A shape space approach to the dynamics of the immune system

A simple mathematical model of Jerne's immune network is proposed where interactions among idiotypes are set according to their location in a shape space. Although the number of interacting idiotypes is potentially infinite, the simplicity of the model makes it possible to compute the attractors of the dynamics, to define the regions in the four parameters space related to the dynamical behavior and to predict the scaling law giving the number of different antigens that can be presented to the network without triggering dangerous instabilities. It is shown that only a low connectivity regime is safe for the immune network.     

Parameter redundancy in discrete state‐space and integrated models

Discrete state‐space models are used in ecology to describe the dynamics of wild animal populations, with parameters, such as the probability of survival, being of ecological interest. For a particular parametrization of a model it is not always clear which parameters can be estimated. This inability to estimate all parameters is known as parameter redundancy or a model is described as nonidentifiable. In this paper we develop methods that can be used to detect parameter redundancy in discrete state‐space models. An exhaustive summary is a combination of parameters that fully specify a model. To use general methods for detecting parameter redundancy a suitable exhaustive summary is required. This paper proposes two methods for the derivation of an exhaustive summary for discrete state‐space models using discrete analogues of methods for continuous state‐space models. We also demonstrate that combining multiple data sets, through the use of an integrated population model, may result in a model in which all parameters are estimable, even though models fitted to the separate data sets may be parameter redundant.     

Character-state space versus rate of evolution in phylogenetic inference

With only four alternative character states, parallelisms and reversals are expected to occur frequently when using nucleotide characters for phylogenetic inference. Greater available character‐state space has been described as one of the advantages of third codon positions relative to first and second codon positions, as well as amino acids relative to nucleotides. We used simulations to quantify how character‐state space and rate of evolution relate to one another, and how this relationship is affected by differences in: tree topology, branch lengths, rate heterogeneity among sites, probability of change among states, and frequency of character states. Specifically, we examined how inferred tree lengths, consistency and retention indices, and accuracy of phylogenetic inference are affected. Our results indicate that the relatively small increases in the character‐state space evident in empirical data matrices can provide enormous benefits for the accuracy of phylogenetic inference. This advantage may become more pronounced with unequal probabilities of change among states. Although increased character‐state space greatly improved the accuracy of topology inference, improvements in the estimation of the correct tree length were less apparent. Accuracy and inferred tree length improved most when character‐state space increased initially; further increases provided more modest improvements. © The Willi Hennig Society 2004.     

From HIV infection to AIDS: a dynamically induced percolation transition?

The origin of the unusual incubation period distribution in the development of AIDS is largely unresolved. A key factor in understanding the observed distribution of latency periods, as well as the occurrence of infected individuals not developing AIDS at all, is the dynamics of the long-lasting struggle between HIV and the immune system. Using a computer simulation, we study the diversification of viral genomes under mutation and the selective pressure of the immune system. In non-HIV infections, vast spreading of viral genomes in genome space usually does not take place. In the case of an HIV infection, this may occur, as the virus successively weakens the immune system by the depletion of CD4+ cells. In a sequence space framework, this leads to a dynamically induced percolation transition, corresponding to the onset of AIDS. As a result, we obtain a prolonged shape of the incubation period distribution, as well as a finite fraction of non-progressors that do not develop AIDS, comparing well with results from recent clinical research.     

A latent state space model for estimating brain dynamics from electroencephalogram (EEG) data

Modern neuroimaging technologies have substantially advanced the measurement of brain activity. Electroencephalogram (EEG) as a noninvasive neuroimaging technique measures changes in electrical voltage on the scalp induced by brain cortical activity. With its high temporal resolution, EEG has emerged as an increasingly useful tool to study brain connectivity. Challenges with modeling EEG signals of complex brain activity include interactions among unknown sources, low signal-to-noise ratio, and substantial between-subject heterogeneity. In this work, we propose a state space model that jointly analyzes multichannel EEG signals and learns dynamics of different sources corresponding to brain cortical activity. Our model borrows strength from spatially correlated measurements and uses low-dimensional latent states to explain all observed channels. The model can account for patient heterogeneity and quantify the effect of a subject's covariates on the latent space. The EM algorithm, Kalman filtering, and bootstrap resampling are used to fit the state space model and provide comparisons between patient diagnostic groups. We apply the developed approach to a case-control study of alcoholism and reveal significant attenuation of brain activity in response to visual stimuli in alcoholic subjects compared to healthy controls.     

