A Series of Adaptive Models Inspired by the Acquired

JASON BROWNLEE Technical Report 070227A Complex Intelligent Systems Laboratory, Centre for Information Technology Research, Faculty of Information Communication Technology, Swinburne University of Technology Melbourne, Australia [email protected]

Abstract-The acquired immune system is capable of the presented series of adaptive models as a novel specialising a defence of an organism in response to the its hierarchal framework for which existing and future antigenic environment. This complex biological system possess acquired inspired adaptive models may be interesting information processing features such as learning, interpreted and related. memory, and the ability to generalize. The clonal selection theory is a cornerstone of modern biology in understanding the acquired II. PRINCIPLE COMPONENTS immune system from the perspective of B- cells and This section lists a series of principles (operators or diversity. This work presents a series of computational mechanisms) that are sufficiently low in complexity to adaptive systems inspired by features of the biological immune be analysed independently. It is expected that the system and the clonal selection theory in particular. Starting with mechanisms listed in this section may act as component basic clonal operators as principle components, models are features in larger adaptive models. Operators are presented in increasing complexity from canonical clonal assigned a notation of O# and are listed in no particular selection models, to discretised architecture models, to finally order. See Table 1 for a quick reference summary of the advanced vaccination, evolution, and ontogenetic models. In operators defined in this section. addition to providing the basis to an interesting line investigation in the field of , this series of adaptive Operator Summary models presents a hierarchal framework from which existing and O1 Clonal Matching Matching properties, affinity, and avidity O2 Clonal Selection Probabilistic selection of future adaptive models inspired by the acquired immune system O3 Clonal Expansion Proportional expansion of selected lymphocytes can be interpreted and related. O4 Clonal Mutation Mutation and of clones O5 Clonal Diversity Initial and on going repertoire diversity Keywords- Clonal Selection Algorithm, Models, Clonal O6 Clonal Homeostasis Maintenance of repertoire size Selection Theory, Adaptive Systems, Acquired Immune System, O7 Clonal Memory Impression and persistence of antigenic exposures Framework Table 1 - Quick-reference summary of operators defined in this section

I. INTRODUCTION This work lists a series of adaptive operators, simple, O1 Clonal Matching and distributed models inspired by aspects of the Lymphocytes have receptors with specificity to one acquired immune system. The intention of this work is surface feature of an , although an antigen will not to describe models accurate in the context of have many different surface features. Thus, a biological experimentation and observation, but rather heterogeneous population of lymphocytes vary in their adaptive models that may serve as the basis and specificity with two general dimensions: (1) The degree inspiration for computational algorithms and systems for to which a given antigen possesses a given surface addressing complex design, engineering, and feature (cells affinity with the antigen), (2) the number information technology problems. of cells with a similar (the same) receptor representing Section II presents a series of general adaptive the strength of the response (summed affinity known as operators derived from the clonal selection theory of avidity). antibody diversity. These operators prove a foundation of principle components, which are employed in the O2 Clonal Selection

canonical clonal selection models presented in section The clona¡ l selection principle refers to the imperfect III. Section IV extends the base clonal selection model ¢ with a series of adaptive models that introduce additional selection of high affinity lymphocytes by antigen. The operators and processes of acquired immunity. Section V selection may be considered probabilistic, a random also extends the base model although with a discretised event, and perhaps serendipitous. The selected version of the immune systems distributed architecture. lymphocyte may be considered high-affinity relative to Section VI presents advanced multiple immune system the lymphocytes around it (local vicinity), and or relative models that incorporate larger system ideas such as to the lymphocytes the antigen may have encountered on vaccination and evolution. Finally, section VII describes its journey (antigen lifetime in vivo).

