in a bacterial bath, may exhibit unidirectional rotational or translational motion. Swimming bacteria that propel with the help of actively rotating flagella are a prototypical example of active agents that can power such microdevices. In this work, we propose a computational model of a micron-sized turbine powered by bacteria that rely on active type IV pili appendages for surface-associated motility. We find that the turbine can rotate persistently over a time scale that significantly exceeds the characteristic times of the single cell motility. The persistent rotation is explained by the collective dynamics of multiple pili of groups of cells attaching to and pulling on turbine. Furthermore, we show that the turbine can rotate permanently in the same direction by altering the pili binding to the turbine surface in an asymmetric fashion. We thus can show that by changing the adhesive properties of the turbine while keeping its symmetric geometry, we can still break the symmetry of its rotation. Altogether, this study widely expands the range of bacteria that can be used to power nanofabricated microdevices, and, due to high pili forces generated by pili retraction, promises to push the harnessed work by several orders of magnitude.
The last years have seen significant advances in nanofabrication, permitting the invention of a wide range of micron-sized artificial devices. A fascinating question is how such devices can be powered by actively moving biological matter, typically consisting of bacteria. Examples are beads that move due to collision or attachment of cells to its surface [1, 2], swimming devices due to individual swimming cells and bacterial carpets attached to their surface  or confined in the microdevice structure [4, 5], and geometrically asymmetric devices immersed in a bath of actively moving cells that rotate due to random collisions with the cells [6–10]. Usually, bacteria that swim with the help of rotating flagella were employed. In this study, we propose to consider twitching bacteria that exhibit surface-associated locomotion mediated by type IV pili [11, 12]. Pili are microns long active polymeric appendages protruding from the cell membrane. They undergo cycles of protrusion and retraction and can bind to a substrate and the pili of other cells. The combination of these two processes leads to aggregation of cells [13–15] and twitching motility on a substrate [16–19] by a mechanism reminiscent of a grappling hook (see Figure 1A).
FIGURE 1. Overview of the computational model of bacteria driving a rotatable turbine by attachment of type IV pili. (A) Sketch of how pili binding and retraction can lead to a force acting on a cell, a process reminiscent of a grappling hook. (B) Overview of the system. Cells are located in a box together with the rotatable turbine. The cells possess pili which they use for the motility on the substrate and for attachment to the turbine. The turbine center is located at r(turb) and has an orientation defined by the angle α. (C) Summary of all forces acting on the cells and turbine. Friction forces with the environment (surrounding liquid and substrate) are not shown.
Here, we investigate how bacteria that can attach type IV pili to a micron-sized turbine can drive its rotation. This system is especially interesting since multiple pili belonging to an individual bacterium can generate total forces in the range of nano-Newtons . In contrast to that, bacteria that swim with the help of flagella typically have thrust forces in the order of 1–10 pN . The molecular motor involved in the disassembly an hence, in the retraction of an individual pilus, called pilT, can generate forces in the range of 100 - 180 pN . This makes pilT the strongest molecular motor known in nature, with forces up to 20 times larger than those generated by kinesins or polymerases . Hence, we are asking if cells with type IV pili that can create so large forces might be more attractive candidates to power microdevices.
In this work, by means of a computational model, we study the dynamics of a rotatable turbine immersed in a bath of twitching bacteria. We investigate how the turbine rotation is affected by the binding and unbinding of the bacterial pili. We find that, due to the adhesion of multiple pili to the turbine over time scales that can strongly exceed the characteristic time scales of the individual pili attachment, the turbine can persistently rotate in one direction over extensive durations. While these persistent rotations have a limited lifetime, one can engineer a system where they become permanently unidirectional by introducing asymmetric binding of the pili to the turbine.
2 Materials and Methods
First, we introduce the computational model of twitching bacteria and their interactions with a turbine. A related version of this computational model was considered previously to describe bacterial surface motility  and bacterial aggregates [23–25].
