Statistical Computations Underlying the Dynamics of Memory Updating

Psychophysical and neurophysiological studies have suggested that memory is not simply a carbon copy of our experience: Memories are modified or new memories are formed depending on the dynamic structure of our experience, and specifically, on how gradually or abruptly the world changes. We present a statistical theory of memory formation in a dynamic environment, based on a nonparametric generalization of the switching Kalman filter. We show that this theory can qualitatively account for several psychophysical and neural phenomena, and present results of a new visual memory experiment aimed at testing the theory directly. Our experimental findings suggest that humans can use temporal discontinuities in the structure of the environment to determine when to form new memory traces. The statistical perspective we offer provides a coherent account of the conditions under which new experience is integrated into an old memory versus forming a new memory, and shows that memory formation depends on inferences about the underlying structure of our experience.     

The Underlying Social Dynamics of Paradigm Shifts

We develop here a multi-agent model of the creation of knowledge (scientific progress or technological evolution) within a community of researchers devoted to such endeavors. In the proposed model, agents learn in a physical-technological landscape, and weight is attached to both individual search and social influence. We find that the combination of these two forces together with random experimentation can account for both i) marginal change, that is, periods of normal science or refinements on the performance of a given technology (and in which the community stays in the neighborhood of the current paradigm); and ii) radical change, which takes the form of scientific paradigm shifts (or discontinuities in the structure of performance of a technology) that is observed as a swift migration of the knowledge community towards the new and superior paradigm. The efficiency of the search process is heavily dependent on the weight that agents posit on social influence. The occurrence of a paradigm shift becomes more likely when each member of the community attaches a small but positive weight to the experience of his/her peers. For this parameter region, nevertheless, a conservative force is exerted by the representatives of the current paradigm. However, social influence is not strong enough to seriously hamper individual discovery, and can act so as to empower successful individual pioneers who have conquered the new and superior paradigm.     

Stochastic Dynamics Underlying Cognitive Stability and Flexibility

Cognitive stability and flexibility are core functions in the successful pursuit of behavioral goals. While there is evidence for a common frontoparietal network underlying both functions and for a key role of dopamine in the modulation of flexible versus stable behavior, the exact neurocomputational mechanisms underlying those executive functions and their adaptation to environmental demands are still unclear. In this work we study the neurocomputational mechanisms underlying cue based task switching (flexibility) and distractor inhibition (stability) in a paradigm specifically designed to probe both functions. We develop a physiologically plausible, explicit model of neural networks that maintain the currently active task rule in working memory and implement the decision process. We simplify the four-choice decision network to a nonlinear drift-diffusion process that we canonically derive from a generic winner-take-all network model. By fitting our model to the behavioral data of individual subjects, we can reproduce their full behavior in terms of decisions and reaction time distributions in baseline as well as distractor inhibition and switch conditions. Furthermore, we predict the individual hemodynamic response timecourse of the rule-representing network and localize it to a frontoparietal network including the inferior frontal junction area and the intraparietal sulcus, using functional magnetic resonance imaging. This refines the understanding of task-switch-related frontoparietal brain activity as reflecting attractor-like working memory representations of task rules. Finally, we estimate the subject-specific stability of the rule-representing attractor states in terms of the minimal action associated with a transition between different rule states in the phase-space of the fitted models. This stability measure correlates with switching-specific thalamocorticostriatal activation, i.e., with a system associated with flexible working memory updating and dopaminergic modulation of cognitive flexibility. These results show that stochastic dynamical systems can implement the basic computations underlying cognitive stability and flexibility and explain neurobiological bases of individual differences.     