Scale-free dynamics of somatic adaptability in immune system

The long-time dynamics of somatic adaptability in immune system is simulated by a simple physical model defined in the shape space. The immune system described by the model exhibits a scale free behavior as is observed in living systems. The balance between the positive and negative feedbacks of the model leads to a robust immune system where the positive one corresponds to the formation of memory cells and the negative one to immunosuppression. Also the immunosenescence of the system is discussed based on the time-dependence of the epigenetic landscape of the adaptive immune cells in the shape space.     

Quantum-like model of brain's functioning: decision making from decoherence

We present a quantum-like model of decision making in games of the Prisoner's Dilemma type. By this model the brain processes information by using representation of mental states in a complex Hilbert space. Driven by the master equation the mental state of a player, say Alice, approaches an equilibrium point in the space of density matrices (representing mental states). This equilibrium state determines Alice's mixed (i.e., probabilistic) strategy. We use a master equation in which quantum physics describes the process of decoherence as the result of interaction with environment. Thus our model is a model of thinking through decoherence of the initially pure mental state. Decoherence is induced by the interaction with memory and the external mental environment. We study (numerically) the dynamics of quantum entropy of Alice's mental state in the process of decision making. We also consider classical entropy corresponding to Alice's choices. We introduce a measure of Alice's diffidence as the difference between classical and quantum entropies of Alice's mental state. We see that (at least in our model example) diffidence decreases (approaching zero) in the process of decision making. Finally, we discuss the problem of neuronal realization of quantum-like dynamics in the brain; especially roles played by lateral prefrontal cortex or/and orbitofrontal cortex.     

Abrupt regime shifts in space and time along rivers and connected lake systems

Regime shifts between clear and turbid water states are commonly found in shallow lakes. These shifts are attributed to a positive feedback between water clarity and submerged macrophytes (underwater plants). Altering the retention time of the water may influence these interactions and thus potentially reduce the probability of alternative stable states. Here we assessed the effect of water retention time on the occurrence of alternative states in water quality of flushed lakes, chains of lakes and rivers using a spatially explicit simple model. Our results indicate that increased flushing of lakes rapidly decreases the range of parameters with alternative stable states up to their total disappearance at a flushing rate of about 50% the algal growth rate. Similarly, in a chain of lakes or in rivers with low flowing velocity, our model predicts that alternative stable states can only occur for systems with a high retention time. Despite the lack of hysteresis at lower water retention times, we predict that abrupt changes between clear and turbid states are still possible both in time and in space. Over a wide range of parameters, the equilibrium state of the chain of lakes shows a steep gradient of vegetation cover. Further, the transient dynamics of the model often include rapid shifts in time. For example, a local regime shift that occurs upstream may propagate through the whole lake chain or river due to a domino effect. All results of the simple model could qualitatively be reproduced with a more mechanistic model. The abrupt rather than gradual response of submerged macrophytes to reduced turbidity levels still makes river systems rather resilient to management measure. The importance of the initial turbidity and the observed domino effect suggest that restoration measures should start upstream and that these measures should eventually trigger regime shifts downstream.     

The race between initial T-helper expansion and virus growth upon HIV infection influences polyclonality of the response and viral set-point

Infection with HIV is characterized by very diverse disease-progression patterns across patients, associated with a wide variation in viral set-points. Progression is a multifactorial process, but an important role has been attributed to the HIV-specific T-cell response. To explore the conditions under which different set-points may be explained by differences in initial CD4 and CD8 T-cell responses and virus inoculum, we have formulated a model assuming that HIV-specific CD4 cells are both targets for infection and mediators of a monoclonal or polyclonal immune response. Clones differ in functional avidity for HIV epitopes. Importantly, in contrast to previous models, in this model we obtained coexistence of multiple clones at steady-state viral set-point, as seen in HIV infection. We found that, for certain parameter conditions, multiple steady states are possible: with few initial CD4 helper cells and high virus inoculum, no immune response is established and target-cell-limited infection follows, with associated high viral load; when CD4 clones are initially large and virus inoculum is low, infection can be controlled by several clones. The conditions for the dependence of viral set-point on initial inoculum and CD4 T-helper clone availability are investigated in terms of the effector mechanism of the clones involved.     

