Fig 1.
Identification of different level SCPs involved in neurite outgrowth and their incorporation into multicompartmental ODE model.
(A) Based on our observations dystrophic bulbs (right panel) revealed by tubulin staining are 8–10 times larger than physiological growth cones (left panel). Characteristics of dystrophic bulbs are an accumulation of anterograde vesicles [35] as well as disorganized microtubules [3]. (B) The three major SCP types, Production of Membrane Components, Vesicle Transport & Exocytosis and Microtubule Growth, describe essential sub-cellular functions involved in neurite outgrowth. We labeled them as Level-1 SCPs and identified their Level-2 children and Level-3 grandchildren SCPs. (C) To model membrane production at the Trans-Golgi network (TGN) and delivery to the growth cone plasma membrane (GC-PM) via vesicle transport, we extended a dynamical model that simulates vesicle transport between the endoplasmic reticulum and the Golgi [8]. In our version, new synthesized membrane is added to the Trans-Golgi network from where it is transported to the growth cone plasma membrane by vesicular transport. Vesicles bud from the TGN, move along the microtubules via active kinesin mediated transport and fuse with the growth cone plasma membrane, leading to neurite shaft growth. The vesicles pass through three intermediate compartments: the cell body cytoplasm (CBC), the neurite shaft cytoplasm (NSC) and the growth cone cytoplasm (GCC). In each compartment kinesin has a different affinity for microtubules, leading to varying fractions of vesicles that are actively transported via kinesin along the MT. Retrograde vesicles are generated via endocytosis at the growth cone plasma membrane and move along the microtubule towards TGN through dynein mediated active transport. Vesicle budding at the TGN or GC-PM is mediated by the interaction of recruitment factors and coat proteins, and vesicle fusion with the TGN or the growth cone membrane by the formation of SNARE complexes between vesicle(v)-SNAREs and target(t)-SNAREs, catalyzed by local tethering machineries. Motor proteins are bound to vesicles through motor protein receptors. AG/BG label vesicles that bud from the TGN with coat protein A/B, APM/BPM vesicles that bud from the GC-PM with coat protein A/B. Since at steady state almost all anterograde vesicles bud with coat protein B from the TGN, and almost all retrograde vesicles bud with coat protein A from the GC-PM, we highlighted their transport routes in brighter colors. (D) To simulate MT growth, we consider two different MT pools, stable and dynamicMTs. After nucleation new MTs are added to the pool of dynamic MTs that is characterized by alternating phases of growth and catastrophic breakdown. The frequency and duration of these phases depend on the tubulin concentration (regulated by the SCP Tubulin Sequestration) and GTP hydrolysis rate (SCP GTP Hydrolysis). Consequently, the length distribution of the dynamic MT pool and the degradation rate of dynamic MTs depends on the activity of both SCPs (S2 Fig). Dynamic MTs are either degraded or converted into stable MTs that form the growing neurite scaffold.
Fig 2.
Top-down based SCP modelling of whole cell dynamics.
Our pipeline for the generation of dynamical models that allow the analysis of relationships between sub-cellular processes (SCPs) during whole cell responses consists of two major steps. First, we build multicompartmental ODE models for the simulation of SCP activities that are based on literature curated data (Step 1a-d). In the second step we develop analytical predictions for kinetic parameters at steady state that allow a systematic analysis of SCP interactions (Step 2a-d).
Fig 3.
Neurites grow with different outgrowth velocities.
Neurons were dissected from rat cortical brain, incubated for 16h to allow initial growth, and followed by image acquisition every 6h up to 70h after plating. (A-B) The growth dynamics of two example neurons, one with a low (A) and one with a high (B) outgrowth velocity, are shown over given time-period. (C) At each timepoint we quantified the length of the longest neurite of each neuron. Histograms show the length distribution of all longest neurites at the indicated timepoints. (D) At each timepoint we identified the top and bottom 10% and 25% quantile length as well as the median length. Exponential interpolation of the lengths for each selected quantile documented outgrowth velocities ranging from 0 to ~20 μm/h.
Fig 4.
Simulation of vesicle transport and microtubule growth during neurite outgrowth.