Collective Dynamics Underlying Allosteric Transitions in Hemoglobin

Hemoglobin is the prototypic allosteric protein. Still, its molecular allosteric mechanism is not fully understood. To elucidate the mechanism of cooperativity on an atomistic level, we developed a novel computational technique to analyse the coupling of tertiary and quaternary motions. From Molecular Dynamics simulations showing spontaneous quaternary transitions, we separated the transition trajectories into two orthogonal sets of motions: one consisting of intra-chain motions only (referred to as tertiary-only) and one consisting of global inter-chain motions only (referred to as quaternary-only). The two underlying subspaces are orthogonal by construction and their direct sum is the space of full motions. Using Functional Mode Analysis, we were able to identify a collective coordinate within the tertiary-only subspace that is correlated to the most dominant motion within the quaternary-only motions, hence providing direct insight into the allosteric coupling mechanism between tertiary and quaternary conformation changes. This coupling-motion is substantially different from tertiary structure changes between the crystallographic structures of the T- and R-state. We found that hemoglobin''s allosteric mechanism of communication between subunits is equally based on hydrogen bonds and steric interactions. In addition, we were able to affect the T-to-R transition rates by choosing different histidine protonation states, thereby providing a possible atomistic explanation for the Bohr effect.     

Modeling the Geographic Spread of Rabies in China

In order to investigate how the movement of dogs affects the geographically inter-provincial spread of rabies in Mainland China, we propose a multi-patch model to describe the transmission dynamics of rabies between dogs and humans, in which each province is regarded as a patch. In each patch the submodel consists of susceptible, exposed, infectious, and vaccinated subpopulations of both dogs and humans and describes the spread of rabies among dogs and from infectious dogs to humans. The existence of the disease-free equilibrium is discussed, the basic reproduction number is calculated, and the effect of moving rates of dogs between patches on the basic reproduction number is studied. To investigate the rabies virus clades lineages, the two-patch submodel is used to simulate the human rabies data from Guizhou and Guangxi, Hebei and Fujian, and Sichuan and Shaanxi, respectively. It is found that the basic reproduction number of the two-patch model could be larger than one even if the isolated basic reproduction number of each patch is less than one. This indicates that the immigration of dogs may make the disease endemic even if the disease dies out in each isolated patch when there is no immigration. In order to reduce and prevent geographical spread of rabies in China, our results suggest that the management of dog markets and trades needs to be regulated, and transportation of dogs has to be better monitored and under constant surveillance.     

Modeling the Infection Dynamics of Bacteriophages in Enteric Escherichia coli: Estimating the Contribution of Transduction to Antimicrobial Gene Spread

Animal-associated bacterial communities are infected by bacteriophages, although the dynamics of these infections are poorly understood. Transduction by bacteriophages may contribute to transfer of antimicrobial resistance genes, but the relative importance of transduction among other gene transfer mechanisms is unknown. We therefore developed a candidate deterministic mathematical model of the infection dynamics of enteric coliphages in commensal Escherichia coli in the large intestine of cattle. We assumed the phages were associated with the intestine and were predominantly temperate. Model simulations demonstrated how, given the bacterial ecology and infection dynamics, most (>90%) commensal enteric E. coli bacteria may become lysogens of enteric coliphages during intestinal transit. Using the model and the most liberal assumptions about transduction efficiency and resistance gene frequency, we approximated the upper numerical limits (“worst-case scenario”) of gene transfer through specialized and generalized transduction in E. coli by enteric coliphages when the transduced genetic segment is picked at random. The estimates were consistent with a relatively small contribution of transduction to lateral gene spread; for example, generalized transduction delivered the chromosomal resistance gene to up to 8 E. coli bacteria/hour within the population of 1.47 × 10⁸ E. coli bacteria/liter luminal contents. In comparison, the plasmidic bla_CMY-2 gene carried by ∼2% of enteric E. coli was transferred by conjugation at a rate at least 1.4 × 10³ times greater than our generalized transduction estimate. The estimated numbers of transductants varied nonlinearly depending on the ecology of bacteria available for phages to infect, that is, on the assumed rates of turnover and replication of enteric E. coli.     

