Bioinformatics Advance Access originally published online on April 7, 2005
Bioinformatics 2005 21(12):2891-2897; doi:10.1093/bioinformatics/bti426
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Modeling and simulation of cancer immunoprevention vaccine
1Faculty of Pharmacy, University of Catania Italy
2Department of Mathematics and Computer Science, University of Catania Italy
3Sezione di Cancerologia, Dipartimento di Patologia Sperimentale, University of Bologna Italy and Centro Interdipartimentale di Ricerche sul Cancro ‘Giorgio Prodi’
4Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche Roma, Italy
*To whom correspondence should be addressed.
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Abstract |
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 TOP Abstract 1 INTRODUCTION2 THE VACCINE MODEL3 RESULTS4 CONCLUSIONSREFERENCES |
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We present an in silico model that simulates the immune system responses to tumor cells in naive and vaccinated mice. We have demonstrated the ability of this model to accurately reproduce the experimental results.
Motivation: In vivo experiments on HER-2/neu mice have shown the effectiveness of Triplex vaccine in the protection of mice from mammary carcinoma. Full protection was conferred using chronic (prophylactic) vaccination protocol while therapeutic vaccination was less efficient. Our in silico model was able to closely reproduce the effects of various vaccination protocols. This model is the first step towards the development of in silico experiments searching for optimal vaccination protocols.
Results: In silico experiments carried out on two large statistical samples of virtual mice showed very good agreements with in vivo experiments for all experimental vaccination protocols. They also show, as supported by in vivo experiments, that the humoral response is fundamental in controlling the tumor growth and therefore suggest the selection and timing of experiments for measuring the activity of T cells.
Contact: francesco{at}dmi.unict.it
Supplementary information: http://www.dmi.unict.it/CIG/suppdata_bioinf.html
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1 INTRODUCTION |
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TOPAbstract1 INTRODUCTION2 THE VACCINE MODEL3 RESULTS4 CONCLUSIONSREFERENCES |
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Cancer immunoprevention is based on the use of immunological approaches to prevent, rather than to cure, cancer. In the field of infectious immunity the best use of vaccines is for the prevention of disease, not for cure. Predictive oncology now provides many instances in which the risk of cancer can be determined with sufficient accuracy to implement preventive strategies based on immune stimulation. Cancer immunoprevention has already been demonstrated in humans for tumors related to viral infections. For example hepatitis B vaccination significantly reduces the risk of hepatocellular carcinoma, and papilloma virus vaccines are being tested to prevent cervical carcinoma (Chang et al., 1997; Koutsky et al., 2002). The challenge now is to devise new vaccines for human tumors not linked to viruses, such as breast, prostate and colorectal carcinomas (Forni et al., 2000). Immunoprevention of spontaneous tumors has been explored in recent years in preclinical systems thanks to the availability of several new transgenic mouse models that closely mimic the natural history of human tumors (Di Carlo et al., 1999). The most thoroughly investigated model of cancer immunoprevention is the mammary carcinoma of HER-2/neu transgenic mouse. In this system it has clearly been shown that the activation of immune defenses in healthy individuals can effectively prevent the subsequent onset of highly aggressive mammary carcinomas. A complete prevention was obtained using a combination of three signals (the so-called ‘triplex’ vaccine) that included the specific antigen (viz. p185, the product of HER-2/neu) and nonspecific signals like allogeneic histocompatibility antigens and interleukin 12 (Lollini et al., 2005). The vaccine cell (VC) that we will model here is similar to the latter one and consists of a HER-2/neu transgenic mammary carcinoma cell allogeneic with respect to the host and transduced with IL-12 genes.
