Contact Inhibition

LFP is a common measure of neuronal activity, but it is still not completely clear how the LFP is related to single neuron variables like synaptic or ionic currents, and membrane potentials. Computational models sometimes use as a description of the LFP the average membrane potential of the neurons of the network [75] (link), even though it seems definitely more likely that the LFP is rather more directly related to the synaptic activity [29] (link). The spectrum of the average membrane potential in our model has a faster decay at high frequencies than the measured LFP, and therefore does not reproduce it well (Figure S4). However, the information content of the average membrane potential turns out to be similar to the one of the recorded LFPs (Table 4).
On the opposite side, LFPs have been computed using compartmental neuron models [32] ,[51] (link). The model used in [51] (link) adopted the neuronal structure described in [76] (link): dendritic branches were divided into cilindrical compartments of 50 µm length. Each compartment contained many synapses, whose characteristics depended on the branch (apical, basal etc). The LFP was computed for every point in the space surrounding the neuron as the total extracellular potential originated by the trasmembrane currents of the hundreds of different compartments. In [32] the procedure was similar but the neuronal structure was reduced to a total of 15 compartments. In both models, LFPs were originated by synaptic currents on pyramidal neurons dendrites.
Here, we resorted to a similar but simpler approach, which takes into account that our model makes no attempt to replicate the spatial organization of cortical neurons, and thus the sum in space of currents has to be abstracted and simplified, as follows. To capture in a simple way the fact that pyramidal cells contribute the most to LFP generation because their apical dendrites are arranged in an approximate open field configuration, we assumed that the LFP is generated by the dipole-like dendrites of pyramidal cells, in which currents flow in the cell through apical excitatory synaptic contacts while they flow out through basal inhibitory contacts [77] . This suggests to model LFPs as the sum of the absolute values of AMPA and GABA currents (|I_A|+|I_G|) on pyramidal cells, which was the model we adopted in this work, and that was able to reproduce correctly both the power spectrum of recorded LFPs and its information content (Table 4, Figure 7B, and Figure S4). Taking the LFP to be a different linear combination of AMPA and GABA currents give rise to qualitatively similar results (Table 4 and Figure S4). LFP signals are high-passed at 1 Hz with a 4th order Butterworth filter to reproduce experimental recording procedures of [14] (link).

Synovial tissues were obtained from synovial biopsies of six patients with RA undergoing joint surgery (synovectomy or joint replacement by prosthesis implantation), who all met the criteria of the American College of Rheumatology [27 (link)]. The tissue samples were obtained during routine surgery at the Department of Orthopedics of the University of Regensburg, where approved by the local ethics committee and patients involved gave informed consent. Culture of SF was performed as described recently [5 (link)]. Following enzymatic digestion, fibroblasts were grown in DMEM (Biochrom, Berlin, Germany) containing 10% heat inactivated FCS (Gibco Life Technologies, Grand Island, NY, USA), 100 U/ml penicillin and streptomycin (PAA Laboratories GmbH, Linz, Austria) and cultured for four passages at 37°C in 10% carbon dioxide. The SF were stained for a fibroblast marker by immunohistochemistry. More than 95% could be stained positively for the fibroblast enzyme prolyl 4-hydroxylase and none were positive for the macrophage marker CD68 or the neutrophil marker cathepsin G after the second passage of cultivation with enzymatic digestion equalling passage 0 (data not shown). Routine tests for mycoplasms were negative. At 85 to 95% confluency, cells were passaged 1:2 and a part of the cells was harvested. Total RNA was extracted and stored at -70°C. Culture conditions were (and have to be) kept constant during the experiments. Passaging of the cells was performed at 85 to 95% confluency as fibroblasts exhibit contact inhibition (unpublished observations) and were passaged 1:2 to provide cell-cell contacts between the cells.

