Русский 
English A minimal mathematical model of neutrophil pseudopodium formation during chemotaxis
, ,
Anastasia Sveshnikova1,3,2,4
show the whole list
Introduction
Neutrophils represent the largest population of leukocytes in human blood and they are the first cells to be recruited to the sites of inflammation
[
1
Neutrophils promote venular thrombosis by shaping the rheological environment for platelet aggregation
D. Puhr-Westerheide, S. Schink, M. Fabritius, L. Mittmann, M. Hessenauer, J. Pircher, G. Zuchtriegel, B. Uhl, M. Holzer, S. Massberg, F. Krombach, C. Reichel
Scientific Reports. 2019, 9, None
]
. To perform their functions, neutrophils need to detect extracellular chemical gradients and move towards higher concentrations of chemoattractants emanating from the sites of injury. This process is called chemotaxis or guided cell migration
[
2
Modeling neutrophil migration in dynamic chemoattractant gradients: assessing the role of exosomes during signal relay
A. Szatmary, R. Nossal, C. Parent, R. Majumdar
Molecular Biology of the Cell. 2017, 28, 3457-3470
]
. Chemotaxis of neutrophils is characterized by gradient sensitivity, polarization, and cell motility
[
3
Ex vivo observation of granulocyte activity during thrombus formation
Daria S. Morozova, Alexey A. Martyanov, Sergei I. Obydennyi, Julia-Jessica D. Korobkin, Alexey V. Sokolov, Ekaterina V. Shamova, Irina V. Gorudko, Anna Shcherbina, Mikhail A. Panteleev, A. N. Sveshnikova
bioRxiv. 2020, None, None
]
. Chemoattractant sensing occurs through G-protein coupled receptors (GPCRs) and other receptors that induce asymmetric localization and activation of key signaling molecules.
For the directed movement an actin cytoskeleton rearrangement should happen. Specifically, actin polymerization happens on the growing towards the source of chemoattractant cell protrusion. This protrusion is sometimes called pseudopodia (or, in neutrophils, lamellipodia).
The neutrophil pseudopodium consists of a core rich in actin surrounded by adhesion and scaffolding proteins. Globular (G) actin monomers are polymerized to form filamentous (F) actin, which is critical for cell migration
[
4,
Cellular Motility Driven by Assembly and Disassembly of Actin Filaments
T. Pollard, G. Borisy
Cell. 2003, 112, 453-465
5
Life at the Leading Edge
A. Ridley
Cell. 2011, 145, 1012-1022
]
. F-actin are oriented filaments that grow at the so-called barbed end push the front of the cell forward, which stimulates cell migration. Actin nucleation and polymerization are regulated by formins (e.g., mDia1 and mDia2) and the Arp2/3 complex
[
5,
Life at the Leading Edge
A. Ridley
Cell. 2011, 145, 1012-1022
6
Actin Dynamics at the Leading Edge: From Simple Machinery to Complex Networks
R. Insall, L. Machesky
Developmental Cell. 2009, 17, 310-322
]
. Formins nucleate regulate the growth of linear actin filaments
[
7,
Review of the mechanism of processive actin filament elongation by formins
A. Paul, T. Pollard
Cell Motility and the Cytoskeleton. 2009, 66, 606-617
8
Mechanism and Function of Formins in the Control of Actin Assembly
B. Goode, M. Eck
Annual Review of Biochemistry. 2007, 76, 593-627
]
. The Arp2/3 complex generates branches from existing actin filaments at an angle of 70° and thus creates a dendritic actin network
[
2
Modeling neutrophil migration in dynamic chemoattractant gradients: assessing the role of exosomes during signal relay
A. Szatmary, R. Nossal, C. Parent, R. Majumdar
Molecular Biology of the Cell. 2017, 28, 3457-3470
]
.
Dynamics of neutrophil movements could be considered as an indicator of neutrophils’ adequacy. Recently we have suggested an experimental model for assessing the adequacy of a patients’ neutrophils in an ex vivo setting of growing thrombi
[
3
Ex vivo observation of granulocyte activity during thrombus formation
Daria S. Morozova, Alexey A. Martyanov, Sergei I. Obydennyi, Julia-Jessica D. Korobkin, Alexey V. Sokolov, Ekaterina V. Shamova, Irina V. Gorudko, Anna Shcherbina, Mikhail A. Panteleev, A. N. Sveshnikova
bioRxiv. 2020, None, None
]
. In that work we looked at the movement of neutrophils of pediatric patients with Wiskott–Aldrich syndrome (WAS) - a rare genetic immunodeficiency characterized by immune dysregulation and cytoskeletal abnormalities. Immune cells from WAS patients display lower chemotaxis velocities
[
3,
Ex vivo observation of granulocyte activity during thrombus formation
Daria S. Morozova, Alexey A. Martyanov, Sergei I. Obydennyi, Julia-Jessica D. Korobkin, Alexey V. Sokolov, Ekaterina V. Shamova, Irina V. Gorudko, Anna Shcherbina, Mikhail A. Panteleev, A. N. Sveshnikova
bioRxiv. 2020, None, None
9
Chemotaxis of macrophages is abolished in the Wiskott-Aldrich syndrome
D Zicha, W E Allen, P M Brickell, C Kinnon, G A Dunn, G E Jones, A J Thrasher
British Journal of Haematology. 1998, 101(4), 659–665
]
. It is known that the Arp2/3 (Actin-related proteins 2/3) complex is activated by the WASP (Wiskott–Aldrich syndrome protein) family
[
10
Role and structural mechanism of WASP-triggered conformational changes in branched actin filament nucleation by Arp2/3 complex
M. Rodnick-Smith, Q. Luan, S. Liu, B. Nolen
Proceedings of the National Academy of Sciences. 2016, 113, E3834-E3843
]
, but the influence of WASp mutations on lamellipodia formation is not clear yet.