A complete prevention of mammary carcinogenesis with the Triplex vaccine was obtained when vaccination cycles started at 6 weeks of age and continued for the entire duration of the experiment, at least 1 year (chronic vaccination). One vaccination cycle consisted of four intraperitoneal administrations of non-replicating (mitomycin-treated) VC over 2 weeks followed by 2 weeks of rest. We made various attempts at reducing the number of vaccination cycles, in particular we studied the effects of just three cycles starting at 6 weeks of age (early vaccination), or at 10 weeks of age (late vaccination), or at 16 weeks of age (very late vaccination). Early vaccination produced a significant delay in the onset of tumors, but all mice eventually succumbed to mammary carcinoma. Late vaccination was less effective than early vaccination, whereas the very late protocol was completely devoid of effect in comparison to untreated control mice (Fig. 1).
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1.1 The problem of vaccination schedules
These results leave open the question whether the chronic protocol is the minimal vaccination protocol yielding complete protection from tumor onset, or whether a lower number of vaccination cycles would provide a similar degree of protection. A biological solution would require an enormous number of experiments, each lasting at least 1 year. This problem was at the root of our endeavor to develop an accurate mathematical model of immune system responses to vaccination.
A significant effort has recently been devoted in searching for an appropriate mathematical approach to describe the immune-tumor competition (see Bellomo et al., 2003b for a recent review). Methods based on generalized kinetic model look very promising for system description; however, they are not necessarily adequate for modeling therapeutic vaccines.
To model the action of a specific tumor vaccine, we used a computational approach which reproduces the ab initio kinetic model that describes the interactions and diffusion of each relevant biological entity. This approach is biologically very flexible; the behavior of entities is modeled using biological knowledge and can be easily modified to reflect observations from new biological experimental results. Compared to the complexity of the real biological system, our model is still a simplification and it can be extended in many aspects. However the model is complete enough and after tuning the model parameters, it recreates a vaccination schedule that prevented the formation of solid tumors in mice.
Practical applications of this model include non-invasive analysis of tumor progression followed by the refinement of preclinical schedules of vaccination, and ultimately to a clinical application of this immunopreventive approach combining preclinical data and immunoinformatics.
The plan of the paper is the following: in Section 2 we describe how the entities of the biological system have been modeled; in Section 3 we present the results of in silico experiments and comparison with in vivo experiments. Finally in Section 4 we draw conclusions and plans for future work.
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2 THE VACCINE MODEL |
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TOPAbstract1 INTRODUCTION2 THE VACCINE MODEL3 RESULTS4 CONCLUSIONSREFERENCES |
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Methods for modeling the behavior of the immune system are driven by the different scales that can be selected to represent the same phenomena (Bellomo and Preziosi, 2003; Bellomo et al., 2004). In all cases, the main problem consists in identifying the appropriate mathematical and computational techniques to describe the system. The interested reader can find extensive reviews in Forrest et al. (2001), Bellomo et al. (2003a), Adam et al. (1996) and Perelson (1988).
The model we have developed is based on lattice gas automata (LGA), a class of dynamical system in which particles move in the lattice in discrete time steps (Rothman and Zaleski, 1997). Our implementation differs from classical LGAs, because the model includes entities which have internal states to better describe their dynamics. Interactions between different entities will stochastically change the internal state of one or both the interacting entities.
2.1 The immune system-vaccine tumor competition model—SimTriplex
The model we use for the present study (SimTriplex) is based on a modification of the Celada–Seiden framework (Celada and Seiden, 1992; Seiden and Celada, 1992). SimTriplex mimics at the cellular level the behavior of immune cells of vaccinated as well as naive mice. This is a generalized cellular automaton based on C-ImmSim version 6 (Castiglione et al., 1997; Bernaschi and Castiglione, 2002).
