A Computational and Experimental Study of the Regulatory Mechanisms of the Complement System
The complement system is pivotal to defending against invading microorganisms ., The complement proteins recognize conserved pathogen-associated molecular patterns ( PAMPs ) on the surface of the invading pathogens 1 to initiate the innate immunity response ., The complement activity also enhances adaptive immunity 2 , 3 and participates in the clearance of apoptotic cells 4 as well as damaged and altered self tissue ., The complement proteins in the blood normally circulate as inactive zymogens ., Upon stimulation , proteases in the system cleave the zymogens to release active fragments and initiate an amplifying cascade of further cleavages ., There are three major complement activation routes: the classical , the lectin and the alternative pathways 5 ., Regardless of how these pathways are initiated , the complement activity leads to proteolytic activation and deposition of the major complement proteins C4 and C3 , which induces phagocytosis , and the subsequent assembly of the membrane attack complex which lyses the invading microbes ., However , complement is a double-edged sword; adequate complement activation is necessary for killing the bacteria and removing the apoptotic cells , while excessive complement activation can harm the host by generating inflammation and exacerbating tissue injury ., Dysregulation of the balance between complement activation and inhibition can lead to rheumatoid arthritis 6 , systemic lupus erythematosus 7 , Alzheimers disease 8 and age-related macular degeneration 9 ., Since the final outcome of complement related diseases may be attributable to the imbalance between activation and inhibition 10 , manipulation of this balance using drugs represents an interesting therapeutic opportunity awaiting further investigation ., In light of this potential , complement inhibitors such as factor H and C4b-binding protein ( C4BP ) are critical since they play important roles in tightly controlling the proteolytic cascade of complement and avoiding excessive activation ., Therefore , a systems-level understanding of activation and inhibition , as well as the roles of inhibitors , will contribute towards the development of complement-based immunomodulation therapies ., Complement is usually initiated by the interaction of several pattern-recognition receptors with the surface of pathogens ., C-reactive protein ( CRP ) 11 and ficolins are two initiators of the classical and lectin pathways , which boost immune responses by recognizing phosphorylcholine ( PC ) or N-acetylglucosamine ( GlcNAc ) , respectively , displayed on the surface of invading bacteria 12 , 13 , 14 ., Recently , it was discovered that under local infection-inflammation conditions as reflected by pH and calcium levels , the conformations of CRP and L-ficolin change which leads to a strong interaction between them 15 ., This interaction triggers crosstalk between classical and lectin pathways and induces new amplification mechanisms , which in turn reinforces the overall antibacterial activity and bacterial clearance ., On the other hand , C4BP , a major complement inhibitor is synthesized and secreted by the liver ., The estimated plasma concentration of C4BP is 260 nM under normal physiological condition 16 but its plasma level can be elevated up to four-fold during inflammation 17 , 18 ., Through its α-chain 19 , 20 , C4BP modulates complement pathways by controlling C4b-mediated reactions in multiple ways 21 , 22 , 23 ., Further , C4BP has been proposed as a therapeutic agent for complement-related autoimmune diseases on the premise that mice models supplemented with human C4BP showed attenuation in the progression of arthritis 24 ., Therefore , it is important to understand the systemic effect and the underlying inhibitory mechanism of C4BP ., With this background , we constructed a detailed computational model of the complement network consisting of a system of ordinary Differential equations ( ODEs ) ., The large model size and the many unknown kinetic rate parameters lead to significant computational challenges ., Using the technique developed in 25 , we approximated the ODE dynamics as a dynamic Bayesian network 26 and used it to estimate the model parameters ., After constructing the model , we investigated the enhancement mechanism induced by local inflammation and its interplay with the inhibition mechanism induced by C4BP ., Our studies confirmed and further elucidated the previous experimental findings 15 ., Specifically , using our model we established a detailed relationship between the antimicrobial response and the strength of the crosstalk between CRP and L-ficolin as determined by various combinations of the pH and calcium levels ., We also found that C4BP prevents complement over-activation and restores homeostasis , but it achieves this in two distinct ways depending on whether the complement activity was initiated by PC or GlcNAc ., Finally , the computational model suggested