Mathematical modeling has been applied to describe actin cytoskeleton growth in lamellipodia
[
11
Predictive assembling model reveals the self-adaptive elastic properties of lamellipodial actin networks for cell migration
X. Chen, H. Zhu, X. Feng, X. Li, Y. Lu, Z. Wang, Y. Rezgui
Communications Biology. 2020, 3, None
]
, filopodia
[
12
Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia
R. Erban, M. Flegg, G. Papoian
Bulletin of Mathematical Biology. 2014, 76, 799-818
]
and presynaptic membrane protrusions
[
13
Modeling the Shape of Synaptic Spines by Their Actin Dynamics
M. Bonilla-Quintana, F. Wörgötter, C. Tetzlaff, M. Fauth
Frontiers in Synaptic Neuroscience. 2020, 12, None
]
. There are several possible approaches to model the neutrophil pseudopodium formation, such as continuous modeling of actin concentration
[
14
Polarization and Movement of Keratocytes: A Multiscale Modelling Approach
A. Marée, A. Jilkine, A. Dawes, V. Grieneisen, L. Edelstein-Keshet
Bulletin of Mathematical Biology. 2006, 68, 1169-1211
]
or stochastic modeling of individual proteins. Since it has been shown that the neutrophil membrane protrusions are intrinsically lamellar
[
15
Actin-based protrusions of migrating neutrophils are intrinsically lamellar and facilitate direction changes
L. Fritz-Laylin, M. Riel-Mehan, B. Chen, S. Lord, T. Goddard, T. Ferrin, S. Nicholson-Dykstra, H. Higgs, G. Johnson, E. Betzig, R. Mullins
eLife. 2017, 6, None
]
, a two-dimensional (2D) geometry could be used to describe the membrane protrusion growth.
Here we made a first attempt to bind together the observed changes in neutrophils’ movements for WAS patients and the known mechanisms of actin polymerization and neutrophil pseudopodium formation. We measured the linear velocities of the neutrophil pseudopodium growth for WAS patients and healthy donors by means of fluorescent microscopy. Surprisingly, the difference between these values was not significant. To explain the observed phenomena, we have built a minimal mathematical model capable of quantitative description of neutrophil membrane protrusion growth. In accordance with experimental data, varying branching velocity in an order of magnitude did not significantly alter the overall protrusion growth velocity. It indicates that the observed disruption of chemotaxis in WAS patients could not be explained by impaired pseudopodium formation.
Materials and Methods
Materials
The sources of the materials were as follows: DiOC-6, bovine serum albumin (BSA), human fibrinogen (Sigma-Aldrich, St Louis, MO); fibrillar collagen type I (Chrono-Log Corporation; Havertown; USA).
Fluorescent microscopy
Parallel-plate flow chambers were mounted as described previously
[
16
Clot Contraction Drives the Translocation of Procoagulant Platelets to Thrombus Surface
D. Nechipurenko, N. Receveur, A. Yakimenko, T. Shepelyuk, A. Yakusheva, R. Kerimov, S. Obydennyy, A. Eckly, C. Léon, C. Gachet, E. Grishchuk, F. Ataullakhanov, P. Mangin, M. Panteleev
Arteriosclerosis, Thrombosis, and Vascular Biology. 2019, 39, 37-47
]
. Channel parameters were: 0.2 x 18 x 0.206 mm. Glass coverslips were coated with fibrillar collagen type I (0.2 mg/ml) for 1h 30min at 37oС, washed with distilled water, blocked with BSA and then inserted into the flow chambers.
Blood was collected from healthy adult volunteers (n=5, men and women 18-35 years old) or from patients with Wiskott-Aldrich syndrome (n = 3) into Sarstedt-Monovette© hirudin (525 ATU/ml blood) vacuum tubes.