2.1.1 The immune system
The model explicitly implements cellular and humoral immune responses in a comprehensive set of rules which apply to a variety of cellular and molecular entities: lymphocyte B (B), lymphocyte T helper (Th), lymphocyte T killer (cytotoxic) (TC), Macrophage (MP), Plasma cells (PLB); and the molecules: antigen (viral, bacterial or tumoral) (Ag), antibody (Ab) and immune complexes or Ab–Ag binding (IC). In addition, some intracellular signals are explicitly represented, for example, interferon-
(IFN), and danger signal (D), while other cytokines, like Interleukin-2 (IL-2) and Interleukin-12 (IL-12), are implicitly taken into account in the rules. The major difference among cellular and molecular entities is that cells may be classified on the basis of a state attribute. The state of a cell is an artificial label introduced by the logical representation of the cell's behavior.
The lymphocyte receptors are represented by l-dimensional bit-strings (Farmer et al., 1986), the so-called ‘shape space’ (Segel and Perelson, 1989). A clonotypic set of cells is characterized by the receptor which is represented by a bit-string of length l; hence the potential repertoire scales as 2l. The receptor–coreceptor binding among the entities are described in terms of matching (i.e. their Hamming distance) between binary strings with a fixed directional reading frame.
Cells and molecules are free to diffuse across the lattice sites. At each time step, representing 8 h of real time, cells and molecules residing on the same lattice are able to interact with each other.
There are about 15 rules that can be grouped using immunological terms: phagocytosis, immune activation, opsonization, infection and cytotoxicity. Phagocytosis comprises the rules that describe the activity of antigen processing cells. Immune activation is defined as the activity of helper T lymphocytes which recognize MHC-peptide complexes and stimulate, by releasing cytokines, B cells for antibody production. Opsonization is the inactivation of an antigen by binding of antibodies. Infection is defined as the action of a virus. Cytotoxicity is defined as a number of rules which account for the killing of the target cells (tumor, infected, or mutated cell) by cytotoxic T cells.
The model also includes the mechanism of hematopoiesis. This takes into account both the generating activity of pluripotent stem cells in the bone marrow and the selective activity of the thymus for what concerns. The generating activity is realized by periodic addition of newly formed cells generated randomly with a mean reverting process implemented to assure that in the absence of an antigenic stimulus, the number of cells is in a steady state. The positive and negative selection of T lymphocytes represents thymic processes required for avoiding autoimmune reactions.
2.1.2 The vaccine
The action of a healthy immune system is effective primarily against non-self antigens. A large proportion of tumor associated antigens (TAA) are self so the immune system responses are often very limited. Tumor vaccines need to stimulate the immune recognition of the TAA which otherwise would be treated as self and tolerated. The three components of the engineered Triplex vaccine perform this action (Section 1).
In order to represent the tumor growth and the vaccine action, we inserted, in the present study, the following entities and interactions: (i) the cancer cells (CCs) which encode their TAA; they interact with Ab, TC and NK; (ii) the vaccine cells (VCs) which include TAAs, IL-12 and allogenic MHCI; VCs interact like CCs, with Ab, TC and NK, but the affinity function is modified by the presence of the two adjuvants; (iii) the natural killer (NK) cells which do not encode receptors; they interact with Ab, VC and CC.
2.1.3 Tumor cells dynamics
Cancer cells can be seen as corrupted normal tissue cells. The transition from normal to tumor cell is a stochastic event. To mimic the above transition, we have introduced three new cancer cells in the lattice at every time step. Once inserted in the system, cancer cells duplicate, and very rarely die by apoptosis. The cancer cell duplication is included as a probabilistic event at each CC once per cycle. The cancer cell population grows following an exponential law with parameters chosen to fit qualitatively the tumor growth observed in the real mice. In this first approach, tumor cells are not allowed to diffuse, i.e. we do not consider formation of metastasis. Vaccine cells are modified tumor cells (Section ); they do not duplicate and have a half life of 1 day. Natural killer cells have a simple structure as they are non-specific entities.
In the model NK cells, macrophages and dendritic cells are not subject to proliferation and their number is kept roughly constant inserting new cells to replace those that die. Their plotted numbers versus time remains mostly flat (see also Supplemental Figures 1 and 2).