that the major inhibitory effect of C4BP is to potentiate the natural decay of C3 convertase ( C4bC2a ) ., These findings regarding the role of C4BP were experimentally validated ., An earlier mathematical study 27 of the complement system focused on the classical pathway ., This study assumed the dynamics to be linear , which is a severe restriction ., A later study by Korotaevskiy et al 28 more realistically assumed the dynamics to be non-linear ., It also included the alternative pathway ., The main focus was to derive quantitative conclusions regarding the lag time of the immune response as the initial concentrations of the constituent proteins were varied ., Relative to 28 , our model additionally includes the lectin pathway and the recently identified amplification pathways induced by the crosstalk between CRP and L-ficolin 15 ., On the other hand , given our focus on the up- and down- regulation mechanisms of the complement , we do not model the alternative pathway in detail since its role is to maintain a basal level of complement activation ., Instead , this basal activity and the effects of other mechanisms such as C2 bypass 29 are implicitly captured by the kinetic parameters in our model ., Given our focus on the amplification and down-regulation mechanisms of complement , we included in our model only the key proteins in the classical and lectin pathways ., The basal activity maintained by the alternative pathway and other mechanisms are implicitly captured by the kinetic parameters in our model ., A schematic representation of the model structure is shown in Figure 1A ., The cascade of events captured by the model can be described as follows ., The classical pathway is initiated by the binding of antibodies or CRP to antigens or PAMPs ., In our model , in order to decouple the involvement of adaptive immune response , the classical pathway is triggered by the binding of CRP to PC , which is a ligand often displayed on the surface of the invading bacteria 30 , 31 ., Deposited CRP then binds to C1-complex ( formed by C1q , two molecules of C1r , and two molecules of C1s ) that is further activated ., The activated C1-complex recruits C4 leading to the cleavage of C4 to its fragments , C4b and C4a ., After binding of C2 to C4b , the same protease complexes are responsible for generating fragments , C2a and C2b , by cleaving C2 ., The C2a and C4b then form the C4bC2a complex , which is an active C3 convertase , cleaving C3 to C3a and C3b ., The formation of C3b exposes a previously hidden thioester group that covalently binds to patches of hydroxyl and amino groups on the bacterial surface 32 ., The surface-deposited C3b plays a central role in all subsequent steps of the complement cascade: ( 1 ) it acts as an opsonin that enhances the binding and leads to the elimination of bacteria by the phagocytes , ( 2 ) it induces the formation of membrane attack complex leading to the lysis of bacteria ., Since the concentration of the deposited C3 reflects the antibacterial activity of complement , we terminated our model at this step to simplify the network ., On the other hand , the lectin pathway is initiated by the binding of mannose-binding lectin ( MBL ) or ficolins to PAMPs on the pathogen surface ., In our model , we focused on the lectin pathway initiated by L-ficolin as it can interact with CRP and induce crosstalk between classical and lectin pathways ., L-ficolin recognizes various PAMPs on the bacterial surface via the acetyl group on the GlcNAc moiety 33 , 34 ., Therefore , in our model the lectin pathway was triggered by binding of L-ficolin and GlcNAc onto the bacterial surface ., Subsequently , a protease zymogen called MASP-2 is recruited and activated ., Activated MASP-2 cleaves C4 and C2 to form C4bC2a which is C3 convertase ., At this point , the classical pathway and lectin pathway merge at the cleavage step of the central complement protein , C3 , and hence constitutes the endpoint of our model ., As discovered in 15 , infection-induced local inflammation conditions ( slight acidosis and hypocalcaemia ) provoke a strong crosstalk between CRP and L-ficolin 15 ., This elicits two new complement-amplification pathways , which reinforce the classical and lectin pathways ., Since we aimed to study the complement activation and modulation under pathophysiological conditions , we included these two amplification pathways ( Figure 1A , purple ) in our model ., Infection by bacteria containing PC will induce the CRP:L-ficolin mediated amplification pathway: PC→CRP:L-ficolin→MASP2→C4→C2→C3 ., On the other hand , infection by bacteria containing GlcNAc will induce the CRP:L-ficolin mediated amplification pathway: GlcNAc→CRP:L-ficolin→C1→C4→C2→C3 ., The complement allows a rapid attack to intruding bacteria while at the same time protecting the host cells from over-activation ., C4BP , a major inhibitor of complement activation , was reported to either accelerate the decay of the convertases or aid proteolytic inactivation of key players in the pathway into inactive