While we consider the bacterium Neisseria gonorrhoeae as the primary biological example, the computational model can be easily adapted to account for other bacteria that use type IV pili, e.g., Neisseria meningitidis  or Pseudomonas aeruginosa . In the following, we focus on the regime of low cell density. This allows us not to consider cell-cell interactions and the formation of bacterial aggregates mediated by the binding of the pili of different cells. As a result, we do not expect three dimensional aggregates to form [23, 24]. This also enables us to only consider a simpler two-dimensional system.
2.1 Geometry of the Cells, Pili and Turbine
The experimental system we are mimicking are bacterial cells confined in a box with the turbine at its center (see Figure 1B). The cells can move over the substrate via pili binding and unbinding and additionally interact with the turbine by pili attachment and excluded volume effects.
While Neisseria gonorrhoeae cells typically have a diplococcus shape , we simplify the in silico cell shape of bacteria as two-dimensional circular disks with a radius R. Please note, however, that a diplococcus shape can be also considered [19, 23–25]. Each cell possesses exactly Np pili that are homogeneously distributed on the cell outline (see Figure 1A). We approximate pili as straight lines connecting two points: their start point (also called anchor point), located at the circular cell surface, and their end point. The distance between these two points is called the contour length lc of the pilus.
The turbine is described by Nturb × 2 disks (with radius R) arranged in a double row array (see Figure 1B). Since the only way how the turbine can move is by rotation, the relative locations of the turbine disks towards each other are fixed. The orientation of the turbine is described by the angle α with respect to the y-axis and the turbine center is located at the position r(turb) (see Figure 1B).
2.2 Pili Dynamics and Binding Properties
Initially, a pilus protrudes with the velocity vp in a direction perpendicular to the cell surface. When a pilus reaches a specific length, drawn from an exponential length distribution with mean length lp [17, 18], it starts to retract with a velocity
A pilus binds stochastically to the substrate or the turbine disks, independently whether it is protruding or retracting. In both cases, a pilus can only bind with its tip and it can bind only to either the substrate or the turbine disks. After binding, a pilus immediately starts to retract . The binding is modeled as a Poisson process with the binding rate
An attached pilus will generate a pulling force that acts on the cell and, if attached to a turbine disk, also on the turbine. Each pilus is modeled as a Hookean spring with the spring constant kp. After attachment, a pilus is stretched due to its retraction and hence, mediates a pulling force. This force is proportional to the difference between the contour length lc and the length of the pilus that it would have if it was not attached, here called the free length lf. Here, we consider the case where a pilus can only generate a pulling force and no pushing force, thus the force is zero if lc ≤ lf.
Experimentally, it has been shown that the pilus force affects the retraction velocity by
with the stalling force Fs . The force of a pilus also affects the unbinding from the substrate. Pilus detachment is modelled by a Poisson process with the rate
for detachment from the substrate, as motivated by . Here, we introduce the detachment times
with the detachment time
2.3 Cell Forces and Motility
We model pili as Hookean springs with the spring constant kp. For a cell i at location
Next to the active pili force, passive excluded volume forces are acting on the cells. Cells are located in a two-dimensional box with size L × L and a cell i that overlaps with the boundary wall is exposed to a repulsive force
The total force of the cell i is given by
Additionally, the total torque acting on a cell is
In the overdamped limit , a force mediates a translational motion of the cell with the velocity
and the torque leads to a rotation with the angular velocity vector
Here, we introduce the translational mobility μt and the rotational mobility μr. The same forces and torques cause an equivalent displacement of the pili anchor points
2.4 Turbine Torque and Rotation
The turbine is only able to undergo rotational motion. The total torque acting on the turbine is given by
The rotation of the turbine is modelled in the overdamped limit with a mobility μturb. In that case, the turbine angular velocity vector is
2.5 Parameters and Details of Numerical Solution
The simulations were performed on the local computing cluster of the Max Planck Institute for the Physics of Complex Systems (Dresden, Germany), consisting of x86-64 GNU/Linux systems. The code was written in C++. We use an Euler algorithm to solve the equations of motion with a time step δt. While this is one of the most simple numerical schemes to solve the equations of our computational model, it often leads to numerical errors and instabilities when modelling molecular dynamics systems for long times . We do not expect that this is a problem in our system due to the stochastic nature of the pili binding and unbinding, which basically represents our system as a series of many short time events, continuously interrupted by rearrangements in the pili network. Hence, we do not expect any differences in the qualitative outcome of the simulations.
