The Pathways of Complement

The Pathways of Complement Jonathan M. Aitken, Tim Clarke, and Jonathan I. Timmis Department of Electronics, University of York, Heslington, York, YO10 5DD, UK [email protected], [email protected], [email protected], Abstract. The natural world has developed very effective methods for dealing with pathogens that are invading an organism. By taking inspiration from the in-built, innate, response this paper develops a new algorithm that mimics activation path of the Alternative Pathway of Complement. The Alternative Pathway is triggered by cell surfaces. If the surfaces display safe characteristics then a strong suppression process prevents activation. In the case of non-safe surfaces a positive feedback loop rapidly identifies the location marking it for removal by phagocytosis.

1

Introduction

This position paper is about solving a difficult engineering problem using techniques inspired by biological systems, viewed at both the organism population level and the organism cellular level. The problem itself is generic. A collection of fallible engineering entities is required to interact to achieve some behavioural goals. Through mutual observation of their behaviours, they must be able to recognise a failure, locate the one of more failing entities and subsequently respond to re-establish goal directed, normal network behaviour. Typical target system could include swarms of Unmanned Aerial Vehicles (UAVs) operating co-operatively to render a mission successful, ad-hoc heterogeneous communications networks which respond to loading variations or node failures [1] and any distributed control system which relies on may rely on a combination of subsystems and sensors such as power distribution networks [2]. 1.1

Socially Attentive Monitoring

The recognition of failure through mutual observation has been considered in a social population context under the guise of Socially Attentive Monitoring. The concept of Socially Attentive Monitoring uses observed aspects of human social behaviour as a driving force for identifying the health of a system. Socially Attentive Monitoring was first investigated by social scientists. Festinger [3] proposed three hypothesis about how humans react in a social situation. The first hypotheses states that “there exists, in the human organism, a drive to evaluate his opinions and his abilities” - therefore any human carrying out a task wishes to work out how well they conduct that task.

Festinger’s second hypothesis states that “to the extent that nonsocial means are available, people evaluate their opinions and abilities by comparison respectively with the opinions and abilities of others”. Therefore humans seek out those that they see as having abilities or opinions in the same area and then judge themselves accordingly. The third hypothesis acts to limit this desire for comparison stating that “the tendency to compare oneself with some other specific person decreases as the difference between his opinions or ability and one’s own increases”. Therefore humans only compare themselves to those that they see of a similar ability or opinion, therefore effectively searching out peers for accurate comparison. Festinger’s work has been picked up by the Distributed Artificial Intelligence community and used in several different applications. Kaminka and Tambe [4– 6] have investigated the use of Socially Attentive Monitoring in the concept of agent coordination. In control engineering a key property of a system are the natural modes. A collection of continuous, complex exponential values that determine how a system responds to a given input. This work uses the identified modes of each network component as a signature representing how that element behaving at that moment in time. From this point the immune inspired algorithm is used to identify the affected element. The remainder of this paper focusses on extending the idea of signatures using inspiration from the complement system to identify point(s) of failure. Subsequent action will be application specific, but we develop a simple mechanism to demonstrate the principles. The paper is organised as follows. We begin by describing the current views of the three biological complement pathways as a focus for inspiration. In Section 2 the Alternative Pathway is introduced; from this an Algorithm is developed in Section 3 and compared to the equivalent biological route. Finally method for comparing the natural modes is outlined in Section 4.

2

The Complement Process

The complement system is named because it was believed to aid the antibody recognition process. However, it is an important system in its own right with a central role in the inflammatory response of the immune system [7–9], being sensitive to small amounts of pathogen. However, it has been found to be effected earlier in the process of the immune response than during any antibody action. The complement process is a combination of many different chemicals that produce a wide range of effects across the immune process. There are three top level routes into the complement process, namely the Classical Pathway, the Mannose-Binding Lectin (MBL) Pathway and the Alternative Pathway. Each of these pathways uses a variety of different chemicals during the process, but at the centre of each process is the C3 Convertase. The basic complement components are labelled C1 to C9, although, in addition, the

MBL Pathway uses mannose-binding-lectin-associated serine proteases (MASP1 and MASP-2) and MBL. The Alternative Pathway uses another group of chemicals whose shorthand names are denoted by capital letters. In the common notation, when a Cx element is cleaved it is split into two components denoted Cxa and Cxb, where x represents the number. The Cxb component is the larger fragment. 2.1

Classical Pathway Trigger

The Classical pathway is started by the C1 complement component. C1 is a complex of C1q and the inactive enzymes C1r and C1s. The Classical pathway starts when the C1q component either binds to antigen or the surface of a pathogen [10]. When the C1q head binds, it activates C1r which in turn, activates C1s. Activated C1s is capable of cleaving both C2 and C4 [11]. Firstly C4 is cleaved into C4a and C4b. C4b may attach to the pathogen surface. C4b binds C2 which can then be cleaved by C1s to form the C3 convertase C4b2b which remains bound to the pathogen surface [12]. 2.2

