Modeling two-oscillator circadian systems entrained by two environmental cycles

Several experimental studies have altered the phase relationship between photic and non-photic environmental, 24 h cycles (zeitgebers) in order to assess their role in the synchronization of circadian rhythms. To assist in the interpretation of the complex activity patterns that emerge from these "conflicting zeitgeber" protocols, we present computer simulations of coupled circadian oscillators forced by two independent zeitgebers. This circadian system configuration was first employed by Pittendrigh and Bruce (1959), to model their studies of the light and temperature entrainment of the eclosion oscillator in Drosophila. Whereas most of the recent experiments have restricted conflicting zeitgeber experiments to two experimental conditions, by comparing circadian oscillator phases under two distinct phase relationships between zeitgebers (usually 0 and 12 h), Pittendrigh and Bruce compared eclosion phase under 12 distinct phase relationships, spanning the 24 h interval. Our simulations using non-linear differential equations replicated complex non-linear phenomena, such as "phase jumps" and sudden switches in zeitgeber preferences, which had previously been difficult to interpret. Our simulations reveal that these phenomena generally arise when inter-oscillator coupling is high in relation to the zeitgeber strength. Manipulations in the structural symmetry of the model indicated that these results can be expected to apply to a wide range of system configurations. Finally, our studies recommend the use of the complete protocol employed by Pittendrigh and Bruce, because different system configurations can generate similar results when a "conflicting zeitgeber experiment" incorporates only two phase relationships between zeitgebers.     

Dissociation of Abeta(16-22) amyloid fibrils probed by molecular dynamics

The mechanisms of deposition and dissociation are implicated in the assembly of amyloid fibrils. To investigate the kinetics of unbinding of Abeta(16-22) monomers from preformed fibrils, we use molecular dynamics (MD) simulations and the structures for Abeta(16-22) amyloid fibrils. Consistent with experimental studies, the dissociation of Abeta(16-22) peptides involves two main stages, locked and docked, after which peptides unbind. The lifetime of the locked state, in which a peptide retains fibril-like structure and interactions, extends up to 0.5 micros under normal physiological conditions. Upon cooperative rupture of all fibril-like hydrogen bonds (HBs) with the fibril, a peptide enters a docked state. This state is populated by disordered random coil conformations and its lifetime ranges from approximately 10 to 200 ns. The docked state is stabilized by hydrophobic side chain interactions, while the contribution from HBs is small. Our simulations also suggest that the peptides located on fibril edges may form stable beta-strand conformations distinct from the fibril "bulk". We propose that such edge peptides can act as fibril caps, which impede fibril elongation. Our results indicate that the interactions between unbinding peptides constitute the molecular basis for cooperativity of peptide dissociation. The kinetics of fibril growth is reconstructed from unbinding assuming the reversibility of deposition/dissociation pathways. The relation of in silica dissociation kinetics to experimental observations is discussed.     

Biomechanical characterization and clinical implications of artificially induced crouch walking: Differences between pure iliopsoas, pure hamstrings and combination of iliopsoas and hamstrings contractures

