Characteristic nonlinearities of the 3/s ictal electroencephalogram identified by nonlinear autoregressive analysis

We describe a method for the characterization of electroencephalographic (EEG) signals based on a model which features nonlinear feedback. The characteristic EEG fingerprints obtained through this approach display the time-course of nonlinear interactions, rather than aspects susceptible to standard spectral analysis. Fingerprints of seizure discharges in six patients (five with typical absence seizures, one with complex partial seizures) revealed significant nonlinear interactions. The timing and pattern of these interactions correlated closely with the seizure type. Nonlinear autoregressive (NLAR) analysis is compared with other nonlinear dynamical measures that have been applied to the EEG.     

An autoregressive method for the measurement of synchronization of interictal and ictal EEG signals

We propose a new measure of synchronization of multichannel ictal and interictal EEG signals. The measure is based on the residual covariance matrix of a multichannel autoregressive model. A major advantage of this measure is its ability to be interpreted both in the framework of stochastic and deterministic models. A preliminary analysis of EEG data from three patients using this measure documents the expected increased synchronization during ictal periods but also reveals that increased synchrony persists for prolonged periods (up to 2 h or more) in the postictal period. Received: 20 July 1997 / Accepted in revised form: 26 January 1999     

Mechanisms underlying the dual-mode regulation of microtubule dynamics by Kip3/kinesin-8

The kinesin-8 family of microtubule motors plays?a critical role in microtubule length control in cells. These motors have complex effects on microtubule dynamics: they destabilize growing microtubules yet stabilize shrinking microtubules. The budding yeast kinesin-8, Kip3, accumulates on plus ends of growing but not shrinking microtubules. Here we identify an essential role of the tail domain of Kip3 in mediating both its destabilizing and its stabilizing activities. The Kip3 tail promotes Kip3's accumulation at the plus ends and facilitates the destabilizing effect of Kip3. However, the Kip3 tail also inhibits microtubule shrinkage and is required for promoting microtubule rescue by Kip3. These effects of the tail domain are likely to be mediated by the tubulin- and microtubule-binding activities that we describe. We propose a concentration-dependent model for the coordination of the destabilizing and stabilizing activities of Kip3 and discuss its relevance to cellular microtubule organization.     

Comparative autoregressive moving average analysis of kinetochore microtubule dynamics in yeast

To elucidate the regulation of kinetochore microtubules (kMTs) by kinetochore proteins in Saccharomyces cerevisiae, we need tools to characterize and compare stochastic kMT dynamics. Here we show that autoregressive moving average (ARMA) models, combined with a statistical framework for testing the significance of differences between ARMA model parameters, provide a sensitive method for identifying the subtle changes in kMT dynamics associated with kinetochore protein mutations. Applying ARMA analysis to G1 kMT dynamics, we found that 1), kMT dynamics in the kinetochore protein mutants okp1-5 and kip3Delta are different from those in wild-type, demonstrating the regulation of kMTs by kinetochore proteins; 2), the kinase Ipl1p regulates kMT dynamics also in G1; and 3), the mutant dam1-1 exhibits three different phenotypes, indicating the central role of Dam1p in maintaining the attachment of kMTs and regulating their dynamics. We also confirmed that kMT dynamics vary with temperature, and are most likely differentially regulated at 37 degrees C. Therefore, when elucidating the role of a protein in kMT regulation using a temperature-sensitive mutant, dynamics in the mutant at its nonpermissive temperature must be compared to those in wild-type at the same temperature, not to those in the mutant at its permissive temperature.     

Nonlinear optical studies of heme protein dynamics: implications for proteins as hybrid states of matter

Protein structure is fundamentally related to function. However, static structures alone are insufficient to understand how a protein works. Dynamics play an equally important role. Given that proteins are highly associated aperiodic systems, it may be expected that protein dynamics would follow glass-like dynamics. However, protein functions occur on time scales orders of magnitude faster than the time scales typically associated with glassy systems. It is becoming clear that the reaction forces driving functions do not sample entirely the large number of configurations available to a protein but are highly directed along an optimized pathway. Could there be any correlation between specific topological features in protein structures and dynamics that leads to strongly correlated atomic displacements in the dynamical response to a perturbation? This review will try to provide an answer by focusing upon recent nonlinear optical studies with the aim of directly observing functionally important protein motions over the entire dynamic range of the protein response function. The specific system chosen is photoinduced dynamics of ligand dissociation at the active site in heme proteins, with myoglobin serving as the simplest model system. The energetics and nuclear motions from the very earliest events involved in bond breaking on the femtosecond time scale all the way out to ligand escape and bimolecular rebinding on the microsecond and millisecond time scale have been mapped out. The picture that is emerging is that the system consists of strongly coupled motions from the very instant the bond breaks at the active site that cascade into low frequency collective modes specific to the protein structure. It is this coupling that imparts the ability of a protein to function on time scales more commensurate with liquids while simultaneously conserving structural integrity akin to solids.     