Modeling the Dynamics of Sensory Reweighting

Reweighting sensory information adaptively is considered critical for flexible postural control, but little is known of the time scale of the reweighting process. We analyzed the transient dynamics of sensory reweighting in a previously published nonlinear adaptive model of sensory integration in the human postural control system. The model’s dynamics of adaptation were tested in response to abrupt changes in the amplitude of the motion of the visual surround. In addition to qualitatively reproducing the correct asymptotic response to such changes in visual amplitude, as previously found, the model qualitatively reproduced the asymmetric transient response elucidated in recent experiments (Oie et al. in Gait Posture 2005). In particular, the model adapts at an initially rapid rate to a switch from low to high amplitude visual motion, but at an initially slower rate upon the return to low amplitude motion. The observed temporal asymmetry has potential functional value. Rapid downweighting of a visual stimulus that suddenly increases is necessary to prevent loss of upright equilibrium. A visual stimulus that decreases in amplitude does not pose a threat to upright balance, allowing for slower upweighting without functional consequence.     

Image-Guided Modeling of Virus Growth and Spread

Although many tools of cellular and molecular biology have been used to characterize single intracellular cycles of virus growth, few culture methods exist to study the dynamics of spatially spreading viruses over multiple generations. We have previously developed a method that addresses this need by tracking the spread of focal infections using immunocytochemical labeling and digital imaging. Here, we build reaction–diffusion models to account for spatio-temporal patterns formed by the spreading viral infection front as well as data from a single cycle of virus growth (one-step growth). Systems with and without the interferon-mediated antiviral response of the host cells are considered. Dynamic images of the spreading infections guide iterative model refinement steps that lead to reproduction of all of the salient features contained in the images, not just the velocity of the infection front. The optimal fits provide estimates for key parameters such as virus-host binding and the production rate of interferon. For the examined data, highly-lumped infection models that ignore the one-step growth dynamics provide a comparable fit to models that more accurately account for these dynamics, highlighting the fact that increased model complexity does not necessarily translate to improved fit. This work demonstrates how model building can facilitate the interpretation of experiments by highlighting contributions from both biological and methodological factors. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics

The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling--and manipulation--of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.     

Modeling the Spatial Spread of Rift Valley Fever in Egypt

Rift Valley fever (RVF) is a severe viral zoonosis in Africa and the Middle East that harms both human health and livestock production. It is believed that RVF in Egypt has been repeatedly introduced by the importation of infected animals from Sudan. In this paper, we propose a three-patch model for the process by which animals enter Egypt from Sudan, are moved up the Nile, and then consumed at population centers. The basic reproduction number for each patch is introduced and then the threshold dynamics of the model are established. We simulate an interesting scenario showing a possible explanation of the observed phenomenon of the geographic spread of RVF in Egypt.     

Bistable Dynamics Underlying Excitability of Ion Homeostasis in Neuron Models

When neurons fire action potentials, dissipation of free energy is usually not directly considered, because the change in free energy is often negligible compared to the immense reservoir stored in neural transmembrane ion gradients and the long–term energy requirements are met through chemical energy, i.e., metabolism. However, these gradients can temporarily nearly vanish in neurological diseases, such as migraine and stroke, and in traumatic brain injury from concussions to severe injuries. We study biophysical neuron models based on the Hodgkin–Huxley (HH) formalism extended to include time–dependent ion concentrations inside and outside the cell and metabolic energy–driven pumps. We reveal the basic mechanism of a state of free energy–starvation (FES) with bifurcation analyses showing that ion dynamics is for a large range of pump rates bistable without contact to an ion bath. This is interpreted as a threshold reduction of a new fundamental mechanism of ionic excitability that causes a long–lasting but transient FES as observed in pathological states. We can in particular conclude that a coupling of extracellular ion concentrations to a large glial–vascular bath can take a role as an inhibitory mechanism crucial in ion homeostasis, while the pumps alone are insufficient to recover from FES. Our results provide the missing link between the HH formalism and activator–inhibitor models that have been successfully used for modeling migraine phenotypes, and therefore will allow us to validate the hypothesis that migraine symptoms are explained by disturbed function in ion channel subunits, pumps, and other proteins that regulate ion homeostasis.     