CIS Technical Report 070227A February 2007 page 1 of 5 through clonal selection and expansion (majority of Selected sub-set of lymphocyte generation). lymphocytes

O6 Clonal Homeostasis Lymphocytes have a finite lifetime, and there is a one-to-many relationship between selected ancestor lymphocyte and resultant clonal progeny. This can be Highest affinity in reduced to a one-to-many relationship between antigen selected subset and resultant clonal progeny. The rate of antigen encounters, the size of progeny clones, and the lifetime (aging) of lymphocytes plays a role in total repertoire size. Another minor contributor is the rate and number of na ve lymphocytes released in the repertoire. Given physiological constraints, the repertoire has a desired Figure 1- Conceptualisation of probabilistic clonal selection (O2) equilibrium point as well as an upper limit in size, although the size fluctuates with antigenic encounters

O3 Clonal Expansion with a time lag before returning to the point of equilibrium. A is a group of lymphocytes that divide from the same ancestor, for the most part genetically identical. O7 Clonal Memory Consider that an antigen molecule does not arrive alone, but also exists within a clone. Thus, clones of A memory of the antigenic environment, that is, lymphocytes compete, based on specificity for a finite the system has been exposed, is imprinted in the number of antigens (selections) which result in biased lymphocyte repertoire. This memory is refreshed proliferation. Higher-affinity lymphocytes have an with each identical antigenic exposure, and even refined increased probability of selection, thus in this scenario given affinity maturation. Forgetting occurs given the we may consider that at a clone level, the proliferation of lack of subsequent exposures, and the reallocation of the a clone is proportional to its affinity with the antigen. repertoire resources. Memory through continued More accurately, the expansion of a clone is exposure is like having a low-grade chronic as proportionate to its relative avidity to other local clones. a reminder. The result is a positive feedback mechanism that may III. BASE MODELS lead to clonal dominance with respect to an antigen (structural feature of antigen the lymphocytes This section lists a series of base adaptive models that bind to). are capable of adaptation and posses one or more adaptive operators and components from section II. They are perhaps still low enough in complexity for analytical O4 Clonal Mutation analysis. The models listed in this section may provide Given the selection and proliferation of a lymphocyte the basis for more elaborate adaptive models through by an antigen, genetic mutations may occur and are augmentation with additional operators and or processes. expressed in the progeny clone. The errors result in a The notation BM# is used and models are listed in no modified cell receptor, and thus a modified (increased or particular order. See Table 2 for a quick reference

decreased) affinity to the same antigen that triggered the summary of model presented in this section. ¢ ancestor s proliferation. Rather than a clone of genetic Model Summary copies, the process results in a clone of slightly varied BM1 Affinity Cloning Model Perfect and proportionate memory (heterogeneous) siblings, some of which, through BM2 Affinity Maturation Model Narrow and specialised memory chance, have an improved affinity for the antigen. BM3 Clonal Selection Model Canonical clonal selection procedure The broader resultant affect in that the clone has a Table 2 - Quick reference summary of base models higher avidity for the antigen given both clone size, and the concentrated or refined specificity for the antigen. BM1 Affinity Cloning Model

O5 Clonal Diversity This model starts with a heterogeneous random repertoire (O5) and assumes clonal matching (O1). The The initial repertoire of cells is heterogeneous with model continually applies the insertion of na ve cells respect to specificity to all antigen given a random (O5) and the repertoire is subject to clonal selection (O2) generation process that seeded it. The heterogeneity of and clonal expansion (O3) in the face of repertoire the repertoire is biased by the antigenic environment of homeostasis (O6). The result is a model that exhibits a the host. Although, there is an on going random perfect and proportional clonal memory (O7) with no generation of unbiased lymphocytes that fulfil a fraction ability to adapt. of the systems original capability of detecting any given antigen. This results in a transition from a random, to Random initial repertoire (O5) biased repertoire, and both on going: (1) random (naive) Repeated exposure to antigen lymphocyte generation (small fraction) and (2) biasing Selection of high-affinity cell (O2) Cloning of selected cells (O3)