Mannose-Binding Lectin Pathway Trigger

The MBL Pathway is initiated by pathogens containing Mannose and similar sugars [13] on their surface. Mannose is a good indicator of pathogen as, in vertebrates, the substance is typically shielded by sialic acid [12]. Although MBL is similar in structure and lineage [14] to the C1 protein [15], experimentation has shown it to be different, operating with less specificity [16]. Upon binding to a pathogen surface Mannose Associated Serine Protease (MASP)-2 becomes activated this cleaves C4 with the C4b element remaining attached. C2 binds to the C4b and is readily cleaved to C2b by MASP-2 forming the C3 convertase C4b2b [12, 17]. 2.3

Alternative Pathway Trigger

The Alternative Pathway of complement differs significantly from the other routes as it leads to a different C3 convertase [12]. The Alternative Pathway also differs as it is not triggered by just a pathogen, it is activated by the presence of any surface with regulation to ensure that the host is not harmed. In addition it possesses a different set of proteins that trigger the process, namely Factors B, D, H, I and Properdin. Figure 1 shows the process of the Alternative Pathway. At the heart of the Alternative Pathway of complement is the natural and spontaneous process of the conversion of C3 to C3(H2 O) [20, 21] in fluid, a functional equivalent version of its cleaved component C3b in binding to Factor B although similar in structure to C3 [19]. The hydrolysed C3(H2 O) binds to Factor B in the presence of Magnesium ions forming C3(H2 O)B, whereupon Factor B in this compound is cleaved by Factor D to form the short-lived fluid phase C3 Convertase C3(H2 O)Bb [19].

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Fig. 1. Alternative Pathway of Complement (Adapted from [18] using [12] and [19])

The fluid phase C3 convertase cleaves local C3, the C3a produced diffuses away from the site. C3b attaches to a cell surface. This process must be completed quickly as C3b is rapidly inactivated [12]. The C3b on the surface binds to Factor B which is acted on again by Factor D to form the C3 convertase C3bBb attached to a cell surface. Up to this point in the process there has been no differentiation between the surface of an invading pathogen and the host. It is the nature of the surface that determines whether complement is activated. This recognition is controlled through the β1H globulin known as Factor H [22, 23]. In host cells Factor H preferentially binds to C3 convertase on the surface of a cell [24] which promotes inactivation by Factor I [25]. This inactive form, iC3b, is further acted upon by Factor I to produce C3c and C3dg [21] that can then be removed.

If Factor H does not act on the C3 convertase, properdin, acts to stabilise the compound. This reduces any potential effect of Factor H [26] providing it with a significantly longer half-life [27]. 2.4

C3 Convertase to the Membrane Attack Complex

The result of the triggering of all three pathways is the production of C3 convertase which is capable of cleaving more C3 which then acts to re-enforce the Alternative Pathway providing a strong amplification loop via positive-feedback [27]. Any C3 cleaved by the C3 Convertase covalently attaches to the surface leaving the pathogen coated in C3b. The next step in the process is the formation of the C5 convertase which results from the binding of an additional C3b molecule to the C3 convertase. The C5 convertase cleaves C5 into C5a and C5b. The C5b molecules attach to the C5 convertase whereas the smaller C5a migrate away from the site of the pathogen. The small components of complement (C3a, C4a and C5a) are known as anaphylatoxins, as they can cause inflammation at the site. These small components diffuse away from the site of infection. Anaphylatoxins are also chemotaxins: phagocytes follow the diffusion gradient and so are attracted to the infection site. Effectively phagocytes are guided to the infection site by the distribution of the smaller complement components. The C3b attached to the surface of the pathogen acts as an opsonin, promoting phagocytosis of the pathogen by the phagocytes that have been recruited to the site by the anaphylatoxins. The remainder of the complement components are involved in the terminal phase of the process. C6, C7 and C8 successively bind to C5b bound to the C5 convertase to produce a compound which results in the formation of a C9 polymer which crosses the membrane causing cell lysis [12]. 2.5

