Fig 1.
Generalized scheme of C3b amplification and regulation.
C3b activation can occur in fluid phase or on surface. Under physiological conditions, C3b amplification in fluid phase is prevented by FH. On cell surfaces, amplification may occur, depending on whether or not FH can be acquired there. If FH cannot be acquired in sufficient amounts, there is a steady but slow conversion of C3 to C3b initiating amplification. C3b then associates with factor B (FB) to form the C3 proconvertase (C3bB), which is activated by factor D, resulting in the active C3 convertase (C3bBb). C3bBb in turn is able to proteolytically convert C3 into C3b at a high rate, starting the loop again and thus acting as an amplifier of C3b production. The amplification loop can be controlled by FH at two stages. Firstly, FH competes with FB for C3b binding, acting as a cofactor for C3b degradation to iC3b. Secondly FH is able to accelerate the decay of C3bBb, reducing proteolytic C3b generation.
Fig 2.
Example C3b distributions with differently weighted trade-off.
This figure illustrates the attack decision problem the host faces for different C3b distributions on host and pathogen cell surfaces. All cells with a higher amount of C3b bound to the cell surface than the threshold will be attacked. (A) Equally weighted trade-off; the probability of erroneously attacking a host cell is equal to the probability of erroneously not attacking a pathogen cell. (B) Trade-off weighted in favour of the effectiveness in clearing mimetic pathogens. (C) Trade-off weighted in favour of low autoreactivity.
Fig 3.
Scheme of C3b surface binding.
Proteolytic cleavage of C3 by either fluid (denoted by the prefix f) or surface bound (denoted by the prefix b) C3 convertase (fC3bBb or bC3bBb) results in a reactive intermediate (fnC3b or bnC3b) which is able to covalently attach to surfaces due to an exposed thioester bond. While chemically there is no difference between fnC3b and bnC3b, we distinguish them in the model, because we assume a higher binding rate of bnC3b to the originating surface (see text and S5 Appendix).
Fig 4.
Plot of essential quantities as functions of the benefit-to-cost ratio, computed by numerical optimization.
a) Mean probabilities of being attacked by phagocytes for pathogen and host cells. b) Payoff. c) Optimal number of binding sites. d) Classification threshold. e) Dissociation constant. Standard deviation is indicated. Maximum number of binding sites nmax, 1001; metabolic cost c, 0.1 for both the host and pathogens, 20 runs. FH concentration was set to 1.61 μM.
Fig 5.
Plot of the fitness landscape of pathogens with fixed host parameters.
Equal pathogen and host concentrations were used. Each blue dot represents one individual with a certain investment into the number of binding sites produced (x-axis location) and a certain fitness (y-axis location, determined by the attack probability solely). The red line represents the goodness of thresholding, which is the relative fitness of a host with attack threshold t, compared to the fitness of a host using the optimal attack threshold t*. Host investment into number of binding sites is arbitrarily fixed to 40% (left) and 60% (right). In the right subfigure, pathogens are restricted to produce a maximum of 90% of host binding sites.
Fig 6.
Computed C3b opsonization per cell if factor H can be acquired on the cell surface of the pathogen.
Upper panels, distributions of opsonization for different C. albicans concentrations. Microbial cell densities for subfigures (I)-(V) can be seen from the corresponding points in the lower panel (see also text). The dotted vertical line in each subfigure represents the mean value of the optimal threshold interval to distinguish the two signals. Lower panel, mean opsonization on host and pathogen surfaces as functions of pathogen concentration, double logarithmic plot. Erythrocyte counts used are indicated by the light blue shaded area (mean 4.64 ⋅ 1012 erythrocytes per litre, low: 1st percentile, high: 99th percentile, see S1 Fig). C3b opsonization is similar to the case where no FH can be aquired up to a C. albicans density of approx. 5 ⋅ 1011 (i.e., erythrocytes are still 10 times more abundant). Beyond this point crypsis is successful with low opsonization in general. If the pathogen concentration increases even more, competition for factor H dominates and opsonization of both species increases with higher opsonization of host cells until the point where the inflow of C3 is not sufficient to maintain opsonization and C3b decreases again, notably faster for pathogen cells. Separability of the two signals for macrophages is only possible for low pathogen densities. At high pathogen load, the host C3b distribution is similar to the pathogen’s C3b distribution at low pathogen load (subfigures (I) and (V)).
Fig 7.
Mean opsonization of erythrocytes and C. albicans cells with different regimes and possible attack thresholds indicated.
Same data as in Fig 6. The two dotted horizontal lines represent possible attack thresholds. Upper line, optimal threshold derived from simulations on E. coli; lower line, already a single C3b molecule is sensed on the surface. Cells with values above those lines would be attacked. Green, non-successful crypsis; blue, regime of successful crypsis; red, autoreactivity. These regimes are indicated for the upper attack threshold. Using the lower threshold, autoreactivity may occur even for low pathogen concentrations. For any of these thresholds and for any other threshold tested (see subfigures of Fig 6), host opsonization drastically increases for high pathogen concentrations, making autoreactivity nearly unavoidable.
Fig 8.
Computed mean C3b opsonization per cell if factor H cannot be acquired on the surface of the microbial cell.
Erythrocyte counts used are indicated by the light blue shaded area (mean 4.64 ⋅ 1012 erythrocytes per litre, low: 1st percentile, high: 99th percentile, see S1 Fig). Microbial cell densities for subfigures (I)-(V) can be seen from the corresponding points in the lower panel. Curves represent mean C3b deposition on host and E. coli surfaces (double logarithmic plot). Subfigures represent C3b distributions at several E. coli concentrations. The dotted vertical lines in subfigures (I)-(V) represent the mean value of the optimal threshold interval to distinguish the two signals described in the section above. C3b opsonization remains low for host cells and high for microbial cells in a wide range of microbial cell densities and the signals are mostly well separable. Only for very large microbial cell densities they become inseparable because of insufficient production of C3 (see S3 Fig).
Fig 9.
Effectiveness in clearing C. albicans cells from the blood of mongrel dogs based on varying infusion rates of C. albicans into the portal vein.
Data was taken from Stone [53], Fig 8. Data was converted from samples positive for C. albicans to relative effectiveness in clearing C. albicans cells and scaled to units used in our model for better comparability. Top: Samples with no C. albicans cells present after 10 minutes, measured in different compartments of the blood system. For infusion rates below 1011 cells per litre per minute, C. albicans cells are removed to a great deal by the liver and cannot be detected in subsequent compartments of the blood system. For higher infusion rates C. albicans cells are present in all compartments. Bottom: Comparison to results of our model. The predicted C3b opsonization (red line) correlates to the effectiveness in clearing C. albicans from the blood (black lines). High opsonization means clear identifiability of mimetic pathogens and therefore easy clearance. As the predicted opsonization decreases, also a decrease in clearance of C. albicans cells can be observed, especially in compartments subsequent to the liver (dashed line).