Limits...
Simulating the complex cell design of Trypanosoma brucei and its motility.

Alizadehrad D, Krüger T, Engstler M, Stark H - PLoS Comput. Biol. (2015)

Bottom Line: As a result, the trypanosome assumes a diversity of complex morphotypes during its life cycle.Changing details of the flagellar attachment generates less efficient swimmers.We also simulate different morphotypes that occur during the parasite's development in the tsetse fly, and predict a flagellar course we have not been able to measure in experiments so far.

View Article: PubMed Central - PubMed

Affiliation: Institute of Theoretical Physics, Technische Universität Berlin, Berlin, Germany.

ABSTRACT
The flagellate Trypanosoma brucei, which causes the sleeping sickness when infecting a mammalian host, goes through an intricate life cycle. It has a rather complex propulsion mechanism and swims in diverse microenvironments. These continuously exert selective pressure, to which the trypanosome adjusts with its architecture and behavior. As a result, the trypanosome assumes a diversity of complex morphotypes during its life cycle. However, although cell biology has detailed form and function of most of them, experimental data on the dynamic behavior and development of most morphotypes is lacking. Here we show that simulation science can predict intermediate cell designs by conducting specific and controlled modifications of an accurate, nature-inspired cell model, which we developed using information from live cell analyses. The cell models account for several important characteristics of the real trypanosomal morphotypes, such as the geometry and elastic properties of the cell body, and their swimming mechanism using an eukaryotic flagellum. We introduce an elastic network model for the cell body, including bending rigidity and simulate swimming in a fluid environment, using the mesoscale simulation technique called multi-particle collision dynamics. The in silico trypanosome of the bloodstream form displays the characteristic in vivo rotational and translational motility pattern that is crucial for survival and virulence in the vertebrate host. Moreover, our model accurately simulates the trypanosome's tumbling and backward motion. We show that the distinctive course of the attached flagellum around the cell body is one important aspect to produce the observed swimming behavior in a viscous fluid, and also required to reach the maximal swimming velocity. Changing details of the flagellar attachment generates less efficient swimmers. We also simulate different morphotypes that occur during the parasite's development in the tsetse fly, and predict a flagellar course we have not been able to measure in experiments so far.

Show MeSH

Related in: MedlinePlus

Swimming velocity, rotational frequency, torsion, and end-to-end distance for varying flagellar attachment.(a) Rescaled swimming velocity  plotted versus the winding angle  of the helically attached flagellum. The snapshots show the model trypanosomes before applying the bending wave. The flagellum winds counter-clockwise around the cell body up to the angle . (b) Rescaled rotational frequency of the cell body, , plotted versus the winding angle . The inset shows how the amplitude of the imposed flagellar bending wave increases from the broader end of the cell body to the tip by a factor  (red line), 1.25 (blue line), and 1 (black line). (c) Mean torsion  and mean curvature  (inset) of the cell's centerline plotted versus . (d) Mean end-to-end distance of the cell body versus . (e) Rescaled swimming velocity  plotted versus reduced distance  from the flagellar pocket, where the helical attachment begins. The snapshots show the model trypanosomes before deformation starts. The flagellum winds around the cell body always by . (f) Range of end-to-end distances  of the cell body during motion plotted versus . (g) Helical swimming trajectories of the posterior end indicated by red dots for  (left) and  (right). Snapshots of model trypanosomes during swimming are illustrated.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4288712&req=5

pcbi-1003967-g005: Swimming velocity, rotational frequency, torsion, and end-to-end distance for varying flagellar attachment.(a) Rescaled swimming velocity plotted versus the winding angle of the helically attached flagellum. The snapshots show the model trypanosomes before applying the bending wave. The flagellum winds counter-clockwise around the cell body up to the angle . (b) Rescaled rotational frequency of the cell body, , plotted versus the winding angle . The inset shows how the amplitude of the imposed flagellar bending wave increases from the broader end of the cell body to the tip by a factor (red line), 1.25 (blue line), and 1 (black line). (c) Mean torsion and mean curvature (inset) of the cell's centerline plotted versus . (d) Mean end-to-end distance of the cell body versus . (e) Rescaled swimming velocity plotted versus reduced distance from the flagellar pocket, where the helical attachment begins. The snapshots show the model trypanosomes before deformation starts. The flagellum winds around the cell body always by . (f) Range of end-to-end distances of the cell body during motion plotted versus . (g) Helical swimming trajectories of the posterior end indicated by red dots for (left) and (right). Snapshots of model trypanosomes during swimming are illustrated.