Whole blood was pre-loaded with DiOC6 (1 µM). Blood was perfused through the parallel-plate chambers over collagen-coated (0.2 mg/ml) surface with wall shear rates of 100 s-1 as described in
[
3
Ex vivo observation of granulocyte activity during thrombus formation
Daria S. Morozova, Alexey A. Martyanov, Sergei I. Obydennyi, Julia-Jessica D. Korobkin, Alexey V. Sokolov, Ekaterina V. Shamova, Irina V. Gorudko, Anna Shcherbina, Mikhail A. Panteleev, A. N. Sveshnikova
bioRxiv. 2020, None, None
]
. Thrombus growth and leukocyte crawling were observed in DIC/epifluorescence modes with an inverted Nikon Eclipse Ti-E microscope (100x/1.49 NA TIRF oil objective). Neutrophil locations were derived based on DiOC6 fluorescence. Alternatively, confocal mode with Z1 microscope (Carl Zeiss, Jena, Germany; 100x objective; Axio Observer) was used. 488 nm laser was applied to assess DiOC6 fluorescence in neutrophils. It has been already shown that the attaching cells in this experimental setup are exclusively neutrophils
[
3
Ex vivo observation of granulocyte activity during thrombus formation
Daria S. Morozova, Alexey A. Martyanov, Sergei I. Obydennyi, Julia-Jessica D. Korobkin, Alexey V. Sokolov, Ekaterina V. Shamova, Irina V. Gorudko, Anna Shcherbina, Mikhail A. Panteleev, A. N. Sveshnikova
bioRxiv. 2020, None, None
]
.
Data analysis
Nikon NIS-Elements software was used for microscope image acquisition; ImageJ
[
17
Fiji: an open-source platform for biological-image analysis
J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona
Nature Methods. 2012, 9, 676-682
]
(http://imagej.net/ImageJ) was used for image processing. ImageJ manual tracking plugin was used for manual granulocyte pseudopod tracking.
Statistics
All experiments were performed at least in triplicate with platelets from different donors. Statistical analysis was performed using Python 3.6; all statistical details are provided in the figure captions.
Results
Experimental measurement of the linear velocities of pseudopodium formation.
To measure the rate of anterior protrusion formation, a series of experiments were carried out in which neutrophils movements were observed during thrombus growth in whole hirudinated blood (without any external chemoattractant). The measurements were performed only for the moving neutrophils. The linear velocity of the protrusion was measured by the following algorithm: a) the moving cell with one distinct pseudopodium was selected; b) the central line in the direction of the protrusion was identified; c) the coordinates of the growing “tip” along this line were taken by means of ImageJ software; d) the instant and average velocities of the protrusion were calculated from these coordinates (Fig. 1A).
For healthy donors the average protrusion velocities appeared to be 0.22 ± 0.04 μm/s, while for WAS patients the average protrusion velocities were 0.23 ± 0.08 μm/s. According to the Manne-Whitney criteria, the difference between healthy and WAS data was not significant.
Figure 1. Experimental measurement of the pseudopodium formation rate. Typical images of the growing protrusion. The pseudopodium tips are marked with red circles. (B) Pseudopod velocities for healthy controls and WAS patients. For healthy controls, mean speed of the pseudopod growth was determined to be 0.22 ± 0.04 μm/s. For WAS patients, mean speed of the pseudopod growth was determined to be 0.23 ± 0.08 μm/s. The difference between control and WAS pseudopod growth speed was not significant.
Construction of the computational model of actin polymerization
To describe the observed experimental data, we have built a minimal stochastic mathematical model of actin cytoskeleton reorganization upon pseudopodium formation. In this model, we have described the following events: the polymerization and depolymerization of F-actin, as well as branching of the growing actin network (Fig. 2A). As the actin polymerization in the pseudopodium occurs only in narrow separate regions on the tips
[
18
Spatial control of actin polymerization during neutrophil chemotaxis
O. Weiner, G. Servant, M. Welch, T. Mitchison, J. Sedat, H. Bourne
Nature Cell Biology. 1999, 1, 75-81
]
, we did not take into account the interaction between different pseudopodia composing the growing protrusion. In the model, the cell plasma membrane was “pushed” by the growing F-actin ends. The critical number of the pushing ends ( \({ Nact }\)) was chosen according to experimental data. The probabilities for actin polymerization, branching and depolymerization were estimated from the known reaction rates for human enzymes. Actin exists in two states bound to either ATP or ADP. Monomeric actin hydrolyzes ATP very slowly, and polymeric hydrolyzes ATP fast and irreversibly
[
19
ATP and ADP actin states
D. Kudryashov, E. Reisler
Biopolymers. 2013, 99, 245-256
]
. The newly assembled part of the filament contains mostly ATP protomers, while older filaments have mainly ADP-protomers
[
19
ATP and ADP actin states
D. Kudryashov, E. Reisler
Biopolymers. 2013, 99, 245-256
]
. The ADP-enriched end (minus or pointed end) of the filament disassembles more readily.