On observation distributions for state space models of population survey data

1.?State space models are starting to replace more simple time series models in analyses of temporal dynamics of populations that are not perfectly censused. By simultaneously modelling both the dynamics and the observations, consistent estimates of population dynamical parameters may be obtained. For many data sets, the distribution of observation errors is unknown and error models typically chosen in an ad-hoc manner. 2.?To investigate the influence of the choice of observation error on inferences, we analyse the dynamics of a replicated time series of red kangaroo surveys using a state space model with linear state dynamics. Surveys were performed through aerial counts and Poisson, overdispersed Poisson, normal and log-normal distributions may all be adequate for modelling observation errors for the data. We fit each of these to the data and compare them using AIC. 3.?The state space models were fitted with maximum likelihood methods using a recent importance sampling technique that relies on the Kalman filter. The method relaxes the assumption of Gaussian observation errors required by the basic Kalman filter. Matlab code for fitting linear state space models with Poisson observations is provided. 4.?The ability of AIC to identify the correct observation model was investigated in a small simulation study. For the parameter values used in the study, without replicated observations, the correct observation distribution could sometimes be identified but model selection was prone to misclassification. On the other hand, when observations were replicated, the correct distribution could typically be identified. 5.?Our results illustrate that inferences may differ markedly depending on the observation distributions used, suggesting that choosing an adequate observation model can be critical. Model selection and simulations show that for the models and parameter values in this study, a suitable observation model can typically be identified if observations are replicated. Model selection and replication of observations, therefore, provide a potential solution when the observation distribution is unknown.     

T helper cell activation and human retroviral pathogenesis.

T helper (Th) cells are of central importance in regulating many critical immune effector mechanisms. The profile of cytokines produced by Th cells correlates with the type of effector cells induced during the immune response to foreign antigen. Th1 cells induce the cell-mediated immune response, while Th2 cells drive antibody production. Th cells are the preferential targets of human retroviruses. Infections with human T-cell leukemia virus (HTLV) or human immunodeficiency virus (HIV) result in the expansion of Th cells by the action of HTLV (adult T-cell leukemia) or the progressive loss of T cells by the action of HIV (AIDS). Both retrovirus infections impart a high-level activation state in the host immune cells as well as systemically. However, diverging responses to this activation state have contrasting effects on the Th-cell population. In HIV infection, Th-cell loss has been attributed to several mechanisms, including a selective elimination of cells by apoptosis. The induction of apoptosis in HIV infection is complex, with many different pathways able to induce cell death. In contrast, infection of Th cells with HTLV-1 affords the cell a protective advantage against apoptosis. This advantage may allow the cell to escape immune surveillance, providing the opportunity for the development of Th-cell cancer. In this review, we will discuss the impact of Th-cell activation and general immune activation on human retrovirus expression with a focus upon Th-cell function and the progression to disease.     

Modeling the T-cell dynamics and pathogenesis of HTLV-I infection

Human T-cell lymphotropic virus type I (HTLV-I) infection in humans causes a chronic infection of CD4⁺ T cells, and is associated with various disease outcomes, among them with the development of adult T-cell leukemia (ATL). The T-cell dynamics after HTLV-I infection can be described in a mathematical model with coupled differential equations. The infection process is modeled assuming cell-to-cell infection of CD4⁺ T cells. The model allows for CD4⁺ T cell subsets of susceptible, latently infected and actively infected cells as well as for leukemia cells. Latently infected T cells may harbor the virus for several years until they become activated and able to infect susceptible T cells. Uncontrolled proliferation of CD4⁺ T cells with monoclonal DNA-integration of HTLV-I results in the development of ATL. The model describes basic features that characterize HTLV-I infection; the chronic infection of CD4⁺ T cells, the increasing number of abnormal cells and the possible progression to ATL.     

Paradoxical inhibition of T-cell function in response to CTLA-4 blockade; heterogeneity within the human T-cell population

T-cell co-stimulation delivered by the molecules B7-1 or B7-2 through CD28 has a positive effect on T-cell activation, whereas engagement of cytotoxic T-lymphocyte antigen 4 (CTLA-4) by these molecules inhibits activation. In vivo administration to mice of blocking monoclonal antibodies or Fab fragments against CTLA-4 can augment antigen-specific T-cell responses and, thus, therapy with monoclonal antibody against CTLA-4 has potential applications for tumor therapy and enhancement of vaccine immunization. The effects of B7-1 and B7-2 co-stimulation through CD28 depend on the strength of the signal delivered through the T-cell receptor (TCR) and the activation state of T cells during activation. Thus, we sought to determine whether these factors similarly influence the effect of B7-mediated signals delivered through CTLA-4 during T-cell activation. Using freshly isolated human T cells and Fab fragments of a monoclonal antibody against CTLA-4, we demonstrate here that CTLA-4 blockade can enhance or inhibit the clonal expansion of different T cells that respond to the same antigen, depending on both the T-cell activation state and the strength of the T-cell receptor signal delivered during T-cell stimulation. Thus, for whole T-cell populations, blocking a negative signal may paradoxically inhibit immune responses. These results provide a theoretical framework for clinical trials in which co-stimulatory signals are manipulated in an attempt to modulate the immune response in human disease.     