Reconstruction of Underlying Nonlinear Deterministic Dynamics Embedded in Noisy Spike Trains

An experimentally recorded time series formed by the exact times of occurrence of the neuronal spikes (spike train) is likely to be affected by observational noise that provokes events mistakenly confused with neuronal discharges, as well as missed detection of genuine neuronal discharges. The points of the spike train may also suffer a slight jitter in time due to stochastic processes in synaptic transmission and to delays in the detecting devices. This study presents a procedure aimed at filtering the embedded noise (denoising the spike trains) the spike trains based on the hypothesis that recurrent temporal patterns of spikes are likely to represent the robust expression of a dynamic process associated with the information carried by the spike train. The rationale of this approach is tested on simulated spike trains generated by several nonlinear deterministic dynamical systems with embedded observational noise. The application of the pattern grouping algorithm (PGA) to the noisy time series allows us to extract a set of points that form the reconstructed time series. Three new indices are defined for assessment of the performance of the denoising procedure. The results show that this procedure may indeed retrieve the most relevant temporal features of the original dynamics. Moreover, we observe that additional spurious events affect the performance to a larger extent than the missing of original points. Thus, a strict criterion for the detection of spikes under experimental conditions, thus reducing the number of spurious spikes, may raise the possibility to apply PGA to detect endogenous deterministic dynamics in the spike train otherwise masked by the observational noise.     

Modeling the Dynamics of Disease States in Depression

Major depressive disorder (MDD) is a common and costly disorder associated with considerable morbidity, disability, and risk for suicide. The disorder is clinically and etiologically heterogeneous. Despite intense research efforts, the response rates of antidepressant treatments are relatively low and the etiology and progression of MDD remain poorly understood. Here we use computational modeling to advance our understanding of MDD. First, we propose a systematic and comprehensive definition of disease states, which is based on a type of mathematical model called a finite-state machine. Second, we propose a dynamical systems model for the progression, or dynamics, of MDD. The model is abstract and combines several major factors (mechanisms) that influence the dynamics of MDD. We study under what conditions the model can account for the occurrence and recurrence of depressive episodes and how we can model the effects of antidepressant treatments and cognitive behavioral therapy within the same dynamical systems model through changing a small subset of parameters. Our computational modeling suggests several predictions about MDD. Patients who suffer from depression can be divided into two sub-populations: a high-risk sub-population that has a high risk of developing chronic depression and a low-risk sub-population, in which patients develop depression stochastically with low probability. The success of antidepressant treatment is stochastic, leading to widely different times-to-remission in otherwise identical patients. While the specific details of our model might be subjected to criticism and revisions, our approach shows the potential power of computationally modeling depression and the need for different type of quantitative data for understanding depression.     