Single actin filaments at steady state add fresh ATP-subunits at the barbed end balanced by dissociation of ADP-actin at the pointed end.
Here, we do not take into account the ADP-actin dissociation because in the present work we are interested only in freshly-assembled actin dynamics in a narrow region near the cell membrane. Typical lengths of actin filaments range from 100 nm to a few microns
[
20
Actin Filament Length Tunes Elasticity of Flexibly Cross-Linked Actin Networks
K. Kasza, C. Broedersz, G. Koenderink, Y. Lin, W. Messner, E. Millman, F. Nakamura, T. Stossel, F. MacKintosh, D. Weitz
Biophysical Journal. 2010, 99, 1091-1100
]
, and actin polymerization in the model occurs only in a narrow region of leading edge several dozens of nm wide, so pointed ends are unlikely to get into the area of interest.
In the following equations, [F] denotes the F-actin concentration, [G] is the denotation for G-actin, \(k_{on} \) is the actin polymerization rate constant, \(k_{off} \) is the actin depolymerization rate, \(k_{b} \) is the branching rate, [Arp] is the Arp2/3 concentration.
The following equations were used for deriving the G-actin attachment and detachment rates and the possibilities of actin filament branching:
- The following equations describe the actin polymerization:
For actin monomer attachment rate to a filament consisting of N filaments \( F_{N}+G \rightarrow F_{N+1} \), we have the following equation:
\begin{equation} \frac{d[F]}{d t}=k_{o n}[G][F]\tag{1}\end{equation}
Separating the variables, we get:
\begin{equation} \frac{d[F]}{[F]}=k_{\text {on }}[G] d t\tag{2}\end{equation}
Integrating the equation above, we get:
\begin{equation} \ln \frac{F_{N+1}}{F_{N}}=k_{o n}[G] d t,\tag{3}\end{equation} where \( {dt} \) is the time interval.
\begin{equation} \frac{F_{N}}{F_{N+1}}=\exp \left(-k_{o n}[G] d t\right)\tag{4}\end{equation}
\begin{equation} \frac{\Delta F}{F_{N+1}}=1-\frac{1}{\exp \left(k_{\text {on }}[G] d t\right)}\tag{5}\end{equation}
For the possibility of the polymerization, we get the following expression:
\begin{equation} P_{o n}=1-\frac{1}{\exp \left(k_{o n}[G] d t\right)}\tag{6}\end{equation}
The possibility of actin depolymerization is acquired in the same fashion:
\begin{equation} F_{N}+G \leftarrow F_{N+1}\tag{7}\end{equation}
\begin{equation} P_{off}=1-\frac{1}{\exp \left(k_{off} d t\right)}\tag{8}\end{equation}
- For the branching reaction, we use a simple approximation to get the expression for the branching possibility:
\begin{equation} F_{N}+Arp \rightarrow F_{N+1}\tag{9}\end{equation}
\begin{equation} P_{b}=k_{b}[A r p] d t\tag{10}\end{equation}
The reasons for not picking the simple approximation for polymerization and depolymerization are listed in SI 1.
The polymerization center was assumed to be located at the maximum distance at which F-actin polymerization is possible (Fig. 2B). As it was shown, filopodia can serve as a template for lamellipodia formation
[
21
F-actin bundles direct the initiation and orientation of lamellipodia through adhesion-based signaling
H. Johnson, S. King, S. Asokan, J. Rotty, J. Bear, J. Haugh
Journal of Cell Biology. 2015, 208, 443-455
]
. Filopodia are membrane protrusions 60-200 nm in diameter and containing parallel bundles of 10-30 actin filaments
[
22
Filopodia: molecular architecture and cellular functions
P. Mattila, P. Lappalainen
Nature Reviews Molecular Cell Biology. 2008, 9, 446-454
]
. Initially, a subset of 10 F-actin filaments consisting of 2 subunits is generated at the cell membrane. Initial cell diameter is equal to 100 nm.
In each time step, a random number ri from U(0,1) is generated for every F-actin branch. If ri is smaller than the possibility of F-actin branch growth (Pon), a single G-actin monomer is added to the branch. In the same fashion, the depolymerization and branching of every branch were modelled. Upon branching, the child branch could start with equal probability both at 70o CW or 70o CCW in respect to the parent branch direction.
In some cases, the branch growth could be hindered by pressing against the cell membrane. Branch overlap is allowed in this model due to three-dimensipnality of the real lamellipodia and low density (<7% v/v) of the actin mesh in lamellipodia leading to infrequent overlaps
[
23
Actin Turnover in Lamellipodial Fragments
D. Raz-Ben Aroush, N. Ofer, E. Abu-Shah, J. Allard, O. Krichevsky, A. Mogilner, K. Keren
Current Biology. 2017, 27, 2963-2973.e14
]
. A variant of model with restricted overlap is described in S2 and Fig. S1. The conclusions drawn from this variant do not differ significantly from the one with allowed branch overlap.