forms such as factor H 32 but the systemic effect of C4BP has remained unclear ., Hence , in our model , we included this major multifunctional inhibitor ., Upstream of the complement cascade , C4BP competes with C1 for the immobilized CRP 23 ., Downstream to this , C4BP binds to C4b and serves as a cofactor to the plasma serine protease factor I in the cleavage of C4b both in the fluid phase and when C4b is deposited on bacterial surfaces 21 ., In addition , C4BP is able to prevent the assembly of the C3 convertase and accelerate the natural decay of the complex 35 ., All of the above effects of C4BP are considered in our model and the relevant components are depicted as red bars in Figure 1A ., The reaction network diagram of the model is shown in Figure 1B ., Processes such as protein association , degradation and translocation are modeled with mass action kinetics and processes such as cleavage , activation and inhibition with Michaelis-Menten kinetics ., The resulting ODE model consists of 42 species , 45 reactions and 85 kinetic parameters with 71 unknown ., The details can be found in the supporting information ( Text S1 ) ., Due to the large model size and many unknown kinetic parameters , tasks such as parameter estimation and sensitivity analyses became very challenging ., Hence , we applied the probabilistic approximation technique developed by Liu et al 25 to derive a simpler model based on the standard probabilistic graphical formalism called Dynamic Bayesian Networks ( DBNs ) 26 ., Briefly , this approximation scheme consists of the following steps:, ( i ) Discretize the value space of each variable and parameter into a finite set of intervals ., ( ii ) Discretize the time domain into a finite number of discrete time points ., ( iii ) Sample the initial states of the system according to an assumed uniform distribution over certain intervals of values of the variables and parameters ., ( iv ) Generate a trajectory for each sampled initial state and view the resulting set of trajectories as an approximation of the dynamics defined by the ODEs system ., ( v ) Store the generated set of trajectories compactly as a dynamic Bayesian network and use Bayesian inference techniques to perform analysis ., A more detailed description of this construction can be found in the Methods section while we explain in the Discussion section how we fixed the number of trajectories to be generated and the maximum time point upto which the trajectories are to be constructed ., In the ODE model the PC-initiated and GlcNAc-initiated complement cascades are merged for convenience ., By suppressing these two cascades to one at a time ( by setting the corresponding expressions in the reaction equations to zero ) , we constructed two dynamic Bayesian networks; one for the PC-initiated complement cascade and the other for GlcNAc-initiated complement cascade ., The range of each variable and parameter was discretized into 6 non-equal size intervals and 5 equal size intervals , respectively ., The time points of interest were set to {0 , 100 , 200 , … , 12600} ( seconds ) ., Each of the resulting DBN approximations encoded trajectories generated by sampling the initial values of the variables and the parameters from the prior , which was assumed to be uniform distributions over certain intervals ., The quality of the approximations relative to the original ODEs dynamics was sufficiently high and the details can be found in the supporting information ( Figure S1 ) ., The values of initial concentrations and 14 kinetic parameters were obtained from literature data ( Table S1 and Table S2 ) ., To estimate the remaining 71 kinetic parameters , we generated test data by incubating human blood under normal and infection-inflammation conditions with beads coated with PC or GlcNAc followed by immunodetection of the deposited CRP , C4 , C3 and C4BP in time series ., For PC-beads , the concentration levels of deposited CRP , C4 , C3 and C4BP were measured at 8 time points from 0 to 3 . 5 h ( Figure 2A , B , red dots ) ., For GlcNAc-beads , the concentration levels of deposited MASP-2 , C4 , C3 and C4BP were also measured at 8 time points from 0 to 3 . 5 h ( Figure 2C , D , red dots ) ., To estimate unknown kinetic parameters , a two-stage DBN based method 25 was deployed ., In the first stage , probabilistic inference applied to the discretized DBN approximation was used to find the combination of intervals of the unknown parameters that have the maximal likelihood , given the evidence consisting of the test data ., As mentioned above , each unknown parameters value space was divided into 5 equal intervals and the inference method called factored frontier algorithm 35 was used to infer the marginal distributions of the species at different time points in the DBN ., We then computed the mean of each marginal distribution and compared it with the time course experimental data ., To train the model by iteratively improving fitness to data , we modified the tool libSRES 36 and used its stochastic ranking