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Interactions of tumor cell entities with vaccine entities are included in the model. A mammary tissue (1 mm3 of the mouse) is represented as two-dimensional triangular lattice (six neighbor sites), with periodic boundary conditions in both directions.
2.2 The SimTriplex simulator
The core of the simulator is an iterative procedure that models the evolution of the system through a specified number of time-steps. The high-level architecture of the program is shown in Figure 2. A set-up routine is first invoked to create the lattice, register the values of the various input parameters and seed the lattice with a specified population of cells.
The simulator includes both cellular and molecular entities. These groups of entities are treated differently as cellular entities are modeled individually, while molecular entities are modeled as a group; only the concentration in each lattice cell is of interest.
The value of the relevant parameters used to successfully recreate in vivo data through computer simulation can be found at in the Supplemental information.
2.2.1 Cellular entities
All cellular entities are specified by: position, specificity, states and age.
Position. Interactions between entities can occur only between those entities which are co-located in the same lattice cell.
Specificity. Specificity refers to the physical shape of each cellular entity that can be recognized by their paratopes (complementary shapes of peptides and receptors). Each entity, except for plasma cells, has at least one receptor (or paratope/epitope, depending on whether they are cellular or molecular entities) which is its primary identifier, i.e. their specificity. The specificity determinant of the plasma cell is the paratope of the antibody produced by that cell. All cells have MHC class I receptors. The APCs and B-cells are implicitly assumed to carry a complete sample of the MHC receptors specified in MHC; this is only used by T-cell receptors. The APCs and B cells also have MHC class II receptors. In addition B cells, TH cells and TC cells are endowed with receptors used for binding antigen. The B cell receptor binds antigen which can then be ingested and endocytosed. The T cell receptors (TCRs) only bind antigen in MHC/peptide complexes. The plasma cells have no specific receptor; however, they do produce antibodies with the same receptor as the B cell from which they originate.
States. Cells have a number of internal states depending on their type, as shown in Table 1.
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New born cells (see Age) are in Resting state. A cell becomes Active when it is stimulated through an interaction with another entity. For example, TH cell activation occurs with the interaction with an antigen if TCR binds the antigen.
Status Intern applies only to APCs. When an APC (MP, DC, B) encounters an antigen, it may be directly recognized by membrane-bound receptors, for example those on the surface of a naive B cell. Unlike B cells, T cells do not recognize antigens directly. They ‘see’ antigens as peptides only in association with the host surface MHC molecules. Since MHC molecules can only bind peptide molecules of 7–15 amino acids long, T cells only recognize their specific antigen in the form of short peptides. The APCs such as dendritic cells and B-cells take up antigen and partially degrade it into peptides which then occupy the antigen-presenting groove in MHC class I and MHC class II molecules. When cells present peptides via MHC molecules, their status changes to PresI (MHC class I) or PresII (MHC class II).
Status Duplica (applies to Th, TC and B cells) is achieved when a cell has been activated and stimulated to start the clonal division.
BoundToAb status applies to CCs and VCs. This state represents the fact that a cell has been recognized by an antibody. Cells in this status may die by action of Ab-complement or by NK cells.
Internal states of each cell type are summarized in Table 1. Each cell can be in a different internal state and all cells are tracked individually throughout the course of an experimental run.
Age. Cellular entities have age structure. They get born (the process of hematopoiesis), they interact and duplicate (and eventually get anergic) and, after a finite lifetime, they die by apoptosis or by lysis. We need to keep track of the age of cellular entities; we do this by keeping a count of the number of time-steps since the cell birth (from stem cells or by clonal division). To simulate memory cells, we increase the half-life of TH, TC and B cells after successful interaction with target antigens. The death probability reaches 1 when the age gets to twice the half-life.