To describe the induction of actin polymerization by phosphoinositides
[
24
The role of phosphoinositide-regulated actin reorganization in chemotaxis and cell migration
C. Wu, M. Lin, D. Wu, Y. Huang, H. Huang, C. Chen
British Journal of Pharmacology. 2014, 171, 5541-5554
]
, we assume that the actin polymerization occurs only if the tip of the branch is no further than a fixed distance H from the cell membrane (Fig. 2B). Similarly, to take into account the fact that activators of the Arp2/3 complex, which render Arp2/3 competent for actin filament nucleation, are typically membrane-associated proteins
[
25
Activation of nucleation promoting factors for directional actin filament elongation: Allosteric regulation and multimerization on the membrane
S. Suetsugu
Seminars in Cell & Developmental Biology. 2013, 24, 267-271
]
, the filaments can branch only if the distance from the cell membrane is lesser than D. The number of pushing cell membrane branches, \( Nact \) , was set to be 241/μm
[
26
The flatness of Lamellipodia explained by the interaction between actin dynamics and membrane deformation
C. Schmeiser, C. Winkler
Journal of Theoretical Biology. 2015, 380, 144-155
]
. Upon reaching the threshold number of filaments abutting against the membrane, the entire membrane was assumed to move.
The parameter values are given in Table 1.
Table 1. Model parameters
The branching of the filaments was modelled in the following manner. Taking into account that the Arp2/3 complex is able to bind with four actin monomers corresponding to a couple of beads on the F-actin, we assumed that the new branch can stem from a couple of segments. In the model, each segment can be in either “free” or “occupied” by a growing child branch state (Fig. 2A). Additionally, a filament can grow only if the absolute value of the angle between the normal to the cell membrane direction and the new branch is more than 70o. In other words, the branches must grow forward.
Figure 2. Scheme of the computational model. (A) The scheme of stochastic events and species included in the model. A single F-actin filament is assumed to be straight and to be divided into segments. Each segment can be considered to be an actin monomer. New G-actin molecules can attach to and detach from the filament “barbed” end. It is assumed that the child filament begins to grow from the middle between two segments of F-actin at the angle of 70o. If there is a branch growing from the F-actin segments, they are considered occupied and no branching can occur there. (B) The spatial restrictions on the filament growth and branching. The filaments can branch if the distance from the cell membrane is lesser than D. Filaments can grow if the distance from the cell membrane is lesser than H, where H > D.
The computational model parameter estimation and validation
The constructed computational model described formation of a network (Fig. 3A). At the first step, we ensured that the growth rate of a single filament is in accordance with the literature data
[
31
Electrostatics Control Actin Filament Nucleation and Elongation Kinetics
A. Crevenna, N. Naredi-Rainer, A. Schönichen, J. Dzubiella, D. Barber, D. Lamb, R. Wedlich-Söldner
Journal of Biological Chemistry. 2013, 288, 12102-12113
]
. In the model, the single filament growth rate was 8 subunits per second for the concentration of G-actin of 1 μM (data not shown), which corresponds to the reported rate of 1 µm/min. Afterwards, a parameter scan was performed to get the values of the parameters k, D and H which would yield the protrusion velocity closest to the experimental ones. The best fit was obtained for the set of parameter values: k = 9000 (M x s)-1, D = H = 7. In the model the protrusion rate was estimated to be 0.23 μm/s. Along the leading edge, the actin filament density is peaked at the center and decreases toward the sides, which came into accordance with experimental data from
[
32
Actin disassembly clock determines shape and speed of lamellipodial fragments
N. Ofer, A. Mogilner, K. Keren
Proceedings of the National Academy of Sciences. 2011, 108, 20394-20399
]
. Filament density of 1300 um F-actin/um3 also was in good accordance with experimental data
[
30
The Actin-Based Nanomachine at the Leading Edge of Migrating Cells
V. Abraham, V. Krishnamurthi, D. Taylor, F. Lanni
Biophysical Journal. 1999, 77, 1721-1732
]
.
The adjustment of the computational model to the data on Wiskott-Aldrich syndrome patients
To account for the WASP loss-of-function mutations, we have lowered the model branching rate one order of magnitude and assumed that if WASP localization is disrupted, actin branching and polymerization may occur further from the membrane. In the model, the protrusion growth velocity did not show any significant dependence on either branching rate k or branching distance from the membrane H in a large interval of parameter values. For H > 6, the protrusion velocity did not change more than for 15%. For k > 3000 (M x s)-1, the protrusion velocity did not change more than for 20%. However, a strong dependency was seen on the number of pushing cell membrane branches, \( Nact \) (Figure 3D). When \(Nact \) was changed from 241 to 482 um/s, lamellipodia growth stopped.