CIS Technical Report 070227A February 2007 page 2 of 5 Generation of na ve cells (O5) clonal selection theory: clonal selection, clonal Aging and removal of cells (O6) expansion, and affinity maturation and may be considered a canonical clonal selection procedure. The Figure 2 - General procedure of the affinity cloning model BM1 model provides a trade-off between generalist (random Selection and ultimately cloning and clonal numbers repertoire O5), greedy proportionist (BM1 with perfect are based by the affinity to the antigenic stimulus, thus memory), and narrow specialist (BM2). the name affinity cloning, but the model could just be

IV. EXTENDED MODELS easily be referred to as selection-cloning a¡ s these are the models core adaptive operators. It is the make more of This section lists a series of adaptive models with something good ¢ principle where the population or moderate complexity; that is models that combine a mixing of the repertoire is defined by the antigenic number of adaptive operators and or processes from exposures. section II in formations that are extensions of the base models of section III (specifically BM3), although

BM2 Affinity Maturation Model include additional operators and or processes. These models may be difficulty to investigate analytically. This model starts with a heterogeneous random Models are assigned the notation of EM# and are listed repertoire (O5) and assumes clonal matching (O1). The in no particular order. See Table 3 for a summary of the model continually applies the insertion of na ve cells extended models presented in this section. (O5) and the repertoire is subject to clonal selection (O2) Model Summary and clonal mutation (O4) in the face of repertoire EM1 Memory Cell Model Repertoire of plasma and memory cells homeostasis (O6). The result is a model that exhibits a EM2 Tolerance Model Feasible and infeasible search space specialised clonal memory (O7). EM3 Dynamic Antigen Model Non-stationary antigenic environment EM4 B & T Lymphocyte Model Two-phase selection and co-evolution Random initial repertoire (O5) Table 3 - Quick reference summary of extended models Repeated exposure to antigen Selection of high-affinity cell (O2)

Mutation of selected cells (O4) EM1 Memory Cell Model

Generation of na ve cells (O5) Aging and removal of cells (O6) An extension of the clonal selection model BM3, although rather than amorphous lymphocytes providing Figure 3 - General procedure of the affinity maturation model BM2 the medium of information and adaptation, the repertoire supports both plasma and memory cells. A clonally Selection and variation via mutation are the core selected cell proliferates and differentiates into plasma principles of this model, thus the name affinity cells and memory cells. Plasma cells provide the

maturation (improvement of affinity), but the model immediate effector response and a short lifespan, could just b¡ e easily be referred to as selection-mutation. ¢ whereas the memory cells are given a longer, perhaps It is the make better that which is already good indefinite lifespan in the repertoire. Both cell types are principle where the repertoire becomes highly selectable in terms of clonal selection (O2). Perhaps specialised to antigenic exposures. memory cells persist after the proliferation and differentiation process, whereas plasma cells are

BM3 Clonal Selection Model destroyed in the process. The extended lifespan of the memory cell type also have an effect on repertoire This model represents the inclusion of all specified homeostasis (O6), and improve clonal memory (O7). An

clonal operators and is the union of the two previous indefinite memory cell lif¡ espan may pose problems in models BM1 and BM2. the repertoires inability to forget £ antigen. This model starts with a heterogeneous random

repertoire (O5) and assumes clonal matching (O1). The EM2 Tolerance Model model continually applies the insertion of na ve cells (O5) and the repertoire is subject to clonal selection This model is an extension of the clonal selection (O2), clonal expansion (O3), and clonal mutation (O4) in model BM3, although rather than having a random the face of repertoire homeostasis (O6). The result is a initial repertoire (O5), the repertoire is bias or made model that exhibits a proportional and specialised clonal tolerant (non-reactive infeasible) to some known sub- memory (O7). space of the possible search space. That is, both in the initialisation of the initial repertoire, and the on-going Random initial repertoire (O5) generation of na ve lymphocytes, those generated cells Repeated exposure to antigen that are auto-reactive (within the sub-space of the search Selection of high-affinity cell (O2) space deemed self) are adjusted. The adjustment may Cloning of selected cells (O3) take on the form of (1) cell death or apoptosis (deletion Mutation of selected cells (O4) O6), (2) non-responsiveness or anergy (ignored by