Communication over the Network of Binary Switches Regulates the Activation of A2A Adenosine Receptor

Dynamics and functions of G-protein coupled receptors (GPCRs) are accurately regulated by the type of ligands that bind to the orthosteric or allosteric binding sites. To glean the structural and dynamical origin of ligand-dependent modulation of GPCR activity, we performed total ~ 5 μsec molecular dynamics simulations of A_2A adenosine receptor (A_2AAR) in its apo, antagonist-bound, and agonist-bound forms in an explicit water and membrane environment, and examined the corresponding dynamics and correlation between the 10 key structural motifs that serve as the allosteric hotspots in intramolecular signaling network. We dubbed these 10 structural motifs “binary switches” as they display molecular interactions that switch between two distinct states. By projecting the receptor dynamics on these binary switches that yield 2¹⁰ microstates, we show that (i) the receptors in apo, antagonist-bound, and agonist-bound states explore vastly different conformational space; (ii) among the three receptor states the apo state explores the broadest range of microstates; (iii) in the presence of the agonist, the active conformation is maintained through coherent couplings among the binary switches; and (iv) to be most specific, our analysis shows that W246, located deep inside the binding cleft, can serve as both an agonist sensor and actuator of ensuing intramolecular signaling for the receptor activation. Finally, our analysis of multiple trajectories generated by inserting an agonist to the apo state underscores that the transition of the receptor from inactive to active form requires the disruption of ionic-lock in the DRY motif.     

Salmonella fecal shedding and immune responses are dose- and serotype- dependent in pigs

Despite the public health importance of Salmonella infection in pigs, little is known about the associated dynamics of fecal shedding and immunity. In this study, we investigated the transitions of pigs through the states of Salmonella fecal shedding and immune response post-Salmonella inoculation as affected by the challenge dose and serotype. Continuous-time multistate Markov models were developed using published experimental data. The model for shedding had four transient states, of which two were shedding (continuous and intermittent shedding) and two non-shedding (latency and intermittent non-shedding), and one absorbing state representing permanent cessation of shedding. The immune response model had two transient states representing responses below and above the seroconversion level. The effects of two doses [low (0.65×10(6) CFU/pig) and high (0.65×10(9) CFU/pig)] and four serotypes (Salmonella Yoruba, Salmonella Cubana, Salmonella Typhimurium, and Salmonella Derby) on the models' transition intensities were evaluated using a proportional intensities model. Results indicated statistically significant effects of the challenge dose and serotype on the dynamics of shedding and immune response. The time spent in the specific states was also estimated. Continuous shedding was on average 10-26 days longer, while intermittent non-shedding was 2-4 days shorter, in pigs challenged with the high compared to low dose. Interestingly, among pigs challenged with the high dose, the continuous and intermittent shedding states were on average up to 10-17 and 3-4 days longer, respectively, in pigs infected with S. Cubana compared to the other three serotypes. Pigs challenged with the high dose of S. Typhimurium or S. Derby seroconverted on average up to 8-11 days faster compared to the low dose. These findings highlight that Salmonella fecal shedding and immune response following Salmonella challenge are dose- and serotype-dependent and that the detection of specific Salmonella strains and immune responses in pigs are time-sensitive.     

Control of virus-specific CD8+ T-cell exhaustion and immune-mediated pathology by E3 ubiquitin ligase Cbl-b during chronic viral infection

A characteristic feature in the immune response to many persistent viral infections is the dysfunction or deletion of antigen-specific T cells (exhaustion). This down-regulation of virus-specific T-cell response represents a critical control mechanism that exists within T-cell activation pathways to prevent lethal disease by inappropriate responses against disseminating virus infections. However, the molecular mechanisms by which the immune system determines whether to mount a full response to such infections remain largely unexplored. Here, we have established that in the murine lymphocytic choriomeningitis virus (LCMV) model, induction of the T-cell receptor signaling inhibitor molecule E3 ligase Cbl-b is critically involved in this decision. In particular, our data revealed that Cbl-b controls the program responsible for T-cell tolerance (exhaustion) induction during a chronic viral infection. Thus, Cbl-b(-/-) mice infected with a low dose of LCMV Docile mount a strong CD8(+) T-cell response that rapidly clears the infection, and the animals remain healthy; in contrast, down-regulation of the epitope-specific CD8(+) T-cell population in persistently infected Cbl-b(-/-) mice, compared to that in chronically infected B6 mice, was significantly delayed, and this was associated with increased morbidity and eventual death in nearly 20% of the animals. Interestingly, infection of Cbl-b(-/-) mice with a moderate virus dose resulted in rapid death with 100% mortality by 7 to 8 days after infection, caused by a dysregulated antiviral T-cell response, whereas the infected B6 mice survived and remained healthy. In conclusion, our results suggest that Cbl-b is critically involved in T-cell exhaustion and prevention of lethal disease.     