If not stated otherwise, we use the parameters provided in Table 1. Most parameters we use are based on previous studies. The excluded volume spring constants k(c−c), k(turb) and k(wall) have no effect on the simulation outcome as long as they are chosen large enough to be able to compete with the pili forces. For the remaining parameters, e.g., the turbine mobility, we do not expect a qualitative difference in the results of the simulation.
We initialize the simulation by randomly distributing the cells in the box and only analyse the turbine rotation after an initialization period of 1,000 s. To calculate the angular velocity of the turbine rotation, we compute
with Δt = 0.5 s and the turbine orientation α (see Figure 1B).
In the following, we first demonstrate that bacteria binding to the turbine with the help of pili can cause a persistent turbine rotation over time scales that exceed the pili detachment times significantly. Next, we study how the persistent turbine rotation depends on the binding properties of the pili to the turbine and the number of cells in the system. This allows us to unravel the underlying mechanism that causes the persistent rotation of the turbine. Finally, we propose a system where an asymmetric binding of the pili to the turbine causes a permanent unidirectional rotation of the turbine.
3.1 Adhesion of Motile Bacteria Drives Turbine Rotation
To investigate how the adhesion of cells to a turbine affects the turbine rotation, we first simulate the computational model for three different cases: 1) pili detach with detachment times of
FIGURE 2. Analysis of rotary motion of a turbine in a bath of twitching bacteria. (A) Snapshots of the initial phase of the simulations of a turbine in a bath of bacteria with pili detachment rate
To quantify how strong the rotation is, we compute the angular mean squared displacement (angular MSD), given by
(see Figure 2C). Indeed, the angular MSD is the highest for
To learn more about how persistent the turbine rotation is, we compute the angular velocity autocorrelation function (angular velocity ACF), given by
Independently of whether pili can bind to the turbine or not, we find that the correlation function ν(Δt) is decaying with time (see Figure 2D). This confirms our previous observation for the angular MSD where we found that for very large time differences the turbine rotation is diffusive and no longer shows signs of persistence. We also find that for
3.2 Turbine Rotation Is Controlled by Bacterial Adhesion Strength and Cell Number
We begin with a systematic analysis of how the angular MSD δα(Δt) depends on the detachment time of pili from the turbine disks
FIGURE 3. Dependence of the turbine rotation on pili detachment time
Next, we investigate the normalised angular velocity ACF ν(Δt)/ν(0) (see Figure 3B) and find that for Δt < 2 s, it rapidly decreases. For Δt ≥ 2 s, it exponentially decreases with the Δt. By fitting a function of the form
Additionally, we investigated how the rotation of the turbine is affected by the density ρ of cells in the system. We find that with increasing density, the angular MSD δα becomes smaller (see Figure 3C). While we observe the diffusive regime of δα(Δt) for Δt < 10 s, a pronounced superdiffusive regime for larger Δt vanishes if the cell density becomes too large. For the normalised angular velocity ACF ν(Δt)/ν(0) (see Figure 3D), the characteristic decay time τ is initially increasing with cell density ρ and then decreases when ρ increases further.
In the following section, we provide qualitative arguments that explain the observed behaviours.