Mentions: We now use our model trypanosome to demonstrate how the flagellar attachment determined from video microscopy optimizes the motility pattern of the real trypanosome. In Fig. 5(a) we continuously tune the winding angle by which the flagellum wraps around the cell body from to well above the half-turn observed in the real cell. As before, the helical attachment begins after a short straight segment near to the flagellar pocket at the posterior end and then runs straight again towards the anterior end. Interestingly, the swimming speed plotted in Fig. 5(a) shows a clear maximum exactly at the half turn of the flagellar attachment. So the helical attachment seems to be optimized for the swimming speed. The helical attachment results in an overall chiral body shape which leads to rotational motion initiated by the flagellar wave [Fig. 5(b)]. The rotational motion then couples back to translational motion and enhances the swimming speed. A recent theoretical study of chiral microswimmers, driven by a torque, shows that the swimming speed is optimal, when the microswimmer has a bowlike shape rather than the form of a full screw such as the flagellum of an E. coli bacterium [41]. To quantify the shape of the model cell body, we determined its centerline and calculated from the local torsion and curvature values a mean torsion and curvature by averaging over the full cell length and several beating cycles of the flagellum. Details are given in the Materials and methods Section a). The results are plotted versus the winding angle in Fig. 5(c), while Fig. 5(d) shows the cell's mean end-to-end distance together with illustrative snapshots. The decreasing indicates the formation of a bow. In particular, for the mean curvature value shows that the whole body is bent on an arc while the mean torsion, as a measure for the strength of chiral distortions, is close to its maximum value. Together with the results from Ref. [41], this gives some indication why the swimming speed in our case becomes maximal for a winding angle around . Fig. 5(b) shows how the rotational speed of the model trypanosome about the longitudinal axis continuously increases with the winding angle , when the trypanosome becomes more chiral. Microscopic imaging reveals that the distortion of the real trypanosome at the anterior end is larger than at the posterior end. In our modeling of the trypanosome we take this into account by an increased bending flexibility of the anterior end but also by increasing the amplitude of the imposed flagellar bending wave. The inset of Fig. 5(b) illustrates the wave of the imposed bending angle for different growth factors , which is the ratio of the wave amplitudes at the anterior and posterior end, and is explained in the Materials and methods Section b). By adjusting the growth factor to a sufficiently large value [two curves in Fig. 5(b)], we can match the rotational velocity with the experimental value indicated by the error bar. This corresponds well with the approximate ratio of two inferred from microscopy images [4].


Simulating the complex cell design of Trypanosoma brucei and its motility.

Alizadehrad D, Krüger T, Engstler M, Stark H - PLoS Comput. Biol. (2015)

Swimming velocity, rotational frequency, torsion, and end-to-end distance for varying flagellar attachment.(a) Rescaled swimming velocity  plotted versus the winding angle  of the helically attached flagellum. The snapshots show the model trypanosomes before applying the bending wave. The flagellum winds counter-clockwise around the cell body up to the angle . (b) Rescaled rotational frequency of the cell body, , plotted versus the winding angle . The inset shows how the amplitude of the imposed flagellar bending wave increases from the broader end of the cell body to the tip by a factor  (red line), 1.25 (blue line), and 1 (black line). (c) Mean torsion  and mean curvature  (inset) of the cell's centerline plotted versus . (d) Mean end-to-end distance of the cell body versus . (e) Rescaled swimming velocity  plotted versus reduced distance  from the flagellar pocket, where the helical attachment begins. The snapshots show the model trypanosomes before deformation starts. The flagellum winds around the cell body always by . (f) Range of end-to-end distances  of the cell body during motion plotted versus . (g) Helical swimming trajectories of the posterior end indicated by red dots for  (left) and  (right). Snapshots of model trypanosomes during swimming are illustrated.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4288712&req=5