2.2.2 Entities concentration in the lattice
Leukocytes form three general classes (granulocytes, lymphocytes and monocytes) which are present in different ratios in blood, tissues and various organs. The absolute numbers and relative proportions of cells used in the present simulation were based on an average mouse leukocyte formula, with the notable omission of granulocytes. In our virtual mouse we initially consider 4500 leukocytes. Of these there are 4200 lymphocytes, comprising 1512 B cells, 1512 T cells (subdivided into 1008 T helper cells and 504 cytotoxic T cells) and 1176 NK cells. This model has 300 monocytes divided into 150 macrophages and 150 dendritic cells.
2.2.3 Molecular entities
Molecular entities included in the simulator are antigens, antibodies, cytokines and damages (danger signal, see Matzinger, 1998). Molecular entities do not have internal states and thus do not need to be modeled individually. Rather, we define populations which represent different specificities of molecular entities. Diffusion on the lattice is performed by appropriate change of the concentrations of entities. The age structure is stochastically increased/decreased as the function of production and half-life time respectively. The molecular entities are ageless since the decay of the individual can be adequately dealt at the population level. In this case, aging takes the form of regular pruning of the whole population though the application of a decay factor.
Antigens. The antigens we consider (p185) (Section 1) is the TAA released by injected vaccine cells and cancer cells when they die. Antigens are represented by a number of binary segments consisting of a fixed number of bits. These segments represent the antigenic sites (epitopes and peptides).
The epitopes and peptides are specified separately in our model. The minimum effective antigen we consider is therefore two segments long, one for B-cell epitope and one for peptide.
Antibodies. Antibodies (Abs) in our model have the same representation as antigens, i.e. bit strings, and have a paratope which is identical to the paratope/receptor of the B cell (plasma cell) that secretes them.
Cytokines and damage. Two cytokines (IL-2 and IL-12) and a danger signal are included in the simulator.
IL-12 is an integral component of the vaccine (see section 1) acting as an adjuvant. The simulator implements this effect by coding TH stimulation by VC only if IL-12 is present.
IL-2 is taken to represent all the interleukins produced by TH cells in the course of the immune response. In the model such cytokines control the strength of the bystander effect which is the activation of cells without direct cell–cell contact. In our model, B cells and T cells are stimulated to divide if the concentration of IL-2 at its site is above a given threshold. In its present form the model takes into account only the concentration of IL-2, but it might easily be modified, through the use of the activation threshold and of interaction probabilities as indicated by the Quantal theory (Smith, 2004).
Damage is used to implement the idea that a danger signal is necessary to activate the clonal response of the immune system. Damage arises from necrotic cell death, Ab/Ag complexes, toxins and injected adjuvant and in turn can activate APCs.
2.2.4 Thymus selection
The model generates a repertoire of MHC-restricted, self-tolerant T cells using selective processes that mimic the events taking place in the thymus during T cell maturation (Abbas and Lichtman, 2003; Morpurgo et al., 1995). Selection has two phases: positive and negative (both stochastic). In the positive selection phase the T cells that have low affinity to the MHC molecules taken alone (class I for TC and class II for TH) are eliminated because they are not useful. In the negative selection phase, the T cell receptors are compared with the MHC attached to a self peptide taken from a suitable set of binary strings; in case of a high match, the T cell is eliminated to limit autoreactivity.
2.2.5 Mutation
The immune system achieves repertoire completeness by the mechanism of mutation of the B-cell receptor. Mutation occurs when a new B cell is formed, i.e. in the duplication phase. This effect is included in the simulator as a stochastic event; this increases the immune system's recognition ability.
2.2.6 Interactions
To be concise we describe only vaccine-induced interactions with immune system components. These are built to simulate the observed vaccine effect, that is: (i) the vaccine stimulates TC cells with a certain probability which depends on the receptor's affinity. The probability is increased by the presence of allogeneic MHC. If the interaction is successful, the VC dies and releases TAA antigens; (ii) when the antibodies' receptor matches with a non-zero affinity the MHC class I TAA, the interaction VC versus Ab occurs producing either VC death or changing the VC state in ‘Bound to Ab’; (iii) vaccine cells which are in the state ‘Bound to Ab’ are recognized and killed by NK cells. All other interactions reproduce standard responses of immune system components against antigens (Table 2).