evolutionary strategy ( SRES ) , to search in the discretized parameter space consisting of 571 combinations of interval values of the unknown parameters ., The result of this first stage was a maximum likelihood estimate of a combination of intervals of parameter values ., In the second stage we then searched within this combination of intervals having maximal likelihood ., Consequently , the size of the search space for the second stage was just 1/571 of the original search space ., We used the SRES search method and the parameter values thus estimated are shown in Table S2 ., In principle , given the noisy and limited experimental data and the high dimensionality of the system , one could stop with the first stage 37 and try to work an interval of values for each parameter rather than a point value ., However , in our setting we wanted to use the ODE model too for conducting in silico experiments such as varying initial concentrations including the down and over expression of C4BP ., This would have been difficult to achieve by working solely with our current DBN approximation ., We address this point again in the Discussion section ., Figure 2A–2D shows the comparison of the experimental time course training data ( red dots ) with the model simulation profiles generated using the estimated parameters ( blue lines ) ., The model predictions fit the training data well for most of the cases ., In some cases , the simulations were only able to reproduce the trends of the data ., This may be due to the simplifications assumed by our model and further refinement is probably necessary ., We next validated the model using previously published experimental observations 15 ., In particular , normalized concentration level of deposited C3 was used to predict the antibacterial activity since C3 deposition initiated the opsonization process and the lysis of bacteria ., We first simulated the concentration level of deposited C3 at 1 h under different conditions ., We next normalized the results so that the maximum value among them equals to 95% which is the maximum bacterial killing rate reported in the experimental observations 15 ., The normalized values were then treated as predicted bacterial killing rates ., The simulation results are shown in Figure 2E and 2F as black bars ., Consistent with the experimental data ( Figure 2E , grey bars ) , our simulation showed that under the infection-inflammation conditions , the P . aeruginosa , a clinically challenging pathogen , can be efficiently killed ( 95% bacterial killing rate ) by complement whereas under the normal condition , only 28% of the bacteria succumbed ( Figure 2E , black bars ) ., Consistent with experimental data , our simulation results show that in the patient serum , depletion of CRP or ficolin induced a significant drop in the killing rate from 95% to 33% or 25% respectively , indicating that the synergistic action of CRP and L-ficolin accounted for around 40% of the enhanced killing effect ., However , in the normal serum , depletion of CRP or ficolin only resulted in a slight drop in the killing rate from 28% to 18% or 10% respectively ., Furthermore , simulating a high CRP level ( such as in the case of cardiovascular disease ) under the normal healthy condition did not further increase the bacterial killing rate ., As shown in Figure 2F , the simulation results matched the experimental data ., Thus , our model was able to reproduce the published experimental observations shown in both Figure 2E and 2F with less than 10% error ., This not only validated our model thus promoting its use for generating predictions , but also yielded positive evidence in support of the hypothesized amplification pathways induced by infection-inflammation condition ., It also suggested that the antibacterial activity can be simulated efficiently by the level of deposited C3 and this was used to generate model predictions described in later sections ., We performed local and global sensitivity analysis of the model to identify species and reactions that control complement activation during infection , and to evaluate the relative importance of initial concentrations and kinetic parameters for the model output ., To identify critical species , we first calculated the scaled absolute local sensitivity coefficients 38 for initial concentrations of major species using the COPASI tool 39 ., The model outputs were defined as the peak amplitude ( maximum activation ) and integrated response ( area under the activation curve that reflects the overall antibacterial activity ) of C3 deposition ., The results are shown in Figure 3A ., Both the peak amplitude and integrative response were strongly influenced by initial concentrations of C2 and C3 , and were mildly influenced by initial concentrations of C4BP , C1 and C4 ., In contrast , the low sensitivities of CRP , MASP-2 and L-ficolin indicate that over-expression of these proteins is unlikely to increase the antibacterial activity ., Interestingly , it was observed that the integrative response was