Figure 3. Results of the computational modeling. (A) Typical actin network predicted by the model for parameters k = 9000 (M x s)-1, D = H = 7 actin units. (B) Dependence of the protrusion velocity on the branching rate k. (C) Dependence of the protrusion velocity on the branching distance H. (D) Dependence of the protrusion velocity on the number of the actin filaments Nact required to push the membrane.
Discussion
Here, we have studied the dynamics of cellular membrane protrusion growth upon neutrophil motility. We have performed experimental measurements of membrane protrusion growth velocity in healthy donors. The acquired velocity corresponds well with existing data on chemotactic cells such as macrophages
[
33
A novel real time imaging platform to quantify macrophage phagocytosis
T. Kapellos, L. Taylor, H. Lee, S. Cowley, W. James, A. Iqbal, D. Greaves
Biochemical Pharmacology. 2016, 116, 107-119
]
or dendritic cells
[
29
Super-Resolution Correlative Light and Electron Microscopy (SR-CLEM) Reveals Novel Ultrastructural Insights Into Dendritic Cell Podosomes
B. Joosten, M. Willemse, J. Fransen, A. Cambi, K. van den Dries
Frontiers in Immunology. 2018, 9, None
]
. Additionally, we have measured the linear velocity of the pseudopodia formation for neutrophils of WAS patients (Fig. 1). Surprisingly, the difference between the healthy donors and patients was not significant.
To explain the observed phenomena, we have built a minimal computational model capable of quantitative description of neutrophil membrane protrusion (pseudopodia) formation. The model was similar in design to the mathematical models of Chen
[
11
Predictive assembling model reveals the self-adaptive elastic properties of lamellipodial actin networks for cell migration
X. Chen, H. Zhu, X. Feng, X. Li, Y. Lu, Z. Wang, Y. Rezgui
Communications Biology. 2020, 3, None
]
and Winkler
[
26
The flatness of Lamellipodia explained by the interaction between actin dynamics and membrane deformation
C. Schmeiser, C. Winkler
Journal of Theoretical Biology. 2015, 380, 144-155
]
, who constructed models of lamellipodia formation in a generic migrating cell. The molecular machinery included into the model was based on the known data on the regulation of neutrophil pseudopodium formation
[
34,
Intracellular signalling during neutrophil recruitment
A. Mócsai, B. Walzog, C. Lowell
Cardiovascular Research. 2015, 107, 373-385
35,
Neutrophil polarization: Spatiotemporal dynamics of RhoA activity support a self-organizing mechanism
K. Wong, O. Pertz, K. Hahn, H. Bourne
Proceedings of the National Academy of Sciences. 2006, 103, 3639-3644
36
Network Crosstalk Dynamically Changes during Neutrophil Polarization
C. Ku, Y. Wang, O. Weiner, S. Altschuler, L. Wu
Cell. 2012, 149, 1073-1083
]
. The correspondence of the membrane protrusion rate predicted by the model to the experimental data indicates the validity of the implied mechanisms.
Although earlier we
[
3
Ex vivo observation of granulocyte activity during thrombus formation
Daria S. Morozova, Alexey A. Martyanov, Sergei I. Obydennyi, Julia-Jessica D. Korobkin, Alexey V. Sokolov, Ekaterina V. Shamova, Irina V. Gorudko, Anna Shcherbina, Mikhail A. Panteleev, A. N. Sveshnikova
bioRxiv. 2020, None, None
]
and others
[
37
The Wiskott-Aldrich syndrome: studies of lymphocytes, granulocytes, and platelets
H. Ochs, S. Slichter, L. Harker, W. Von Behrens, R. Clark, R. Wedgwood
Blood. 1980, 55, 243-252
]
have observed disruption in the movement of WAS patients’ neutrophils, the velocity of their protrusions were similar to those of healthy neutrophils. Parameter scan performed here implied that changing of the branching rate or the branching distance in an order of magnitude did not significantly alter the overall protrusion velocity. Together, these data indicate that the chemotaxis disruption in WAS patients could not be explained by the absence of WASP in these patients, which is in general accordance with existing data
[
38
The Wiskott-Aldrich syndrome: The actin cytoskeleton and immune cell function
Blundell, M. P., Worth, A., Bouma, G. & Thrasher, A. J.
Disease Markers. 2010, 29, 157-75
]
.
However, strong dependence of lamellipodia growth on the number of actin bundles required to push the membrane suggests impaired pseudopod formation as one of the possible mechanisms for cell motility reduction in patients with mutations in force-generating protein machinery, for example, MYH9
[
39
A Fundamental Role of Myh9 for Neutrophil Migration in Innate Immunity
A. Zehrer, R. Pick, M. Salvermoser, A. Boda, M. Miller, K. Stark, L. Weckbach, B. Walzog, D. Begandt
The Journal of Immunology. 2018, 201, 1748-1764
]
.
Acknowledgments
The authors are grateful to Ms Daria Morozova (CTP PCP RAS) for the valuable discussions and experimental assistance.