(A-B) We identified a set of kinetic parameters (S7 Table) that allows neurite outgrowth via coordinated neurite shaft (A) and microtubule bundle growth (B) with a velocity of 10 μm/h. (C) The growing neurite shaft cytoplasm (NSC) within the growing neurite acts as a sink for anterograde and retrograde vesicles, causing an accumulation of vesicles within this compartment. (D) Our identified set of kinetic parameters allows NOG without violation of the model constraints that we selected to define physiological outgrowth conditions.
Fig 5.
Generation of an analytical solution for the prediction of kinetic parameters at steady state.
(A) The development of the analytical solution depends on the categorization of membrane fluxes based on their destination compartment. Such classification distinguishes four different membrane types (I-IV) (that should not be confused with the four different vesicle types we show in Fig 2B). Initial and final anterograde and retrograde transport rates (which refer to budding and fusion rates at the TGN and GC) are the sum of the transport rates of the encircled membranes types. (B) Calculation of kinetic parameter for v-SNARE V. VV/YY/UU refer to total count of SNAREs, V/Y/U describe concentration of SNAREs (per membrane area). See supplementary methods for complete derivation of analytical solution. (C) Microtubule bundle (MTB) growth is mediated by the conversion of dynamic MTs into stable MTs. Dynamic MTs nucleate de-novo, followed by their degradation or stabilization. (D) Nucleation, stabilization and degradation rates for dynamic MTs are calculated as shown. (E) To verify our analytical solution we analyzed, whether our predicted parameter sets allow neurite outgrowth with the selected velocity and without violation of model constraints. For each velocity, we selected 6 different parameter sets that differ in the number of v-SNARE V and the tethering rate at the growth cone plasma membrane (S5A Fig). Every 500 min over a simulation period of 5,000 min (~3.5days), we documented the indicated outputs. Averages and standard deviations were calculated for each velocity. As shown for a velocity of 15 μm/h, our analytical solution predicts steady state dynamics that match the anticipated model constraints (horizontal lines) with high accuracy.
Fig 6.
Redundancies among vesicle transport level-3 sibling SCPs.
To analyze the relationships between Level-3 SCPs, we used our analytical solution to predict steady state dynamics that enable neurite outgrowth for specified velocities. (A), (B) & (C) Level-3 SCPs show complementary relationships between their activities to generate higher level SCP function without violation of the model constraints. (A) Different activities of the SCPs Coat Recruitment and Formation at TGN and Vesicle Invagination and Scission at TGN were modeled by changing the amount of Recruitment Factor 1 and the budding rate at the TGN. SCP activities were inversely related and increased with increasing velocity. Line colors indicate selected velocities as shown in (G). (B) A similar SCP redundancy was observed for the SCPs Kinesin Recruitment to Vesicle (simulated by # number of kinesin receptors) and Kinesin Mediated Vesicle Transport along the MT (simulated by fraction of bound kinesin). (C) Inverse relationship between SCP activities was also observed for the SCPs Vesicle Tethering (simulated via the tethering rate at the GC) and Vesicle Fusion (simulated by amount # of v-SNARE V). (D) Velocities were color coded in each figure as indicated. (E) & (F) The more a Level-2 SCP activity is generated by a Level-3 SCP that contains a vesicle membrane protein, the higher the SCP activity of membrane protein production to compensate for the loss of membrane protein in the growing NSC reservoir. (E) In dependence of the selected fraction of MT-bound kinesin, vesicles need a different amount of kinesin receptors to ensure NOG without violation of the model constraints. A higher kinesin receptor concentration per vesicle directly translates into the need for a higher kinesin production rate. Lines refer to pre-defined fractions of MT-bound kinesin: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 (from top to bottom). (F) Different tethering rates demand different v-SNARE V concentrations per vesicle and consequently different V production rates to ensure NOG without violation of the model constraints (t-SNARE Y is kept constant). Lines refer to different tethering rates: 2.5 x10-6, 3 x10-6, 3.5 x10-6, 4 x10-6, 4.5 x10-6, 5 x10-6 (from top to bottom).
Fig 7.
Redundancies among microtubule growth Level-3 sibling SCPs.