The purpose of this study was to characterize biomechanically three different crouch walking patterns, artificially induced in eight neurologically intact subjects and to compare them to selected cases of pathological crouch walking. The subjects were equipped with a lightweight mechanical exoskeleton with artificial muscles that acted in parallel with hamstrings and iliopsoas muscles. They walked at a speed of approximately 1m/s along the walkway under four experimental conditions: normal walking (NW), hamstrings contracture emulation (HAM), iliopsoas contracture emulation (IPS) and emulation of both hamstrings and iliopsoas contractures (IPSHAM). Reflective markers and force platform data were collected and ankle, knee and hip-joint angles, moments and powers were calculated. HAM and IPSHAM shifted ankle-angle rotation profiles into dorsiflexion during midstance compared to IPS and NW where ankle-angle trajectories were similar. HAM, IPS and IPSHAM shifted the knee angle of rotation profiles into flexion during stance, compared to NW. IPS and IPSHAM shifted hip angle of rotation profiles toward pronounced flexion while HAM shifted hip angle of rotation profile toward extension, compared to NW. HAM and IPSHAM significantly increased ankle moment during midstance, compared to IPS and NW where ankle moment profiles were similar. All experimental conditions exhibited similar behavior in the knee-moment profiles during midstance while IPS and IPSHAM knee-moment profiles exhibited significantly higher knee-extension moment during terminal stance and pre-swing. In the hip joint all experimental conditions exhibited similar shape of hip moment profiles throughout the gait cycle. HAM and IPS kinematic and kinetic patterns were qualitatively compared to two selected clinical cases, showing considerable similarity. This implies that distinct differences in kinematics and kinetics between HAM, IPS and IPSHAM may be clinically relevant in helping determine the relative contribution of hamstrings and iliopsoas muscles contractures to particular crouch walking.     

Synchronization of delayed coupled neurons in presence of inhomogeneity

In principle, two directly coupled limit cycle oscillators can overcome mismatch in intrinsic rates and match their frequencies, but zero phase lag synchronization is just achievable in the limit of zero mismatch, i.e., with identical oscillators. Delay in communication, on the other hand, can exert phase shift in the activity of the coupled oscillators. In this study, we address the question of how phase locked, and in particular zero phase lag synchronization, can be achieved for a heterogeneous system of two delayed coupled neurons. We have analytically studied the possibility of inphase synchronization and near inphase synchronization when the neurons are not identical or the connections are not exactly symmetric. We have shown that while any single source of inhomogeneity can violate isochronous synchrony, multiple sources of inhomogeneity can compensate for each other and maintain synchrony. Numeric studies on biologically plausible models also support the analytic results.     

Numerical simulations suggest that counting sums and taxonomic resolution of diatom analyses to determine IPS pollution and ACID acidity indices can be reduced

Implementation of the European Union Water Framework Directive and associated national guidelines has emphasized the value of using biota, such as epilithic diatoms in streams, as indicators of water quality. However, guidelines for evaluating diatom samples have been established without explicitly evaluating their statistical robustness. We used epilithic diatom samples from 73 streams in northern Sweden and simulated the effects of variations in the counting sum size and taxonomic resolution of classifications for two indices indicating pollution (Indice de Polluo-sensibilité Spécifique, IPS) and acidity (acidity index for diatoms, ACID). Instead of the stipulated 400, we found that a count sum of 40 diatom valves for 50 streams, and 80 valves for 60 streams, would have been sufficient to obtain the same IPS index classification. The ACID index is more sensitive to count sum reductions, since the same classification would only have been obtained for 12 streams with 40 counted diatom valves or 24 streams with a count of 80 valves. Excluding rare taxa had negligible effects on the IPS and ACID indices. Excluding taxa occurring with less than 1.0% frequency affected the IPS classification of only one stream, and excluding taxa with less than 2.5% and 5.0% frequencies affected those of just one and no streams, respectively. The ACID index was affected for none, five, and 12 streams, respectively. At least in relatively unpolluted regions such as northern Sweden, our simulations suggest that a simplified methodological approach with site-specific counting sum sizes and reduced taxonomical resolution could be adopted, taking into account the way sites are classified in relation to established class boundaries. The simplified method is a step forward in improving the cost efficiency for stream monitoring, as costs of diatom analysis to obtain identical IPS and ACID classifications of our streams could be reduced considerably. Before the simplified method can be widely adopted, further simulations including regions with a higher proportion of polluted streams are required.     