Factor H

Factor H [28] is crucial in the identification of danger within the Alternative pathway of complement. It exists in high concentration in the blood plasma of humans [29] and its absence or mutation can result in serious harm to the host [30]. It acts to start the process of inactivation of C3 convertase only if found on host surfaces. Once this has been achieved it promotes the binding of Factor I to complete the inactivation. Several experiments have been conducted examining the effect of Factor H on C3 Convertase bound to surfaces. The first molecule reported to influence C3b deposition on a surface was Sialic Acid [31]. Further investigation revealed that other polyanionic molecules such as the glycosaminoglycans and sulphated polysaccharides [29], of which heparin is a notable case - being a strong polyanion. This binding of polyanions and sialic acid is especially significant as it provides host cells with a method for protecting themselves from Alternative Path-

way complement attack. The presence of Factor H gives this key ability to differentiate host and pathogen surfaces [32]. Therefore any surface expressing polyanionic molecules will be deemed as not being dangerous to the host and so inhibit complement activation. The inability of molecules to express these key compounds can result in unchecked action of the complement cascade resulting in damage to the host [33]. The host possesses a method for suppressing complement activation via the Alternative Pathway by expressing polyanionic molecules. However, pathogens have developed methods for using such tactics to avoid detection [34] by, for example, binding sialic acid or Factor H to their own surfaces [35] in order to mask themselves from the Alternative Pathway. Therefore the Alternative Pathway is capable of protecting the host unless the invading pathogens become “host-like” [36].

3

Applying Ideas from the Innate Immune System

The review of the Innate Immune System has revealed a collection of complex processes that co-operate together to provide not only an accurate and reliable indication of pathogen infiltration but are also capable of directing the initial stages of the immune attack to the infected area. Therefore the Innate Immune System provides a system worthy of investigation in its ability to protect a group of individual units. In order to protect such a group it would be beneficial to utilise joint information between the separate units. This scheme is typical of Socially Attentive Monitoring (SAM) [3, 4]. By sharing information, the members of the group are then capable of identifying failures within their network. To this end, we have devised the Alternative Pathway Algorithm. 3.1

The Dynamic Element Swarm Problem

The problem considered in this paper consists of a fallible swarm network. A set of dynamic swarm elements must navigate a simple slalom course as a coherent group within a time limit. Should any element change dynamic behaviour characteristics such that the swarm interactive behaviour impedes the collective group temporal goal achievement, it must be identified and corrective action taken. 3.2

The Alternative Pathway Algorithm

This algorithm is based around the interactions at surfaces during the Alternative Pathway of complement and the utilises several key features: – The Alterative Pathway relies on having large numbers of molecules of the element C3 circulating in the blood stream that are then allowed to interact with any surface that they meet. The process is widely distributed. Not all of the possible sites are compared at once - and there is no need to compare one site with every other in order to make a local decision, since knowledge about safe factors is widespread.

– The interaction with surfaces is non-deterministic but is influenced by the state of the surface at that time. If the surface is in the process of being identified as harmful, it is more likely that deposition will occur. – The process of deposition is modified by the presence of expressible polyanionic molecules by the surface. These can prevent further deposition, causing inactivation and removal of the initial C3 from the bloodstream. – The process of expression of the molecules is dependent on the nature of the surface. Pathogens may acquire Factor H or sialic acid which masks their true nature and prevents further activation. – Failure to inactivate the deposition results in rapid, exponential growth through positive feedback which alerts the body to the problem location, attracting more deposition of C3b and attracting neutrophils as a result of release of chemoattractants from the process. The implementation of the algorithm focuses on the process of message passing between software agents. The key features of the algorithm can be directly compared with the process of the Alterative Pathway: – The elements are widely dispersed but have natural paths of communication between each other. There is no need for specific comparison in such a group. An element need not compare itself to the entire group at once. Therefore the comparison can be allowed to circulate information around the group. However, attention needs to be directed towards problem areas in a similar method to the release of chemoattractants. – The process relies on the ability of each agent to identify a picture of how it is behaving at that instant in time. These signatures can be viewed as encapsulating the behaviour style of the agent for that period of time. In essence, their behaviour is similar to C3, which is allowed to flow freely around the network randomly, selecting a surface. – These signatures can be used to modulate the behaviour of the network. A mismatch between a local signature and one received from another agent implies that all is not correct. Therefore, a matching function is required which can measure the separation between two signatures. If they are close, the process is similar to polyanionic expression, allowing inactivation. As the distance increases, the desire to compare with neighbours must be increased, as there is the potential that a problem has occurred but further investigation is required. This is analogous to the stabilisation of C3 convertase on the surface by properdin with additional release of chemoattractants. Algorithm 1, reflects these basic properties found in the Alternative Pathway. The algorithm is implemented on each agent separately, within the context of an agent framework such as the Java Agent Development Framework [37]. The basic terms used in the algorithm are outlined below: – sigself (t) - The signature of the agent running the algorithm at time t representing the surface of the agent.