(A) Summary of the basic reaction for the simulation of MT growth. (See S1 Fig) for details. (B), (C), (D) & (E) Level-3 SCPs that define sub-functions of the Level-2 SCP Dynamic MT growth show complementary activities to allow NOG without violation of the model constraints. Multiple combinations of the SCP activities Tubulin Sequestration, GTP Hydrolysis and Nucleation of Dynamic MTs enable NOG with a given velocity. (B-C) The influence of the SCPs Tubulin Sequestration (which determines the effective tubulin concentration) and GTP Hydrolysis on the length distribution (B) and degradation rate (C) of the dynamic MTs were determined in a pre-simulation using a stochastic model for the simulation of single dynamic MT growth (Margolin et al). Colored lines refer to the selected GTP hydrolysis rates shown in (B) and (C) (pink: 0.72/sec, d) and (yellow: 0.675/sec, e). (D-E) Multiple combinations of dynamic MT nucleation rates and effective tubulin concentrations allow NOG under a given velocity for each GTP hydrolysis rate, as shown for the hydrolysis rate of 0.72/sec (d) and 0.675/sec (e). (F) Velocities in (D) and (E) were color coded as indicated.
Fig 8.
Loss of function of Level-2 SCPs requires multiple adaptations to allow NOG under physiological conditions.
We predicted a parameter set that allows steady neurite outgrowth with a velocity of 10 μm/h. To investigate Level-2 SCP dependencies we reduced the activity of the SCP Vesicle budding at the TGN by reducing the amount of Recruitment Factor 1 without compensatory increase of the budding rate. In consequence, the activities of multiple Level-2 SCPs needed to be coordinatively adapted to secure neurite outgrowth under physiological conditions (as defined by our model constraints). One possible adaptation involves the reduction in the activity of the SCPs Membrane Lipid Production, of Anterograde Microtubule-Based Vesicle Transport (via reduced kinesin receptors), of Vesicle Exocytosis (via reduced v-SNARE V) and of Membrane Protein Production of the involved transmembrane molecules. Since this option includes a constant cycling rate (i.e. rate of back transported membrane), it causes a reduction in neurite outgrowth velocity.
Fig 9.
Imbalanced SCP dynamics disturb neurite outgrowth.
(A-B) We predicted four sets of kinetic parameters that allow coordinated NOG at the velocities 5, 10, 15 and 20 μm/h. To simulate the effect of uncoordinated vesicle SCP dynamics we decreased the count and production rate of v-SNARE V to 25%, 50% and 75% of the original prediction, without modifying any other parameters. Numerical simulations predict that reduced exocytosis causes an increase in the count of vesicles in the growth cone cytoplasm (A) without reducing NOG velocity (B). (C) We validated our prediction by analyzing neurite outgrowth after knockdown of the v-SNARE VAMP7. P1 rat cortical neurons transfected with siRNA against VAMP7 or scrambled siRNAs were stained for β-III tubulin to document neurite growth across the microgroove of the chamber. In agreement with our prediction, VAMP7 knock down did not decrease total outgrowth length. It caused a significant number of physiological growth cones to turn into dystrophic bulbs. (D) Analysis of quantified neurite lengths confirmed that there was no significant difference in outgrowth length. Shown are average values and standard deviations (three independent experiments). (E) Neurites growing from neurons after VAMP7 knock down showed a significant increase in the number of dystrophic bulbs, indicative for impaired NOG. (F) To simulate the effect of reduced MT stabilization, we reduced the stabilization rate that turns dynamic into stable MTs to 25%, 50% and 75% of the original prediction, without changing the predicted values for all other kinetic parameters. Numerical simulations propose that decreasing stabilization leads to a significant decrease in NOG outgrowth over the investigated time. (G) We validated our predictions by knock down of the microtubule crosslinking protein MTCL1. MTCL1 knock down caused reduced NOG outgrowth and dystrophic bulb formation. (H) Outgrowth quantification confirms significant decrease in NOG (3 independent experiments). (I) Mtcl1 also significantly increased the number of dystrophic bulbs. *p<0.05, **p<0.01, ***p<0.001based on unpaired t-test for all panels.