Single-cell behavior and population heterogeneity: solving an inverse problem to compute the intrinsic physiological state functions

The dynamics of isogenic cell populations can be described by cell population balance models that account for phenotypic heterogeneity. To utilize the predictive power of these models, however, we must know the rates of single-cell reaction and division and the bivariate partition probability density function. These three intrinsic physiological state (IPS) functions can be obtained by solving an inverse problem that requires knowledge of the phenotypic distributions for the overall cell population, the dividing cell subpopulation and the newborn cell subpopulation. We present here a robust computational procedure that can accurately estimate the IPS functions for heterogeneous cell populations. A detailed parametric analysis shows how the accuracy of the inverse solution is affected by discretization parameters, the type of non-parametric estimators used, the qualitative characteristics of phenotypic distributions and the unknown partitioning probability density function. The effect of finite sampling and measurement errors on the accuracy of the recovered IPS functions is also assessed. Finally, we apply the procedure to estimate the IPS functions of an E. coli population carrying an IPTG-inducible genetic toggle network. This study completes the development of an integrated experimental and computational framework that can become a powerful tool for quantifying single-cell behavior using measurements from heterogeneous cell populations.     

Generalizability of the Individual Placement and Support (IPS) model of supported employment outside the US

While reviews of controlled studies of the Individual Placement and Support (IPS) model of supported employment for clients with severe mental illness have documented its effectiveness in the US, its generalizability to other countries has not been systematically evaluated. This is the first review to compare US to non-US studies. We identified 15 randomized controlled trials of IPS programs, 9 in the US and 6 outside the US. We examined competitive employment outcomes, including employment rate, days to first job, weeks worked during follow-up, and hours worked. We also considered noncompetitive employment, program retention, and nonvocational outcomes. IPS programs had significantly better outcomes across a range of competitive employment indicators and higher retention in services than control groups. The overall competitive employment rate for IPS clients in US studies was significantly higher than in non-US studies (62% vs. 47%). The consistently positive competitive employment outcomes strongly favoring IPS over a range of comparison programs in a group of international studies suggest that IPS is an evidence-based practice that may transport well into new settings as long as programs achieve high fidelity to the IPS model, but further research is needed on international adaptations.     

Morphological patterns of the intraparietal sulcus and the anterior intermediate parietal sulcus of Jensen in the human brain

Distinct parts of the intraparietal sulcal cortex contribute to sensorimotor integration and visual spatial attentional processing. A detailed examination of the morphological relations of the different segments of the complex intraparietal sulcal region in the human brain in standard stereotaxic space, which is a prerequisite for detailed structure-to-function studies, is not available. This study examined the intraparietal sulcus (IPS) and the related sulcus of Jensen in magnetic resonance imaging brain volumes registered in the Montreal Neurological Institute stereotaxic space. It was demonstrated that the IPS is divided into two branches: the anterior ramus and the posterior ramus of the IPS, often separated by a submerged gyral passage. The sulcus of Jensen emerges between the anterior and posterior rami of the IPS, and its ventral end is positioned between the first and second caudal branches of the superior temporal sulcus. In a small number of brains, the sulcus of Jensen may merge superficially with the first caudal branch of the superior temporal sulcus. The above morphological findings are discussed in relation to previously reported functional neuroimaging findings and provide the basis for future exploration of structure-to-function relations in the posterior parietal region of individual subjects.     

Coupled positive and negative feedback circuits form an essential building block of cellular signaling pathways

Cellular circuits have positive and negative feedback loops that allow them to respond properly to noisy external stimuli. It is intriguing that such feedback loops exist in many cases in a particular form of coupled positive and negative feedback loops with different time delays. As a result of our mathematical simulations and investigations into various experimental evidences, we found that such coupled feedback circuits can rapidly turn on a reaction to a proper stimulus, robustly maintain its status, and immediately turn off the reaction when the stimulus disappears. In other words, coupled feedback loops enable cellular systems to produce perfect responses to noisy stimuli with respect to signal duration and amplitude. This suggests that coupled positive and negative feedback loops form essential signal transduction motifs in cellular signaling systems.     