3.3 Unbinding Dynamics of Attached Bacteria Explains Characteristic Time of Turbine Rotation
To understand how the persistent rotation of the turbine in an otherwise symmetric system can emerge, we first consider how strongly cells bind to the turbine disks with the help of their pili and how pili binding affects substrate attachment of the remaining pili. Our hypothesis is the following: if cells stay attached to the same position on the turbine surface for an extended time, which is considerably larger than average attachment times of individual pili, the cells will continuously pull the turbine in the same direction. This mechanism is dramatically different to the previously reported rotary microdevices driven by swimming bacteria [6, 7], where cells collide with the microdevice and hence, push it. Instead, in our simulations, cells pull on the turbine. In Figure 4A, we show sketch of a cell which is attached to the turbine disk with some of its pili, while the other pili bind or unbind from the substrate. Only pili that protrude towards the turbine disks can attach, while pili protruding away from the turbine can only attach to the substrate. Thus, cells preferentially bind to the substrate in the direction away from the turbine. Since the cell is also attached with some of its pili to the turbine disks, it is pulling the turbine along the direction pointing from the turbine towards the cell. Thus, the cell pulls on the turbine, leading to a rotation of the turbine in the direction of the attached cell. This process is enhanced by the cooperation of multiple pili of a cell. To clarify this, we investigate the durations of cells attaching to the turbine disk before they detach again. To this aim, we solve a stochastic model of pili binding and unbinding, where a cell, possessing in total N0 pili that are all growing in the direction of the turbine, has n pili attached to the turbine. With a rate katt (N0 − n) a non-attached pilus attaches to the turbine, while with the rate kdetn a pilus detaches from the turbine (see Figure 4B). By describing the attachment and detachment as Poisson processes, we can numerically solve this system with the help of a Gillespie algorithm and investigate the mean time for a complete unbinding of all pili of a cell from the turbine (see Figure 4C). We find that the mean unbinding time is increasing rapidly with the pili detachment time
FIGURE 4. Overview of the mechanism driving the persistent rotation of the turbine. (A) A cell (light blue circle) with n =3 or n =0 pili attached to a turbine (dark blue circles). (B) Stochastic model of n pili attached to a turbine with pili binding (with constant rate katt) and unbinding (with constant rate kdet). (C) Mean unbinding time to reach for the first time the state n =0 in the stochastic model. Here, we chose N0=5, n (t =0)=5, katt =2 Hz, kdet =(exp 1)/τoff. (D) Sketch of how turbine rotation is affected by multiple cells binding to the turbine surface. The turbine rotates in the direction in which more cells are attached to its surface (turbine is pulled by cells). (E) Sketch of how turbine rotation leads to a pickup and binding of cells on the turbine surface.
We can now provide an explanation of the three time regimes observed in the angular MSD in Figure 2C and angular velocity ACF in Figure 2D. For short times, Δt < 10 s, individual pili stochastically bind and unbind to the substrate, pulling on the turbine, and additionally, cells randomly collide with the turbine. This causes small displacements of the turbine angle α in one direction, also explaining the very sudden drop of the angular velocity ACF for short times since the life time of such displacements is very small. This leads to random fluctuations of the turbine, and as a result, to a diffusive scaling. For larger times, 10 s < Δt < 103 s, asymmetries in the distribution of cells on the surface of the turbine lead to a unidirectional rotation of the turbine and as a result, to a superdiffusive regime. The persistence in the turbine rotation also explains the positive angular velocity ACF. The duration of this regime depends on how strong pili bind to the turbine disk (see Figure 4C). Finally, for Δt > 103 s, the distribution of cells on the turbine surface is re-arranged up to such a degree that the turbine can change its direction of motion. This will then lead to a diffusive regime again. This time also corresponds to the characteristic time of the angular velocity ACF decay, confirming that for large enough times, the turbine forgets its initial direction of motion.
For cases where pili bind stronger to the turbine, we expect to not only have more pili to bind to the turbine, but also more cells to be bound to the turbine with its pili. To this aim, we check the number of cells and pili bound to the turbine as a function of time (see Supplementary Figure S2). We find that after an initial phase of pili attachment, for larger pili-turbine detachment times
Next, we consider the origin of the cell density dependent rotation of the turbine, see Figure 3C and Figure 3D. If the cell density is very small, often no cell will bind to the turbine most of the time and thus, the angular MSD is initially increasing with cell density. For moderate cell densities the difference between cells attaching to different sides of the turbine (see Figure 4D) will be significant and due to the random asymmetry, the turbine will rotate persistently in one direction until cells randomly unbind from the turbine. If the cell density gets too large, more and more cells are pulling in the opposite direction of the turbine rotation, reducing its persistence.