Imaging and Modeling the Dynamics of Clathrin-Mediated Endocytosis

Clathrin-mediated endocytosis (CME) plays a central role in cellular homeostasis and is mediated by clathrin-coated pits (CCPs). Live-cell imaging has revealed a remarkable heterogeneity in CCP assembly kinetics, which can be used as an intrinsic source of mechanistic information on CCP regulation but also poses several major problems for unbiased analysis of CME dynamics. The backbone of unveiling the molecular control of CME is an imaging-based inventory of the full diversity of individual CCP behaviors, which requires detection and tracking of structural fiduciaries and regulatory proteins with an accuracy of >99.9%, despite very low signals. This level of confidence can only be achieved by combining appropriate imaging modalities with self-diagnostic computational algorithms for image analysis and data mining.Clathrin-mediated endocytosis (CME) drives the uptake of diverse receptor-bound macromolecules and is one of the main endocytic mechanisms constitutively active in all mammalian cells. Clathrin-coated vesicles (CCVs) were the first transport vesicles to be isolated (Pearse 1975), which subsequently led to the identification of clathrin and the heterotetrameric adaptor protein AP2 as the major coat components (Pearse 1976, 1978). Further research in this area was spurred by the discovery that familial hypercholesterolemia is caused by a single substitution of a cysteine for a tyrosine in the cytoplasmic tail of the low-density lipoprotein receptor (LDLR), which disrupts its endocytic internalization motif and prevents its concentration in clathrin-coated pits (CCPs) (Anderson et al. 1977). In the following decades, biochemistry combined with molecular biology and electron microscopy (EM) have revealed much about the molecular players involved in CME (reviewed by Conner and Schmid 2003; Schmid and McMahon 2007; McMahon and Boucrot 2011; Boettner et al. 2012). Today, we know that CME is initiated via assembly of clathrin and AP2 to form CCPs and that receptor–ligand complexes (referred to as “cargo”) are concentrated in CCPs via direct interactions between endocytic motifs within their cytoplasmic domains and adaptor molecules that recruit clathrin. With the aid of a multitude of endocytic accessory proteins (EAPs)—many with as-yet poorly defined functions—CCPs undergo stabilization, maturation, and invagination. Finally, membrane fission, catalyzed by the GTPase dynamin, pinches off the CCV carrying its cargo into the cell.Although powerful and invaluable, bulk biochemical assays can only report cumulative and ensemble-averaged effects on CME, whereas EM only provides static snapshots of highly dynamic structures. Both approaches are not sufficient to resolve critical, rate-limiting stages of CCP maturation and alternative outcomes that prevent CCV internalization. They are also not sufficient to probe the frequently overlapping functions of individual components in CCP formation and maturation. Perturbation of molecular players in a system with such redundancy may lead to no detectable shifts, or to detectable shifts that merely represent system adaptation, and thus may not reveal the actual function of the targeted component itself. Moreover, perturbing CME may globally interfere with cell homeostasis, which can also elicit phenotypes unrelated to the actual functions of the target. To remedy these issues, it is necessary to follow the dynamics of CME at the level of individual CCPs and to correlate these behaviors with differential patterns of cargo and EAP recruitment and activity.These goals became approachable with the “GFP revolution” in the 1990s, which was paralleled by leaps in the sensitivity of digital light microscopy. For CME, the power of these technologies was first shown by Keen and colleagues, who used a green fluorescent protein (GFP) fusion of the clathrin light chain (CLC) to image clathrin dynamics by time-lapse wide-field epifluorescence microscopy (Gaidarov et al. 1999). Since then, numerous live-cell imaging studies have revealed remarkable heterogeneity in CCP assembly kinetics and internalization (Rappoport and Simon 2003; Ehrlich et al. 2004; Keyel et al. 2004; Merrifield et al. 2005; Loerke et al. 2009; Taylor et al. 2011). Although the physiological and molecular bases for this heterogeneity remain to be uncovered, the working hypothesis is that CCP heterogeneity arises from variations in molecular composition, in cortical membrane mechanics, and in differences between cell types. More recent advances in imaging and computational image data analyses have made it possible to determine the order in which EAPs are incorporated or released from growing CCPs. Thus, multidimensional live-cell imaging and mathematical models, in combination with very mild chemical, molecular, and mechanical perturbations, may uncover how the molecular composition of an assembling CCP affects its behavior. In the following we describe the developments of imaging modalities and image analysis methods that have led to the current state of the art in quantitative imaging of CME.     

Modeling the Afferent Dynamics of the Baroreflex Control System

In this study we develop a modeling framework for predicting baroreceptor firing rate as a function of blood pressure. We test models within this framework both quantitatively and qualitatively using data from rats. The models describe three components: arterial wall deformation, stimulation of mechanoreceptors located in the BR nerve-endings, and modulation of the action potential frequency. The three sub-systems are modeled individually following well-established biological principles. The first submodel, predicting arterial wall deformation, uses blood pressure as an input and outputs circumferential strain. The mechanoreceptor stimulation model, uses circumferential strain as an input, predicting receptor deformation as an output. Finally, the neural model takes receptor deformation as an input predicting the BR firing rate as an output. Our results show that nonlinear dependence of firing rate on pressure can be accounted for by taking into account the nonlinear elastic properties of the artery wall. This was observed when testing the models using multiple experiments with a single set of parameters. We find that to model the response to a square pressure stimulus, giving rise to post-excitatory depression, it is necessary to include an integrate-and-fire model, which allows the firing rate to cease when the stimulus falls below a given threshold. We show that our modeling framework in combination with sensitivity analysis and parameter estimation can be used to test and compare models. Finally, we demonstrate that our preferred model can exhibit all known dynamics and that it is advantageous to combine qualitative and quantitative analysis methods.