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In the model, cancer cells (but also other cells) express just one MHC–peptide complex at a time; i.e. MHC–peptide expression is represented by 1 bitstring per cell. Therefore MHC expression is an all-or-none property, whereas a discrete down-modulation of MHC expression by cancer cells was frequently found in practice (Lollini et al., 1998), and is thought to influence recognition by T and NK cells. However, the model can take into account such aspects because each cell–cell interaction is assigned a probability. In particular we have a very low probability of interaction between T cells and cancer cells to simulate a reduced interaction caused by low MHC expression.
2.2.7 Diffusion
All entities are allowed to move with uniform probability (not by chemotaxis) between neighboring sites on the lattice.
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3 RESULTS |
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TOPAbstract1 INTRODUCTION2 THE VACCINE MODEL3 RESULTS4 CONCLUSIONSREFERENCES |
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In vivo experiments have shown that once a solid tumor is formed, the action of the vaccine is negligible. In other words, the effect of the vaccine is to control the tumor which has not reached a solid tumor state. In vivo experiments have been carried out on different statistical samples of HER-2/neu transgenic mice using four different vaccination protocols: early, late, very late and chronic. The vaccination protocols used are described in Section 1. The case of untreated mice has been analyzed in order to tune with experimental tumor growth and ensure that simulation shows no significant immune response.
We performed 200 in silico experiments for each of the four vaccination protocols plus 200 to compute statistics of the untreated case. Time zero of the simulation corresponds to a 6-week old mouse, the experimentally observed time of appearance of tumor cells. The simulation ends at week 66.
The percentage of experiments for which a solid tumor if formed is shown in Figure 3 as function of mice's age. A comparison with Figure 1 shows excellent agreement with in vivo experiments.
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The model allows recording the evolution of all populations of entities as a function of space and time.
The number of the immune cells as a function of time in the case of early, chronic and untreated is shown in Figure 4. The remaining plots in the case of late and very late vaccinations can be found in the Supplemental material.
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Curves referring to untreated, early, late and very late reach zero at the time when all mice die as shown in Figure 3.
The simulation clearly shows the critical effect of vaccination on numbers of both T helpers and cytotoxic T cells. T cells show an increase approximately at the end of the first vaccination cycle. The chronic schedule produces small humps which are the effect of successive vaccine inoculations. The main effect of chronic vaccination is to keep the number of cancer cells around 103. For other schedules, the cytotoxic T cell population relaxes back to the initial value; at the same time, the number of cancer cells starts to rise again. Looking at the humoral response, one can notice that T helpers activate B cells which then produce a large number of antibodies shortly after the beginning of vaccination. This transient phase is then followed by a steady phase in which TH and B cells go back to the initial values. This happens for all schedules including the chronic one.
The number of antibodies produced in the early schedule is sufficient to control the cancer cells up to 60 weeks. For the chronic schedule, the number of antibodies remains constant after the initial increase. This shows that while the initial burst of cytotoxic T cells reduces the initial population of cancer cells, the subsequent growth of cancer cells is controlled by the antibodies. To explain this effect we need to remember that CTL response initially appears after three cycles of vaccine injections as in in vivo experiments. Once stimulated, CTLs rapidly duplicate as they are continuously stimulated by a large number of cancer cells (landslide effect). When the number of cancer cells decreases drastically, unstimulated CTLs die and antibodies, having a longer lifetime, take over in controlling the tumor.
Humoral response is therefore the dominant action which prevents the formation of the solid tumor. This effect was also observed in vivo (De Giovanni et al., 2004; Lollini et al., 2005). Biological results show that the Triplex vaccine indeed induces a strong release of gamma-interferon, and that Th1-dependent immunoglobulin isotypes are very important in maintaining long-term protection from tumor onset (De Giovanni et al., 2004). However the mathematical model does not include a Th1–Th2 component.