more sensitive than the peak amplitude to the changes in the initial concentration of PC ., Since the concentration of PC is correlated to the amount of invading bacteria , this result implies that the maximum complement response level may not increase as the amount of bacteria increases but the overall response ( i . e . the area under the curve obtained by integrating the response level over time ) will be enhanced to combat the increased number of bacteria ., In order to identify critical reactions , we next computed global sensitivities for kinetic parameters ., To reduce complexity , we used the DBN approximations ., Multi-parametric sensitivity analysis ( MPSA ) 40 was performed on the DBN for PC-initiated complement cascade ( the details are presented in the Materials and Methods section ) ., The results are shown in Figure 3B ., Strong controls over the whole system are distributed among the parameters associated with the immobilisation of C3b with the surface , interaction between CRP and L-ficolin , cleavage of C2 and C4 , and the decay of C3 convertase ( see Figure 1B , reactions labeled in red ) ., The sensitivity of reactions associated with C3 , C2 and C4 is consistent with the local sensitivity analysis , which highlighted the significant role of major complement components ., The high sensitivity of interaction of CRP and L-ficolin confirms that the overall antibacterial response depends on the strength of the crosstalk between the classical and lectin pathways ., In addition , since the decay of C3 convertase is one of the regulatory targets of C4BP , the sensitivity of the system to a change in the rate of decay of C3 convertase suggested that the regulatory mechanism by C4BP plays an important role in complement ., Since the critical reactions identified are common in PC- and GlcNAc-initiated complement cascades , MPSA results using the other DBN will produce similar results and hence this analysis was not performed ., We next focused our investigation on the enhancement mechanism by the crosstalk and the regulatory mechanism by C4BP ., Under infection-inflammation conditions where PC-CRP:L-ficolin or GlcNAc-L-ficolin:CRP complex is formed , the amplification pathways are triggered ., Model simulation showed that if C1 and L-ficolin or CRP and MASP-2 competed against each other , the antibacterial activity of the classical pathway or lectin pathway might be deprived of the amplification pathways ( see Figure S2 ) ., Therefore , in order to achieve a stable enhancement , C1 and L-ficolin ( or CRP and MASP-2 ) must simultaneously bind to CRP ( or L-ficolin ) ., Further , the abilities of CRP and L-ficolin to trigger subsequent complement cascade were not affected by the formation of this complex ., This is consistent with the previous experimental observation that two amplification pathways co-exist with the classical and lectin pathways 15 ., According to 15 , slight acidosis and mild hypocalcaemia ( pH 6 . 5 , 2 mM calcium ) prevailing at the vicinity of the infection-inflammation triggers a 100-fold stronger interaction between CRP and L-ficolin compared to the normal condition ( pH 7 . 4 , 2 . 5 mM calcium ) ., This can be explained by the fact that the pH value and calcium level influence the conformations of CRP and L-ficolin which in turn govern their binding affinities ., Therefore , the overall antibacterial response which is influenced by the binding affinity of CRP and L-ficolin will be sensitive to the pH value and calcium level ., To confirm this and further investigate the effects of pH and calcium on the antibacterial response , we simulated the complement system under different pH and calcium conditions ., Based on the previous biochemical analysis 15 , we first estimated functions using polynomial regression to predict the binding affinity of CRP and L-ficolin for different pH values and calcium levels ( Figure 4A , B , right panel ) ., In the right panels of Figure 4A and 4B , the reported binding affinities 15 were normalized and are shown as dots ., By curve fitting the dots , we estimated polynomial functions that can be used to predict the binding affinity ., The curves of these functions are shown in red ., We then simulated the C3 deposition dynamics using the predicted binding affinities at pH ranging from 5 . 5 to 7 . 4 in the presence of 2 mM and 2 . 5 mM calcium ., The simulation time was chosen to be 3 . 5 h which is the time frame of the response peaks ., The results are shown in Figure 4A and 4B ., Under both 2 mM and 2 . 5 mM calcium conditions , decreasing pH induces not only the increase of the peak amplitude ( maximum activation ) but also hastens the peak time ( time of maximum activation ) ., To further compare the effects of the two calcium levels , the dose-response curves were generated as shown in Figure 4C ., The antibacterial response was predicted by simulating the system for 1 . 5 h ., At 2 mM calcium ( blue curve ) , the antibacterial response was clearly greater than at 2 . 