There are additional processes that can have a significant impact on the turbine rotation: 1) Due to the rotation of the turbine, it will constantly “pick up” cells it collides with. For the traditional rotary microdevices that are driven by swimming bacteria that collide with the device and push it [6–8], this would lead to a torque that acts in the opposite direction of the original rotation. When cells pull on the turbine instead, the persistent rotation is being enhanced since asymmetric distribution of cells bound to the turbine disks is getting even stronger (see Figure 4E). 2) In Section 3.1, we found that the angular velocity ACF seems to decay faster for the case with pili attachment and
To summarise, the persistent rotation of the turbine originates from persistent attachment of cells to the turbine over times scales much longer than the characteristic detachment times of individual pili. While the resulting rotation is indeed persistent and, depending on the binding properties, can go on over multiple revolutions, it is not permanently unidirectional. There is no asymmetry in the initial rotational direction of the turbine and even though the turbine can move in one direction over an extended time, this rotation will at some point reverse direction. Next, we will provide an example of how cells using type IV pili can drive a permanent unidirectional rotation of a turbine.
3.4 Permanent Unidirectional Rotation due to Asymmetric Cell-Turbine Attachment
In order to produce a permanent unidirectional rotation of the turbine, an asymmetry of the turbine is required. Typically, such assymetries are created by altering the turbine geometry [7, 8, 12], but here we have a chance to exploit asymmetries in the adhesion of cells to the turbine instead. In Figure 5A, Figure 5B and Supplementary Movie S4, we provide an example of how altered pili binding properties on one side of the turbine wings can lead to a unidirectional rotation. Here, we consider different cases: 1) pili bind stronger to the manipulated turbine disks, corresponding to a larger detachment time
FIGURE 5. Unidirectional persistent turbine rotation is caused by asymmetric pili binding to the turbine. (A) Overview of the different types of turbine disks considered here. (B) Angle α of the turbine as a function of time t for different combinations of the manipulated turbine disks. We also provide the average angular velocity ⟨ω⟩ and its standard error for each condition. (C) The angular mean squared displacement exhibits superdiffusive (ballistic) scaling, δα ∝Δt2. (D) The normalised angular velocity auto correlation function is no longer decaying with increasing time differences Δt, corresponding to the unidirectional rotation.
We also estimate the average angular velocity ω of the turbine and find values around 2–4°/s. For the used rotational mobility of the turbine μturb (see Table 1), this corresponds to a turbine torque around 10 pN μm, comparable to previously published values for rotary devices in bacterial baths of hundreds of swimming cells . Here, however, the system consists of 40 cells only. Note that this is only the lower limit of the turbine torque and the same turbine might be able to generate larger torques if it experiences an opposing torque. In the absence of a counteracting torque, the rotation speed of the turbine is limited by the retraction velocity of pili, around 2 μm/s .
We see evidence that the rotation is permanently unidirectional in the angular MSD (see Figure 5C) which is superdiffusive (ballistic) for arbitrary time differences Δt, equivalent to a rotation in one direction. Additionally, the normalised angular velocity ACF (see Figure 5D) is no longer decaying with time Δt, suggesting a constant rotation in the same direction.
In experiments, such manipulated regions on the surface of the turbine could be generated by coating it with a chemical such as BSA, which has been shown to alter the detachment time of the pili [17, 18, 32].
In this study, we investigated how bacteria that use type IV pili for surface motility may drive the rotation of a micron-sized turbine. We found that due to spatial asymmetries in the amount of cells that are bound to the turbine, a persistent rotation is observed over time scales that can strongly exceed the characteristic time scales of the pili. The persistent rotation is enhanced when pili bind more strongly to the turbine and weaker when the density of cells becomes larger. The observed persistent rotation of a symmetric turbine has a characteristic time scale. For larger times, the rotation direction is reversed stochastically and there is no preferred direction of rotation. A persistent and unidirectional rotation can be generated by altering the binding properties of the type IV pili on parts of the turbine in an asymmetric manner.