In our model we assume that the Wnt-activity of the individual cells is determined by the local curvature of the basal membrane. Thus, the crypt geometry impacts the lineage specification and differentiation and consequently the crypt turnover. In order to study these interrelations we set the shape parameter λ₁ to zero and varied the crypt length and width. By assigning the thresholds TP_WNT and TD_WNT fixed Gaussian curvatures 4×10⁻⁴/µm² and 0/µm², respectively, the shape changes resulted in a shifted position of these thresholds along the crypt axis. We found that the shape changes did result in quantitative changes of the systems behavior only. Selected results can be found in the Table S1. In all further simulations we considered a defined cell shape that agrees with experimental data on crypt geometry [8] (link). The crypt with this defined shape is called ‘reference crypt’ in the following. The parameters of the reference crypt are listed in Table 1.
In a series of simulations we varied the threshold TP_Wnt for a reference crypt (see Table S2). In this case the total number of cells remains approximately fixed. The changes result in changes of the size of the Paneth cell compartment (undifferentiated and Paneth cells) which are balanced by changes of the number of enteroytes and Goblet cells. A decrease of the size of the Paneth cell compartment increases the number of proliferative cells in the crypt and thus decreases the turnover time. We selected the position of the threshold TP_Wnt such that cell number of the Paneth cell compartment is about 40 [40] (link).
For a given position of TP_Wnt the steady state cell production of a crypt still depends on cell interaction parameters as well as internal parameters regulating fate decisions. For example the turnover is decreased as a result of an increase of the cell-cell interaction strength ε_c, an increase of the sensitivity to contact inhibition V_p or a decrease of the Wnt-activity threshold TD_Wnt. We used TD_Wnt, together with F_A^other and η_BM, to fit the turnover the results of the BrdU labelling experiments.
This was most efficient provided that the average apoptosis rate in the crypt was smaller than about 5% per day. Such low apoptosis rates were ensured assuming a high cell-knot interaction constant ε_k>5 nNm for all cells. Note that a migration force F_A^other>0 was required to fit the BrdU labelling data.
Steady state cell patterning also underlies a complex regulation as seen from the organisation of the Paneth cell population. For a given crypt geometry and Wnt-activity threshold TP_Wnt the sum of undifferentiated and Paneth cells is approximately fixed. Thereby, the number of Paneth cells depends sensitively on the cell-knot interaction strength ε_k^paneth, the migration force for Paneth cells F_A^Paneth and the Notch-activation strength LP^Paneth. Stable Paneth cell adhesion to the BM over their life time t_p required ε_k^paneth≥35 nN defining a constraint to this parameter. Moreover, a minimum ‘migration force’ F_A^Paneth of about 7nN is required to ensure that Paneth cells remain confined at the crypt bottom. Thus, we adjusted the number of Paneth cells using LP^Paneth (Fig. 5).

In order to avoid cell–cell-contact-induced inhibition of cell proliferation due to cell confluency, we seeded 3-5 × 10⁵ cells per well in 6 wells plate. This procedure ensured that cells were in a sub confluent state after 1 day and 3 days of incubation. 10 μM of 5-bromo-2′-deoxyruridine (BrdU, Sigma-Aldrich) was added to cell cultures for 1 hour. After 1 hour pulse, the cells were fixed in ice-cold 70% ethanol dropwise on a vortex and left at 4 °C for 30 minutes, washed twice with PBS and suspended in 2 M HCl for 30 minutes at room temperature (RT) with occasional mixing. The cells were subsequently washed twice in PBS and 2.5ul of anti-BrdU mAb (B44, BD biosciences) in BSA-PBS-Tween (PBS + 0.1% BSA + 0.2% Tween20, pH 7.4) were added to the cell pellet at RT for 30 minutes in the dark. After washing the cells twice, 2.5ul of goat anti-mouse FITC (BD555988, goat anti mouse) in PBS-Tween was added to the cells at RT for 30 minutes. The pellet was washed in PBS, 10μg/ml of RNAse (Ribonuclease A, R4642, Sigma-Aldrich) was added for 15 minutes at 37 °C and 50μg/ml of PI (Propidium Iodide, Sigma-Aldrich, #P4170) was added prior flow cytometry analysis. We collected at least 30,000 events at the BD FACS Canto II (BD Biosciences).