Nonlinear dynamics in ecosystem response to climatic change: Case studies and policy implications

Many biological, hydrological, and geological processes are interactively linked in ecosystems. These ecological phenomena normally vary within bounded ranges, but rapid, nonlinear changes to markedly different conditions can be triggered by even small differences if threshold values are exceeded. Intrinsic and extrinsic ecological thresholds can lead to effects that cascade among systems, precluding accurate modeling and prediction of system response to climate change. Ten case studies from North America illustrate how changes in climate can lead to rapid, threshold-type responses within ecological communities; the case studies also highlight the role of human activities that alter the rate or direction of system response to climate change. Understanding and anticipating nonlinear dynamics are important aspects of adaptation planning since responses of biological resources to changes in the physical climate system are not necessarily proportional and sometimes, as in the case of complex ecological systems, inherently nonlinear.     

Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis

We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seenin vivo, including immunostimulation of tumor growth, “sneaking through” of the tumor, and formation of a tumor “dormant state”. The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL₁ in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measuredin vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.     

Brain dynamics underlying the nonlinear threshold for access to consciousness

When a flashed stimulus is followed by a backward mask, subjects fail to perceive it unless the target-mask interval exceeds a threshold duration of about 50 ms. Models of conscious access postulate that this threshold is associated with the time needed to establish sustained activity in recurrent cortical loops, but the brain areas involved and their timing remain debated. We used high-density recordings of event-related potentials (ERPs) and cortical source reconstruction to assess the time course of human brain activity evoked by masked stimuli and to determine neural events during which brain activity correlates with conscious reports. Target-mask stimulus onset asynchrony (SOA) was varied in small steps, allowing us to ask which ERP events show the characteristic nonlinear dependence with SOA seen in subjective and objective reports. The results separate distinct stages in mask-target interactions, indicating that a considerable amount of subliminal processing can occur early on in the occipito-temporal pathway (<250 ms) and pointing to a late (>270 ms) and highly distributed fronto-parieto-temporal activation as a correlate of conscious reportability.     

Modelling the social dynamics of a sex industry: Its implications for spread of HIV/AIDS

A theoretical model is proposed for a community which has the structure of two classes (direct and indirect) of commercial sex workers (CSW), and two classes of sexually active male customers with different levels of sexual activity. The direct CSW’s work in brothels while the indirect CSW’s are based in commercial establishments such as bars, cafes, and massage parlours where sex can be bought on request and conducted elsewhere. Behaviour change and the resulting change of activity class occurs between the two classes of CSW’s and two classes of males under the setting of the proliferation of human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome epidemic and the subsequent intervention programmes. In recently years, this phenomenon has been observed in several countries in Asia. Given the lower levels of condom use and higher HIV prevalence of the indirect CSW’s, ascertaining the impact of this change in the structure of the sex industry on the spread of HIV is the main focus of this paper. The complete analysis of the disease-free model is given. For the full model, local analysis will be performed for the case of preferred mixing without activity class change, as well as the case with activity class change and restricted mixing. The basic reproduction number for the spread of epidemic will be derived for each case. Results of biological significance include: (i) the change of behaviour by the CSW’s has a more direct effect on the spread of HIV than that of the male customers; (ii) the basic reproduction number is obtained by considering all possible infection cycles of the heterosexual transmission of HIV which indicates the importance of understanding the sexual networking in heterosexual transmission of HIV; (iii) the social dynamics of the sex industry is not just a simple ’supply and demand’ mechanism driven by the demand of the customers, hence highlighting the need for further understanding of the changing structure of the sex industry. The main points of this work will be illustrated with numerical examples using the HIV data of Thailand.     