Down-regulation of macaque gammadelta + T cells in lymphoid compartments after rectal infection with SIVsmmPBj14

The dynamics of T cells expressing the gammadelta T-cell receptor in mucosae and other compartments during the course of human immunodeficiency virus (HIV)-1 infection are poorly understood. To examine the impact of an acquired immunodeficiency syndrome virus on the gammadelta + T-cell population, rectal inoculation of macaques with simian immunodeficiency virus (SIV)-PBj14 was used as a model. After rectal inoculation, five macaques were sacrificed on days 4, 5, or 7 and then assessed for changes in the gammadelta T-cell receptor repertoire in different lymphoid compartments. There was decreased representation of gammadelta + T cells in the intestinal mucosae, blood, and spleens. Overall, the reduced number of total gammadelta + T cells was consistent with decreases in the Vgamma or Vdelta T-cell sub-populations. Nevertheless, there was no consistent deletion or expansion of a selected Vdelta + or Vdelta + cell sub-population. These results demonstrate that SIV-PBj14 replication and dissemination after mucosal inoculation resulted in a decline of detectable gammadelta + T cells, suggesting that macaque gammadelta + T cells are susceptible to down-regulation or destruction during acute SIV-PBj14 infection.     

Efficient Optimization of Stimuli for Model-Based Design of Experiments to Resolve Dynamical Uncertainty

This model-based design of experiments (MBDOE) method determines the input magnitudes of an experimental stimuli to apply and the associated measurements that should be taken to optimally constrain the uncertain dynamics of a biological system under study. The ideal global solution for this experiment design problem is generally computationally intractable because of parametric uncertainties in the mathematical model of the biological system. Others have addressed this issue by limiting the solution to a local estimate of the model parameters. Here we present an approach that is independent of the local parameter constraint. This approach is made computationally efficient and tractable by the use of: (1) sparse grid interpolation that approximates the biological system dynamics, (2) representative parameters that uniformly represent the data-consistent dynamical space, and (3) probability weights of the represented experimentally distinguishable dynamics. Our approach identifies data-consistent representative parameters using sparse grid interpolants, constructs the optimal input sequence from a greedy search, and defines the associated optimal measurements using a scenario tree. We explore the optimality of this MBDOE algorithm using a 3-dimensional Hes1 model and a 19-dimensional T-cell receptor model. The 19-dimensional T-cell model also demonstrates the MBDOE algorithm’s scalability to higher dimensions. In both cases, the dynamical uncertainty region that bounds the trajectories of the target system states were reduced by as much as 86% and 99% respectively after completing the designed experiments in silico. Our results suggest that for resolving dynamical uncertainty, the ability to design an input sequence paired with its associated measurements is particularly important when limited by the number of measurements.     

Parasites and immune responses: memory illusion?

Immunological memory responses to intracellular protozoa and extracellular helminths govern host resistance and susceptibility to reinfection. Humans and livestock living in parasitic disease endemic regions face continuous exposure from a very early age that often leads to asymptomatic chronic infection over their entire lifespan. Fundamental immunological studies suggest that the generation of T-cell memory is driven by tightly coordinated innate and adaptive cellular immune responses rapidly triggered following initial host infection. A key distinguishing feature of immune memory maintenance between the majority of parasitic diseases and most bacterial or viral diseases is long-term antigen persistence. Consequently, functional parasite immune memory is in a continuous, dynamic flux between activation and deactivation producing functional parasite killing or functional memory cell death. In this sense, T-cell immune memory can be regarded as "memory illusion." Furthermore, due to the finite capacity of memory lymphocytes to proliferate, continuous parasite antigen stimulation may exceed a threshold level at some point in the chronically infected host. This may result in suboptimal effector immune memory leading to host susceptibility to reinfection, or immune dysregulation yielding disease reactivation or immune pathology. The goal of this review is to highlight, through numerous examples, what is currently known about T-cell immune memory to parasites and to provide compelling hypotheses on the survival and maintenance of parasite "memory illusion." These novel concepts are discussed in the context of rationale parasite vaccine design strategies.