5 mM calcium ( pink curve ) indicating that slight hypocalcaemia enhanced the antibacterial activity in a stable manner ., In addition , the pH-responses were reaching saturation levels when pH was near 5 . 5 ( Figure 4C ) , implying that the undesirable complement-enhancement by extreme low pH condition can be avoided ., This also suggests that the saturation of the pH-response was influenced by the calcium level in the milieu ., We next investigated the complement regulation by the major inhibitor , C4BP , under infection-inflammation conditions ., We varied the initial concentration of C4BP and simulated the PC- and GlcNAc- initiated complement under infection-inflammation conditions ., The simulation time was chosen to be 5 h which is slightly beyond the largest time point of our training experimental data ., The predicted effects of the initial concentration of C4BP on the antibacterial response in terms of C3 deposition are shown in Figure 5A and 5B ., For PC-initiated complement activation , when the starting amount of C4BP was perturbed around the normal level of 260 nM 16 , increasing C4BP level only delayed the peak time but did not decrease the peak amplitude significantly ., In contrast , reducing the initial C4BP level clearly hastened the complement activation and maximized the activity ., Interestingly , the GlcNAc-initiated complement activation ( Figure 5B ) behaved differently from the PC-mediated complement activation ( Figure 5A ) ., Around the normal level of 260 nM , perturbing the initial C4BP changed the maximum activity but did not affect the peak time , suggesting that C4BP plays distinct roles in regulating the classical and lectin pathways ., To experimentally verify the model predictions , we perturbed the initial amount of C4BP in the patient sera by, ( i ) spiking with purified C4BP ( high C4BP ) and, ( ii ) reducing it by immunoprecipitation ( low C4BP ) ., The resulting C4BP levels in the normal and patient sera are shown in Figure S3 ., The sera were then incubated with PC- or GlcNAc-beads to initiate complement ., Unaltered serum served as the normal control ., The time profiles of the deposited C4BP level was measured over 4 h using Western blot ( Figure 5C ) ., Comparing the kinetic profiles in the C4BP deposition initiated by both PC and GlcNAc , we observed the following order of peak time: high C4BP>normal C4BP>low C4BP , indicating that the pre-existing initial level of C4BP was indeed the driving force controlling the deposition of complement components onto the simulated bacterial surface ., We then measured the time profiles of deposited C3 ., Figure 5D shows that with PC-beads , high C4BP sera induced an early peak and low C4BP delayed the peak of C3 deposition ., The peak amplitude for all three conditions was at a similar level ., These observations are consistent with the simulation results shown in Figure 5A ., With GlcNAc-beads , reducing C4BP led to a slight increase in the peak height although the peak coincided with the normal condition ., In contrast , spiking the sera ( high C4BP ) delayed and lowered the peak amplitude of C3 deposition ., Thus the experimental results broadly agree with our model predictions presented in Figure 5B ., We next investigated how C4BP mediates its inhibitory function ., As shown in Figure 1A , the inhibitory effects of C4BP target different sites in complement:, ( a ) binding to CRP and blocking C1 ,, ( b ) preventing the formation of C4bC2a by binding to C4b ,, ( c ) acting as a cofactor for factor I in the proteolytic inactivation of C4b , and, ( d ) accelerating the natural decay of the C4bC2a complex , which prevents the formation of C4bC2a and disrupts already formed convertase ., To identify the dominant mechanism , we employed in silico knockout of the reactions involved for each mechanism and performed simulations ., Figure 6A–6D shows the model predictions ., Among the four inhibitory mechanisms , only the knockout of reaction, ( d ) significantly enhanced the complement activation suggesting that facilitating the natural decay of C4bC2a ( C3 convertase ) is the most important inhibitory function of C4BP ., This is consistent with our previous observations derived from sensitivity analysis , which identified the decay of C3 convertase as a critical reaction ., In addition , as the inhibitory effect of reaction, ( d ) is stronger than others , knocking out reaction, ( a ) and, ( b ) can even reduce the complement activity , which is counter-intuitive and emphasizes the significance of the systems-level understanding ., To confirm our hypothesis that the major inhibitory role of C4BP relies on accelerating the decay of C3 convertase , we measured the C4 cleavage at different time points ., Figure 6E ( black triangles ) indicates the inactive C4b fragments presented from the time points of 20 , 30 and 90 min under high , normal , and low C4BP conditions , suggesting that C4BP aided cleavage and inactivation of C4b , and thereby caused the natural decay of the C4bC2a ., Here , we developed an ODE-based dynamic model for the complement