Long-term forest-savannah dynamics in the Bolivian Amazon: implications for conservation

The aim of this paper is to evaluate the respective roles of past changes in climate, geomorphology and human activities in shaping the present-day forest-savannah mosaic of the Bolivian Amazon, and consider how this palaeoecological perspective may help inform conservation strategies for the future. To this end, we review a suite of palaeoecological and archaeological data from two distinct forest-savannah environments in lowland Bolivia: Noel Kempff Mercado National Park (NKMNP) on the Precambrian Shield and the 'Llanos de Moxos' in the Beni basin. We show that they contain markedly contrasting legacies of past climatic, geomorphic and anthropogenic influences between the last glacial period and the Spanish Conquest. In NKMNP, increasing precipitation caused evergreen rainforest expansion, at the expense of semi-deciduous dry forest and savannahs, over the last three millennia. In contrast, pre-Hispanic indigenous cultures were instrumental in facilitating recent forest expansion in the Llanos de Moxos by building a vast network of earthworks. Insights from Mid-Holocene palaeodata, together with ecological observations and modelling studies, suggest that there will be progressive replacement of rainforest by dry forest and savannah in NKMNP over the twenty-first century in response to the increased drought predicted by general circulation models. Protection of the latitudinal landscape corridors may be needed to facilitate these future species reassortments. However, devising appropriate conservation strategies for the Llanos de Moxos will be more difficult due to its complex legacy of Palaeo-Indian impact. Without fully understanding the degree to which its current biota has been influenced by past native cultures, the type and intensity of human land use appropriate for this landscape in the future will be difficult to ascertain.     

Molecular dynamics simulation and coarse-grained analysis of the Arp2/3 complex

A molecular dynamics investigation and coarse-grained analysis of inactivated actin-related protein (Arp) 2/3 complex is presented. It was found that the nucleotide binding site within Arp3 remained in a closed position with bound ATP or ADP, but opened when simulation with no nucleotide was performed. In contrast, simulation of the isolated Arp3 subunit with bound ATP, showed a fast opening of the nucleotide binding cleft. A homology model for the missing subdomains 1 and 2 of Arp2 was constructed, and it was also found that the Arp2 binding cleft remained closed with bound nucleotide. Within the nucleotide binding cleft a distinct opening and closing period of 10 ns was observed in many of the simulations of Arp2/3 as well as isolated Arp3. Substitution studies were employed, and several alanine substitutions were found to induce a partial opening of the ATP binding cleft in Arp3 and Arp2, whereas only a single substitution was found to induce opening of the ADP binding cleft. It was also found that the nucleotide type did not cause a substantial change on interfacial contacts between Arp3 and the ArpC2, ArpC3 and ArpC4 subunits. Nucleotide-free Arp3 had generally less stable contacts, but the overall contact architecture was constant. Finally, nucleotide-dependent coarse-grained models for Arp3 are developed that serve to further highlight the structural differences induced in Arp3 by nucleotide hydrolysis.     

HIV-1 dynamics in vivo: implications for therapy

The advent of potent combination antiretroviral therapy has been an important breakthrough in the treatment of HIV-1 infection, resulting in marked reductions in HIV-1-related morbidity and mortality. Antiretroviral therapy has also provided researchers with a powerful tool to perturb the equilibrium of viral production and viral clearance, allowing them to dissect the underlying dynamics that control the pathogenesis of AIDS. Here, we review our current understanding of the sources of HIV-1 production, the estimates for the virion and the host-cell half-lives, and the pathways of virion trafficking and clearance. We also discuss the obstacles that result from the ability of HIV-1 to remain dormant for a prolonged period of time in a subset of long-lived cells, despite an apparently effective antiretroviral treatment.     

Large-scale properties of clustered networks: implications for disease dynamics

We consider previously proposed procedures for generating clustered networks and investigate how these procedures lead to differences in network properties other than clustering. We interpret our findings in terms of the effect of the network structure on the disease outbreak threshold and disease dynamics. To generate null-model networks for comparison, we implement an assortativity-conserving rewiring algorithm that alters the level of clustering while causing minimal impact on other properties. We show that many theoretical network models used to generate networks with a particular property often lead to significant changes in network properties other than that of interest. For high levels of clustering, different procedures lead to networks that differ in degree heterogeneity and assortativity, and in broader scale measures such as ?(0) and the distribution of shortest path lengths. Hence, care must be taken when investigating the implications of network properties for disease transmission or other dynamic process that the network supports.