Funding
This research was supported by Russian Foundation for Basic Research, grant number 17-00-00138 and 21-51-10005 and Lomonosov Moscow State University Digital Medicine School
References of this article:
Neutrophils promote venular thrombosis by shaping the rheological environment for platelet aggregation
D. Puhr-Westerheide, S. Schink, M. Fabritius, L. Mittmann, M. Hessenauer, J. Pircher, G. Zuchtriegel, B. Uhl, M. Holzer, S. Massberg, F. Krombach, C. Reichel
Scientific Reports. 2019, 9,
Modeling neutrophil migration in dynamic chemoattractant gradients: assessing the role of exosomes during signal relay
A. Szatmary, R. Nossal, C. Parent, R. Majumdar
Molecular Biology of the Cell. 2017, 28, 3457-3470
Ex vivo observation of granulocyte activity during thrombus formation
Daria S. Morozova, Alexey A. Martyanov, Sergei I. Obydennyi, Julia-Jessica D. Korobkin, Alexey V. Sokolov, Ekaterina V. Shamova, Irina V. Gorudko, Anna Shcherbina, Mikhail A. Panteleev, A. N. Sveshnikova
bioRxiv. 2020, ,
Cellular Motility Driven by Assembly and Disassembly of Actin Filaments
T. Pollard, G. Borisy
Cell. 2003, 112, 453-465
Life at the Leading Edge
A. Ridley
Cell. 2011, 145, 1012-1022
Actin Dynamics at the Leading Edge: From Simple Machinery to Complex Networks
R. Insall, L. Machesky
Developmental Cell. 2009, 17, 310-322
Review of the mechanism of processive actin filament elongation by formins
A. Paul, T. Pollard
Cell Motility and the Cytoskeleton. 2009, 66, 606-617
Mechanism and Function of Formins in the Control of Actin Assembly
B. Goode, M. Eck
Annual Review of Biochemistry. 2007, 76, 593-627
Chemotaxis of macrophages is abolished in the Wiskott-Aldrich syndrome
D Zicha, W E Allen, P M Brickell, C Kinnon, G A Dunn, G E Jones, A J Thrasher
British Journal of Haematology. 1998, 101(4), 659–665
Role and structural mechanism of WASP-triggered conformational changes in branched actin filament nucleation by Arp2/3 complex
M. Rodnick-Smith, Q. Luan, S. Liu, B. Nolen
Proceedings of the National Academy of Sciences. 2016, 113, E3834-E3843
Predictive assembling model reveals the self-adaptive elastic properties of lamellipodial actin networks for cell migration
X. Chen, H. Zhu, X. Feng, X. Li, Y. Lu, Z. Wang, Y. Rezgui
Communications Biology. 2020, 3,
Multiscale Stochastic Reaction–Diffusion Modeling: Application to Actin Dynamics in Filopodia
R. Erban, M. Flegg, G. Papoian
Bulletin of Mathematical Biology. 2014, 76, 799-818
Modeling the Shape of Synaptic Spines by Their Actin Dynamics
M. Bonilla-Quintana, F. Wörgötter, C. Tetzlaff, M. Fauth
Frontiers in Synaptic Neuroscience. 2020, 12,
Polarization and Movement of Keratocytes: A Multiscale Modelling Approach
A. Marée, A. Jilkine, A. Dawes, V. Grieneisen, L. Edelstein-Keshet
Bulletin of Mathematical Biology. 2006, 68, 1169-1211
Actin-based protrusions of migrating neutrophils are intrinsically lamellar and facilitate direction changes
L. Fritz-Laylin, M. Riel-Mehan, B. Chen, S. Lord, T. Goddard, T. Ferrin, S. Nicholson-Dykstra, H. Higgs, G. Johnson, E. Betzig, R. Mullins
eLife. 2017, 6,
Clot Contraction Drives the Translocation of Procoagulant Platelets to Thrombus Surface
D. Nechipurenko, N. Receveur, A. Yakimenko, T. Shepelyuk, A. Yakusheva, R. Kerimov, S. Obydennyy, A. Eckly, C. Léon, C. Gachet, E. Grishchuk, F. Ataullakhanov, P. Mangin, M. Panteleev
Arteriosclerosis, Thrombosis, and Vascular Biology. 2019, 39, 37-47
Fiji: an open-source platform for biological-image analysis
J. Schindelin, I. Arganda-Carreras, E. Frise, V. Kaynig, M. Longair, T. Pietzsch, S. Preibisch, C. Rueden, S. Saalfeld, B. Schmid, J. Tinevez, D. White, V. Hartenstein, K. Eliceiri, P. Tomancak, A. Cardona
Nature Methods. 2012, 9, 676-682
Spatial control of actin polymerization during neutrophil chemotaxis
O. Weiner, G. Servant, M. Welch, T. Mitchison, J. Sedat, H. Bourne
Nature Cell Biology. 1999, 1, 75-81