system accompanied by DBN-based approximations of the ODEs dynamics to understand how the complement activity is boosted under local inflammation conditions while a tight surveillance is established to attain homeostasis ., Previously published models of complement system have focused on the classical and alternative pathways 27 , 28 ., Our model includes the lectin pathway and more interestingly , the recently identified amplification pathways induced by local inflammation conditions 15 ., It also encompasses the regulatory effects of C4BP in the presence of enhanced complement activity ., The ODE model incorporated both the PC-initiated and GlcNAc-initiated complement together for convenience ., By setting the corresponding expressions to zero one at a time , two DBN approximations were then derived; one for the PC-initiated complement cascade and the other for GlcNAc-initiated complement cascade ., For constructing the DBN approximation from an ODE model , one needs to fix , the maximal time point upto which each trajectory is to be explored and , the number of trajectories to be generated ., is set to be suitably beyond the largest time point for which experimental data is available ., In the present study 3 . 5 h , is the largest time point of our training experimental data ., Based on this we set to be 5 h ., After constructing the model , we simulated the system upto 10 h and found no relevant dynamics after 3 . 5 h ., As for the choice of , the number of trajectories , ideally one would like to specify the acceptable amount of error between the actual and the approximated dynamics and use to determine ., This is however difficult to achieve due to the following: The dynamic Bayesian network we construct is a factored Markov chain ., It approximates the idealized Markov chain induced by the ODEs dynamics ., This i
The complement system is key to innate immunity and its activation is necessary for the clearance of bacteria and apoptotic cells ., However , insufficient or excessive complement activation will lead to immune-related diseases ., It is so far unknown how the complement activity is up- or down- regulated and what the associated pathophysiological mechanisms are ., To quantitatively understand the modulatory mechanisms of the complement system , we built a computational model involving the enhancement and suppression mechanisms that regulate complement activity ., Our model consists of a large system of Ordinary Differential Equations ( ODEs ) accompanied by a dynamic Bayesian network as a probabilistic approximation of the ODE dynamics ., Applying Bayesian inference techniques , this approximation was used to perform parameter estimation and sensitivity analysis ., Our combined computational and experimental study showed that the antimicrobial response is sensitive to changes in pH and calcium levels , which determines the strength of the crosstalk between CRP and L-ficolin ., Our study also revealed differential regulatory effects of C4BP ., While C4BP delays but does not decrease the classical complement activation , it attenuates but does not significantly delay the lectin pathway activation ., We also found that the major inhibitory role of C4BP is to facilitate the decay of C3 convertase ., In summary , the present work elucidates the regulatory mechanisms of the complement system and demonstrates how the bio-pathway machinery maintains the balance between activation and inhibition ., The insights we have gained could contribute to the development of therapies targeting the complement system .
The complement system , which is the frontline immune defense , constitutes proteins that flow freely in the blood ., It quickly detects invading microbes and alerts the host by sending signals into immune responsive cells to eliminate the hostile substances ., Inadequate or excessive complement activities harm the host and may lead to immune-related diseases ., Thus , it is crucial to understand how the host boosts the complement activity to protect itself and simultaneously establishes tight surveillance to attain homeostasis ., Towards this goal , we developed a detailed computational model of the human complement system ., To overcome the challenges resulting from the large model size , we applied probabilistic approximation and inference techniques to train the model on experimental data and explored the key network features of the model ., Our model-based study highlights the importance of infection-mediated microenvironmental perturbations , which alter the pH and calcium levels ., It also reveals that the inhibitor , C4BP induces differential inhibition on the classical and lectin complement pathways and acts mainly by facilitating the decay of the C3 convertase ., These predictions were validated empirically ., Thus , our results help to elucidate the regulatory mechanisms of the complement system and potentially contribute to the development of complement-based immunomodulation therapies .
computational biology/systems biology, immunology/innate immunity