pcbi-1003967-g005: Swimming velocity, rotational frequency, torsion, and end-to-end distance for varying flagellar attachment.(a) Rescaled swimming velocity plotted versus the winding angle of the helically attached flagellum. The snapshots show the model trypanosomes before applying the bending wave. The flagellum winds counter-clockwise around the cell body up to the angle . (b) Rescaled rotational frequency of the cell body, , plotted versus the winding angle . The inset shows how the amplitude of the imposed flagellar bending wave increases from the broader end of the cell body to the tip by a factor (red line), 1.25 (blue line), and 1 (black line). (c) Mean torsion and mean curvature (inset) of the cell's centerline plotted versus . (d) Mean end-to-end distance of the cell body versus . (e) Rescaled swimming velocity plotted versus reduced distance from the flagellar pocket, where the helical attachment begins. The snapshots show the model trypanosomes before deformation starts. The flagellum winds around the cell body always by . (f) Range of end-to-end distances of the cell body during motion plotted versus . (g) Helical swimming trajectories of the posterior end indicated by red dots for (left) and (right). Snapshots of model trypanosomes during swimming are illustrated.
Mentions: We now use our model trypanosome to demonstrate how the flagellar attachment determined from video microscopy optimizes the motility pattern of the real trypanosome. In Fig. 5(a) we continuously tune the winding angle by which the flagellum wraps around the cell body from to well above the half-turn observed in the real cell. As before, the helical attachment begins after a short straight segment near to the flagellar pocket at the posterior end and then runs straight again towards the anterior end. Interestingly, the swimming speed plotted in Fig. 5(a) shows a clear maximum exactly at the half turn of the flagellar attachment. So the helical attachment seems to be optimized for the swimming speed. The helical attachment results in an overall chiral body shape which leads to rotational motion initiated by the flagellar wave [Fig. 5(b)]. The rotational motion then couples back to translational motion and enhances the swimming speed. A recent theoretical study of chiral microswimmers, driven by a torque, shows that the swimming speed is optimal, when the microswimmer has a bowlike shape rather than the form of a full screw such as the flagellum of an E. coli bacterium [41]. To quantify the shape of the model cell body, we determined its centerline and calculated from the local torsion and curvature values a mean torsion and curvature by averaging over the full cell length and several beating cycles of the flagellum. Details are given in the Materials and methods Section a). The results are plotted versus the winding angle in Fig. 5(c), while Fig. 5(d) shows the cell's mean end-to-end distance together with illustrative snapshots. The decreasing indicates the formation of a bow. In particular, for the mean curvature value shows that the whole body is bent on an arc while the mean torsion, as a measure for the strength of chiral distortions, is close to its maximum value. Together with the results from Ref. [41], this gives some indication why the swimming speed in our case becomes maximal for a winding angle around . Fig. 5(b) shows how the rotational speed of the model trypanosome about the longitudinal axis continuously increases with the winding angle , when the trypanosome becomes more chiral. Microscopic imaging reveals that the distortion of the real trypanosome at the anterior end is larger than at the posterior end. In our modeling of the trypanosome we take this into account by an increased bending flexibility of the anterior end but also by increasing the amplitude of the imposed flagellar bending wave. The inset of Fig. 5(b) illustrates the wave of the imposed bending angle for different growth factors , which is the ratio of the wave amplitudes at the anterior and posterior end, and is explained in the Materials and methods Section b). By adjusting the growth factor to a sufficiently large value [two curves in Fig. 5(b)], we can match the rotational velocity with the experimental value indicated by the error bar. This corresponds well with the approximate ratio of two inferred from microscopy images [4].

Bottom Line: As a result, the trypanosome assumes a diversity of complex morphotypes during its life cycle.Changing details of the flagellar attachment generates less efficient swimmers.We also simulate different morphotypes that occur during the parasite's development in the tsetse fly, and predict a flagellar course we have not been able to measure in experiments so far.

View Article: PubMed Central - PubMed

Affiliation: Institute of Theoretical Physics, Technische Universität Berlin, Berlin, Germany.

ABSTRACT
The flagellate Trypanosoma brucei, which causes the sleeping sickness when infecting a mammalian host, goes through an intricate life cycle. It has a rather complex propulsion mechanism and swims in diverse microenvironments. These continuously exert selective pressure, to which the trypanosome adjusts with its architecture and behavior. As a result, the trypanosome assumes a diversity of complex morphotypes during its life cycle. However, although cell biology has detailed form and function of most of them, experimental data on the dynamic behavior and development of most morphotypes is lacking. Here we show that simulation science can predict intermediate cell designs by conducting specific and controlled modifications of an accurate, nature-inspired cell model, which we developed using information from live cell analyses. The cell models account for several important characteristics of the real trypanosomal morphotypes, such as the geometry and elastic properties of the cell body, and their swimming mechanism using an eukaryotic flagellum. We introduce an elastic network model for the cell body, including bending rigidity and simulate swimming in a fluid environment, using the mesoscale simulation technique called multi-particle collision dynamics. The in silico trypanosome of the bloodstream form displays the characteristic in vivo rotational and translational motility pattern that is crucial for survival and virulence in the vertebrate host. Moreover, our model accurately simulates the trypanosome's tumbling and backward motion. We show that the distinctive course of the attached flagellum around the cell body is one important aspect to produce the observed swimming behavior in a viscous fluid, and also required to reach the maximal swimming velocity. Changing details of the flagellar attachment generates less efficient swimmers. We also simulate different morphotypes that occur during the parasite's development in the tsetse fly, and predict a flagellar course we have not been able to measure in experiments so far.

Show MeSH
Related in: MedlinePlus