ATP and ADP actin states
D. Kudryashov, E. Reisler
Biopolymers. 2013, 99, 245-256
Actin Filament Length Tunes Elasticity of Flexibly Cross-Linked Actin Networks
K. Kasza, C. Broedersz, G. Koenderink, Y. Lin, W. Messner, E. Millman, F. Nakamura, T. Stossel, F. MacKintosh, D. Weitz
Biophysical Journal. 2010, 99, 1091-1100
F-actin bundles direct the initiation and orientation of lamellipodia through adhesion-based signaling
H. Johnson, S. King, S. Asokan, J. Rotty, J. Bear, J. Haugh
Journal of Cell Biology. 2015, 208, 443-455
Filopodia: molecular architecture and cellular functions
P. Mattila, P. Lappalainen
Nature Reviews Molecular Cell Biology. 2008, 9, 446-454
Actin Turnover in Lamellipodial Fragments
D. Raz-Ben Aroush, N. Ofer, E. Abu-Shah, J. Allard, O. Krichevsky, A. Mogilner, K. Keren
Current Biology. 2017, 27, 2963-2973.e14
The role of phosphoinositide-regulated actin reorganization in chemotaxis and cell migration
C. Wu, M. Lin, D. Wu, Y. Huang, H. Huang, C. Chen
British Journal of Pharmacology. 2014, 171, 5541-5554
Activation of nucleation promoting factors for directional actin filament elongation: Allosteric regulation and multimerization on the membrane
S. Suetsugu
Seminars in Cell & Developmental Biology. 2013, 24, 267-271
The flatness of Lamellipodia explained by the interaction between actin dynamics and membrane deformation
C. Schmeiser, C. Winkler
Journal of Theoretical Biology. 2015, 380, 144-155
Real-Time Measurements of Actin Filament Polymerization by Total Internal Reflection Fluorescence Microscopy
J. Kuhn, T. Pollard
Biophysical Journal. 2005, 88, 1387-1402
The interaction of Arp2/3 complex with actin: Nucleation, high affinity pointed end capping, and formation of branching networks of filaments
R. Mullins, J. Heuser, T. Pollard
Proceedings of the National Academy of Sciences. 1998, 95, 6181-6186
Super-Resolution Correlative Light and Electron Microscopy (SR-CLEM) Reveals Novel Ultrastructural Insights Into Dendritic Cell Podosomes
B. Joosten, M. Willemse, J. Fransen, A. Cambi, K. van den Dries
Frontiers in Immunology. 2018, 9,
The Actin-Based Nanomachine at the Leading Edge of Migrating Cells
V. Abraham, V. Krishnamurthi, D. Taylor, F. Lanni
Biophysical Journal. 1999, 77, 1721-1732
Electrostatics Control Actin Filament Nucleation and Elongation Kinetics
A. Crevenna, N. Naredi-Rainer, A. Schönichen, J. Dzubiella, D. Barber, D. Lamb, R. Wedlich-Söldner
Journal of Biological Chemistry. 2013, 288, 12102-12113
Actin disassembly clock determines shape and speed of lamellipodial fragments
N. Ofer, A. Mogilner, K. Keren
Proceedings of the National Academy of Sciences. 2011, 108, 20394-20399
A novel real time imaging platform to quantify macrophage phagocytosis
T. Kapellos, L. Taylor, H. Lee, S. Cowley, W. James, A. Iqbal, D. Greaves
Biochemical Pharmacology. 2016, 116, 107-119
Intracellular signalling during neutrophil recruitment
A. Mócsai, B. Walzog, C. Lowell
Cardiovascular Research. 2015, 107, 373-385
Neutrophil polarization: Spatiotemporal dynamics of RhoA activity support a self-organizing mechanism
K. Wong, O. Pertz, K. Hahn, H. Bourne
Proceedings of the National Academy of Sciences. 2006, 103, 3639-3644
Network Crosstalk Dynamically Changes during Neutrophil Polarization
C. Ku, Y. Wang, O. Weiner, S. Altschuler, L. Wu
Cell. 2012, 149, 1073-1083
The Wiskott-Aldrich syndrome: studies of lymphocytes, granulocytes, and platelets
H. Ochs, S. Slichter, L. Harker, W. Von Behrens, R. Clark, R. Wedgwood
Blood. 1980, 55, 243-252
The Wiskott-Aldrich syndrome: The actin cytoskeleton and immune cell function
Blundell, M. P., Worth, A., Bouma, G. & Thrasher, A. J.
Disease Markers. 2010, 29, 157-75
A Fundamental Role of Myh9 for Neutrophil Migration in Innate Immunity
A. Zehrer, R. Pick, M. Salvermoser, A. Boda, M. Miller, K. Stark, L. Weckbach, B. Walzog, D. Begandt
The Journal of Immunology. 2018, 201, 1748-1764