– sigpeer (t − x) - The signature of another agent in the system at a time x units prior to the present time. This represents circulating components of C3, free to move in the blood stream, eventually coming into contact with a surface. – C3self - The stress of the agent at that time through complement deposition. This is linked to how likely an agent will accept a signature for comparison from a peer in the network. The lower the value the more likely a comparison is to take place. Therefore its level acts as an attractant for signatures circulating in the network, like an anaphylatoxin. The variable gives an indication of the level of stabilised C3 Convertase deposition on the surface. – match() - This function acts to generate a score indicating how similar the signature from a peer is to the agent at that time. – R - A value representing the result of the matching function. The nearer to unity the value then the more similar the two pairs. Therefore, it acts as a stimulant for polyanionic compounds. At values close to unity, it will be more likely that the signatures match and that the surfaces are safe. – C3inc - If signatures match C3self is incremented by this constant value. This results in suppressed activation of the cascade following a successful surface match. – C3max - Maximum value of agent stress, representing the minimum level of C3 deposition on the cell. In order to maintain some comparison, the level must be set to less than unity so that there is some probability of comparison. – C3dec - The decrement equivalent of C3inc . It promotes activation of the cascade on an unsuccessful surface match. – TM axSig - Maximum age of a signature. Any signature older than this limit is removed from the system.

4

The Matching Problem

It is essential that signatures from other peers are correctly compared at each agent location. Therefore a matching function is required that can successfully cope with a variable length list of complex valued numbers. The basis for the matching function is the Cauchy-Schwarz inequality [38] (1). | < a, b > | ≤ #a#2 #b#2 (1) Where < . > denotes the inner product and #.#2 denotes a 2-norm. Therefore any evaluation of the function in the form of (2) will provide a result that lies between zero (no similarity) and unity (identical). | < a, b > | (2) R1 = #a#2 #b#2 Selecting a random set of six eigenvalues of a discrete state space system to be 0.9969, 0.9698, 0.9768 + 0.1456i, 0.9768 − 0.1456i, 0.9434 and 0.9234. The effectiveness of (2) can be evaluated by moving the pair of complex poles around the available space, the unit circle of the argand diagram achieving the result in figure 2(a). A good match of eigenvalues can be achieved through (2) when the two vectors are closely aligned. As the eigenvalues drift apart then the value of R1 decreases but for very dissimilar vectors then there is insufficient distinction.

Algorithm 1 Algorithm to Mimic the Alternative Pathway of Complement Evaluate sigself (t) Send sigself (t) to random peer Receive sigpeer (t − x) from peers for All sigpeer (t − x) received do if rand > C3self then R = match(sigpeer (t − x), sigself (t)) if rand < R then Signatures Match Inactivate Process if C3self + C3inc < C3max then C3self = C3self (t) + C3inc end if else if C3self − C3dec > 0 then C3self = C3self (t) − C3dec end if Store sigpeer (t − x) and sigself (t) end if else Add sigpeer (t − x) to outbound queue end if end for for All sigpeer (t − x) in outbound queue do if (t − x)) > TM axSig then Delete signature else Send sigpeer (t − x) to random peer end if end for

Additionally (2) does not give any distinction between a doubling of eigenvalues. The equation is normalised so that then providing that the shape of the values contained in the vector are identical the result will be the same. Therefore (2) can be modified to be adjusted to be normalised to the maximum norm of the two vector of eigenvalues so that a doubling in the total eigenvalue will produce a lower match. The modified version is shown in (3). This removes the similarity in value for similar shapes of different magnitude and produces a slightly improvement in the ability to distinguish different vectors shown in figure 2(b). | < a, b > | (3) R2 = max(#a#22 , #b#22 ) Although the corrected matching functions perform well they remain relatively insensitive to the movement of one or two poles. Therefore it would require a large movement from the complete vector to bring about a low matching score. In order to produce a matching function more sensitive to changes in pole locations then a factor can be introduced that provides a non-linearity. This modification is shown in (4).

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Fig. 2. Effectiveness of Basic Cauchy Equations shown in (2) and (3)

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R3 = eF R2 −F (4) In order to produce a higher variability in the result of the match an exponential function is introduced to give a highly localised comparison. In order that result of the function is bound between unity and zero an additional factor F is used to limit the swing of F R2 − F from zero to −F . In addition it allows the matching function to have a variable component that allows the shape of the matching region to be adjusted as suited to the problem area. Figures 3(a) and 3(b) shows the evaluation of (4) over the unit circle in the complex plane. As can be seen (4) is sensitive to changes in the evaluation of R2 , but can be adjusted by varying F to give a sharper region of suppression shown in Figures 3(a) and 3(b).

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Conclusion

In this paper we have explored the possibility for an algorithm based on the Alternative Pathway of Innate Immune system. The Alternative Pathway is triggered by all cell surfaces. However, the surface of safe body cells strongly inhibit the process by attracting Factor H. The algorithm is based around a network of homogeneous agents sharing information on how they are reacting to their environment. This information is akin to the picture presented by a cell surface

in the Alternative Pathway. Further work is planned to exploit the algorithm in the fallible swarm problem to remove rogue elements.

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