Figure 5 shows the behavior of antibodies in chronic and early treatment and in untreated mice. A comparison with Figure 4 shows that the model has very similar behavior.
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In vivo experiments for chronic schedule have measured the cytotoxic response only for long-term periods (>30 weeks) and found no response (Lollini et al., 2005). This is in good agreements with long-term model results.
The oscillations of the number of cancer cells in the last 20 weeks (Fig. 3) are due to the fact that the number of simulated mice for all schedules, except for chronic, is low, and as a consequence, the statistical significance of the sample decreases. In general all schedules show a transient phase lasting roughly for the period of the first vaccination cycles, followed by a phase in which the tumor growth is controlled by the immune system as a consequence of the vaccination; finally, except for chronic, when the vaccine effect ends, the tumor grows undisturbed.
The error analysis shows that in the ‘steady phase’ in which the sample has a strong statistical significance, the standard deviation always reaches a maximum of 5–8% for all entities.
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4 CONCLUSIONS |
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TOPAbstract1 INTRODUCTION2 THE VACCINE MODEL3 RESULTS4 CONCLUSIONSREFERENCES |
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We presented a model that describes the competition between the tumor and the immune system reaction fostered by a vaccine. The model applies to the very early stage of tumorigenesis, i.e. before a solid tumor is formed. In silico experiments on two samples of 100 virtual mice show excellent agreements with in vivo experiments on HER-2/neu mice for all vaccination schedules. The model and its computer implementation is very flexible and new biological entities, behavior, and interactions can be easily added to the model. This helps achieve a realistic description of the immune responses that target solid tumor formation.
Moreover, the model produced an important suggestion for future biological experiments on the role of cytotoxic T cells. Experimental evaluation of the immune response in vaccinated mice was performed after multiple cycles of vaccination, and revealed a prevalent antibody response and a lack of cytotoxic T cell activity (De Giovanni et al., 2004; Lollini et al., 2005), a fact also correctly mirrored in the model described here. In addition the model shows early activation of the cytotoxic T cell response, after the first cycles of vaccination, at time points which were not yet tested experimentally.
Future work in this direction will focus upon a more detailed model that can describe the action of the single component of the Triplex vaccine on the immune response. Work in this direction is already in progress.
Once the model fits all the experimental data, it will be used for predictions. The choice of the vaccination schedule is driven either by statistical data or by the immunologist's intuition. However the first approach requires a large number of in vivo experiments. The in silico model can be used to perform a large number of simulated experiments which suggest key in vivo experiments on a small set of schedules which take into account biological or clinical constraints. We expect that optimum search algorithms, like simulated annealing or genetic algorithms, can be used for this purpose.
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Acknowledgments |
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F.P. and S.M. acknowledge partial support from University of Catania research grant and MIUR (PRIN 2004: Problemi matematici delle teorie cinetiche). Part of this work was done while F.P. was the research fellow of the Faculty of Pharmacy of University of Catania.
P.-L.L. acknowledges financial support from the University of Bologna, the Department of Experimental Pathology (‘Pallotti’ fund) and MIUR.
Received on February 14, 2005; revised on March 29, 2005; accepted on March 31, 2005
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F. Pappalardo, S. Musumeci, and S. Motta Modeling immune system control of atherogenesis Bioinformatics, August 1, 2008; 24(15): 1715 - 1721. [Abstract] [Full Text] [PDF]
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D. Santoni, M. Pedicini, and F. Castiglione Implementation of a regulatory gene network to simulate the TH1/2 differentiation in an agent-based model of hypersensitivity reactions Bioinformatics, June 1, 2008; 24(11): 1374 - 1380. [Abstract] [Full Text] [PDF]
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