Generation of na ve cells (O5) clonal selection O2), or finally (3) receptor editing Aging and removal of cells (O6) (regenerated O5). Figure 4 - General procedure of the clonal selection model BM3 This model involves the three core principles of the

CIS Technical Report 070227A February 2007 page 3 of 5 localities as a discrete version of the distributed immune Possible search space system architecture. These models may be considered a distributed repertoire models of the immune system. Models are assigned the notation of DM# and are listed in no particular order. See Table 4 for a summary of the discretised models presented in this section. Tolerated (infeasible) Model Summary regions of the search DM1 Discretised Circulation Distributed and circulating population space DM2 Discretised Lymphatic Lymphatic and normal tissue with memory and plasma cells Table 4 - Quick reference summary of discrete models

Figure 5 - Conceptualisation of the tolerance model (EM2) DM1 Discretised Circulation Model This model is an extension of the clonal selection EM3 Dynamic Antigen Model model (BM3) that has a distributed repertoire. The An extension of the clonal selection model BM3, repertoire structure is spread out into multiple discrete although rather than adapting the repertoire to an although connected sub-repertoires in a discretised unknown but static antigenic environment the antigenic abstraction of the distributed biological system. environment is dynamic providing a moving target to Lymphocytes circulate between the localities of the host which to adapt. This model has implications particularly organism, and antigenic encounters are considered a if it were combined with the memory cell model EM1 spatial and temporal random events. Repertoire where the need forgetting antigen would be critical. It is homeostasis (O6) is varied such that each locality also expected that the number of clones in clonal manages its homeostasis autonomously in the context of

expansion O3 would be reduced and the generation the circulating nature of the repertoire. na ve cells O5 increased in an attempt to minimise the time lag for repertoire adaptation. Critical factors in terms of the antigen include the rate of change in presented antigens, and the likelihood of reoccurrence of old antigens.

Discretised localities EM4 B & T Lymphocyte Model of a distributed An antigen clonally selects (O2) a plasma and immune architecture the lymphocyte binds to the antigen consuming it, breaking it up and in turn presenting parts of it on the cells surface. Thus, the B lymphocyte becomes an antigen-presenting cell (APC) to other cells such as helper T lymphocytes. Before the can begin Figure 6 - Conceptualisation of the discretised circulation model (DM1) proliferation and differentiation (clonally expand O3) it must be activated by a helper . Thus, this model provides a two-phase clonal selection process by two DM2 Discretised Lymphatic Model different lymphocyte types. This model is an extension of the discretised This model is an extension of the clonal selection circulation model (DM1), although incorporates the model BM3. B cells are clonally selected (O2) by the memory cell model (EM1). The DM1 model is extended antigen, the selected cells transform or mask the antigen to support both normal tissue and lymphatic tissue pattern in someway and in turn clonally select (O2) from localities (sub-repertoires). The EM1 model is applied a second population of T cells before clonally expanding such that the repertoire consists of plasma cells and (O2). The two-phase selection provides a richer memory cells. Plasma cells remain in lymphatic tissue localities and may release effectors, which circulate the adaptation process where antigen may be transformed into another search space, simplified using a mask, a system. Memory cells and na ve lymphocytes are created

many other manipulation processes before being selected in lymphatic tissues although unlike plasma cells may circulate throughout the entire system. Cells, ¡ which upon again. The result is the cooperative-evolution of £ two complementary lymphocyte repertoires. undergo clonal selection (O2), must migrate or home to lymphatic tissue before they may clonally expand (O3). Antigenic encounters may only occur in normal V.DISCRETISED MODELS tissue localities. This section lists a number of models that extend the canonical clonal selection VI.MULTIPLE SYSTEM MODELS model (BM3), although are discretised. Although all models discussed thus far are discrete as opposed to This section lists a number of adaptive immune continuous, discrete in this section refers to models of a system models that are composed of multiple instances single immune system that are partitioned into multiple of the canonical clonal selection model (BM3). They may be considered multiple-immune-system models, and