To build a rotatable micron-sized device, typically microfabrication technologies are used [5, 6, 8]. Established technologies make it easy to construct the turbine body, but normally the microdevices are not attached to the substrate . In that case, a geometrically symmetric turbine becomes comparable to a passive rod or polymer in a bath of active particles [33, 34], with two major differences: forces are exerted by pulling instead of pushing, and the attachment of a pulling cell to the microdevice can last longer compared to the single pilus retraction time. In this case, we may expect to see rotational and translational diffusion but also some more complex trajectories, e.g., where the turbine rotates itself and its center of mass is on a circular track. Interestingly, if the rod is not straight, but has a concave shape, it can lead to trapping of particles and persistent motion of the turbine [33, 35, 36] Harnessing the power of the turbine is considerably harder if the turbine exhibits translational motion. Hence, it is required to immobilise the center of rotation of the turbine to only allow for rotation. One way to do that would be to plug the turbine onto a immobile column. The column must have been microfabricated such that it is tightly connected to the substrate and can withstand the forces generated by the cells. An alternative solution could be to trap the turbine in a circular depression  that has the same radius as the turbine, so that the only degree of freedom is the turbine rotation.
Here, we have shown that microdevices immersed in a bath of bacteria that use pili, such as Neisseria gonorrhoeae or Pseudomonas aeruginosa, can efficiently harness the power of the type IV pilus machinery. This system is particularly superior to previously reported microdevices driven by swimming bacteria [6–8], since the involved molecular motor pilT is the strongest known molecular motor  and a single cell is capable of generating forces in the nano-Newton range.
In the future, it will be interesting to investigate the interplay of asymmetries in the geometrical and adhesive properties of the turbine. Additionally, we expect that the binding of pili with the substrate will also have an effect on the turbine rotation. Higher values of the pili-substrate detachment times
Data Availability Statement
The source code of the computational model can be accessed via https://github.com/wolframponisch/Pili-Driven-Bacterial-Turbine. The Matlab scripts used to analyse the data and generate the figures are available upon request.
WP and VZ designed the research. WP carried out all numerical solutions. WP carried out analytical calculations. WP analyzed the data. WP and VZ wrote the article.
WP kindly acknowledges support from the Herchel Smith Fund (Herchel Smith Postdoctoral Fellowship).
Conflict of Interest
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.
WP and VZ would like to thank the MPI-PKS IT department for access and help with the computer cluster.
The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fphy.2022.875687/full#supplementary-material
Supplementary Figure S1 | Turbine angle α as a function of time t > 50000 s after the simulations started for three cases: Small Pili-turbine detachment rate τ (turb) det = 2 s, larger τ (turb) det = 50 s and no attachment of pili to the turbine. The turbine seems to be constantly rotating and does not exhibit extended periods without motion.
Supplemental Figure S2 | Number of cells that are attached to the turbine via its pili, number of pili attached to the turbine and number of pili per cell attached to the turbine as a function of time for two different cases: pili-turbine detachment rate τ (turb) det = 2 s and τ (turb) det = 50 s. We find that for τ (turb) det = 50 s the highest number of pili and cell are bound to the turbine. Additionally, we observe an intitial phase where the number of attached cells and pili increases before reaching a plateau. This corresponds to the phase where randomly distributed cells move into the vicinity of the turbine and binding to it randomly.
Supplementary Movie S1 | Movie of turbine in a bath of twitching bacteria with pili-turbine detachment time τ (turb) 378 ret = 50 s
Supplementary Movie S2 | Movie of turbine in a bath of twitching bacteria with pili-turbine detachment time τ (turb) 380 ret = 2 s.
Supplementary Movie S3 | Movie of turbine in a bath of twitching bacteria that do not bind to the turbine with their pili.
Supplementary Movie S4 | Movie of turbines with binding properties specified in Figure 5.
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Keywords: bacterial turbine, bacterial motility, microdevice, type IV pili, active motion
Citation: Pönisch W and Zaburdaev V (2022) A Pili-Driven Bacterial Turbine. Front. Phys. 10:875687. doi: 10.3389/fphy.2022.875687
Received: 14 February 2022; Accepted: 16 March 2022;
Published: 18 May 2022.
Edited by:Sujit Datta, Princeton University, United States
Reviewed by:Stefan Klumpp, University of Göttingen, Germany
Hepeng Zhang, Shanghai Jiao Tong University, China
Copyright © 2022 Pönisch and Zaburdaev. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Wolfram Pönisch, email@example.com; Vasily Zaburdaev, firstname.lastname@example.org