CIS Technical Report 070227A February 2007 page 4 of 5 bare some conceptual similarity to the distributed MSM1, although without vaccination. This model uses a population models of section V. Models are assigned the genetic basis to generate the initial repertoire for each notation of MSM# and are listed in no particular order. sub-model, and the quality or fitness of the system See Table 5 for a summary of the models presented in (organism) is determined based on its performance over this section. its lifetime in the context of a given antigenic

Model Summary environment. An e¢ volutionary process subsumes the MSM1 Vaccination Model Multiple systems with lymphocyte population of BM3 s and seeks to adapt a population of vaccinations genetic material that determines the initial repertoire of MSM2 Evolutionary Model Evolution of the genetic basis that individual immune systems. Thus, this model describes generates an immune systems initial an adaptive evolutionary process to bias the random repertoire generation of the clonal selection models (BM3) initial MSM3 Evolutionary Ontogenetic Evolution of genetic basis of initial Model repertoire and vertical vaccination of repertoire (O5). young by parents

Table 5 - Quick reference summary of multiple system models MSM3 Evolutionary Ontogenetic Model This mode is an extension of the Evolutionary Model

MSM1 Vaccination Model (MSM2), although in addition, progeny in the evolutionary processes are vaccinated after birth with a This system contains a number of sub-models, each small sample of lymphocytes from the mother. This is a an example of the clonal selection model (BM3). Each mimic of the manner in which mammals pass sub-model may be considered an organism with its own to their young through the milk, which young suckle immune system, thus the collection of sub-models may from the mother. This model has similarities with the be considered a population of organisms. Each organism vaccination model (MSM1), although in this case the has a different antigenic environment, specifically in vaccinations are directed and vertical through terms of the spatial and temporal properties of antigen generations, rather than horizontal across a single exposures. generation. Vaccination involves training an immune system based on a harmless antigen the effects of which protect VII. FUTURE WORK the organism from harmful antigens given that both This work has provided a series of adaptive models antigens have the same surface features. In this inspired by the acquired immune system, starting with vaccination model, when an organism (specific simple operators, which provided principle components individual case of BM3) is identified to have addressed in the base or canonical clonal selection models that

(fought off) a specific antigen, a sample of the resultant followed. The base models provided the foundation for antibodies/lymphocytes are r¡ emoved or replicated from extended models, distributed models and multiple the identified organism and injected £ into one or more system models. other organisms in the population. The properties of Although the series of adaptive models presented did vaccination include (1) how to identify a good response, not cover abstractions of all features of the acquired (2) how to select lymphocytes to extract/duplicate, and immune system, it introduced a novel hierarchical (3) which other organisms to vaccinate. framework in which existing and future adaptive models This system has a conceptual similarity to the of clonal selection and acquired immunity can be discretised circulation model (DM1), although this interpreted and related to each other. This is an model possesses larger repertoires and selective important contribution to the infant field of artificial (unordered) migrations (vaccinations). immune systems (AIS), which is still struggling for clarity and direction.

Selected organism The utility and behaviour of the proposed models is vaccinating other unknown and may only be conjectured. An important immune systems extension of this work is the investigation, implementation, demonstration, and ultimately evaluation of the more promising of the adaptive systems presented in this work, particularly in the context of application to engineering, design and information technology domains. It is speculated that most if not all of the models presented in this work may find utility in application to pattern recognition and optimization domains.

Figure 7 - Conceptualisation of the vaccination model (MSM1) ACKNOWLEDGMENTS Professor Tim Hendtlass for his patience and for

MSM2 Evolutionary Model providing useful feedback on drafts of this paper This model has the same population of immune systems (BM3) approach as the vaccination model

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