Computational investigation of the effect of thermal perturbation on the mechanical unfolding of titin I27

The emergence of single-molecule force measurement experiments has facilitated a better understanding of protein folding pathways and the thermodynamics involved. Computational methods such as steered molecular dynamics (SMD) simulations are helpful in providing atomistic level information on the unfolding pathways. Recent experimental studies have showed that combinations of single-molecule experiments with traditional methods such as chemical and/or thermal denaturation yield additional insights into the folding phenomenon. In this study, we report results from extensive computations (a total of about 60 SMD simulations with a total length of about 0.4 μs) that address the effect of thermal perturbation on the mechanical stability of the I27 domain of the protein titin. A wide range of temperatures (280-340 K) were considered for the pulling, which was done at both constant velocity and constant force using SMD simulations. Good agreement with experimental data, such as for the trends in changes in average force and the maximum force with respect to the temperature, was obtained. This study identifies two competing pathways for the mechanical unfolding of I27, and illustrates the significance of combining various techniques to examine protein folding.     

The role of local hydration and hydrogen-bonding dynamics in ion and solute release from ion-coupled secondary transporters

Recent progress in crystallographic studies of sodium-coupled secondary transporters has revealed striking similarities in the structural organization of ion and solute binding. Previous reports suggested that the Na2 sodium binding site in the neurotransmitter sodium symporter (NSS) leucine transporter (LeuT) is conserved across sodium/proton coupled secondary transporters of many distantly related families. This site is implicated in the conformational dynamics controlled by the binding and release of both translocated solute and ion(s) through a mechanism that largely remains unknown. In this study, we used extensive equilibrium molecular dynamics simulations, potential of mean force (PMF) computations, and quasi-harmonic analysis of the LeuT transporter with and without sodium ion bound at the Na2 site to delineate the role of this site in the conformational dynamics of the protein. PMF computations show that in presence of the sodium ion in Na2 the conserved T354 residue is locked into a single rotameric state in contrast to two degenerate states available in the absence of ion in Na2. Molecular dynamics (MD) simulations suggest the formation of a stable water wire from the cytoplasm to the Na2 site in the occluded state. It is plausible that local hydration plays an important role in transport cycle facilitating release of the ion from Na2. An unbinding of the ion from the Na2 site leads to a tightening of the extracellular thin gates and a destabilization of the intracellular thin gate and thus may promote an unbinding of the cotransported substrate. The study lends additional support to the hypothesis that one of the main drivers in the transport cycle of Na-coupled secondary transporters is the binding of the Na2 ion that controls dynamical equilibrium between an inward-facing to an outward-facing conformation.     

Embryonic cell commitment by a simultaneous alteration in nucleo/cytoplasmic ratio in sibling cells between subsequent cell cycles

Studies on murine embryonal carcinoma (EC) cell lines have revealed a mechanism for commitment of early embryonic cells. By means of a particular intraclonal cell surface glycoprotein and intermitotic time heterogeneity found in the EC lines used, we have devised a cell cycle model and written a computer program for cell cycle stimulation. In the present investigation experimental tissue culture data obtained from the EC lines were inserted into the computer program and the simulations represent a good fit to experimental data. It is shown that the dynamics of the driving forces in the 'cell growth cycle' and the 'DNA-division cycle', when assumed to be loosely coupled and analyzed in subsequent cell cycles, reveal a mechanism that can commit the mother cell to impel her daughter cells into the next stage in embryonic development by altering the relationship between those two uncoupled subcycles. Thereby the nucleo/cytoplasmic ratio (DNA/mass) is altered in a similar way in the two daughter cells. The simulations increase the reliability of the model and open up possibilities to test other embryonic cell systems.     

Revealing Atomic-Level Mechanisms of Protein Allostery with Molecular Dynamics Simulations

Molecular dynamics (MD) simulations have become a powerful and popular method for the study of protein allostery, the widespread phenomenon in which a stimulus at one site on a protein influences the properties of another site on the protein. By capturing the motions of a protein’s constituent atoms, simulations can enable the discovery of allosteric binding sites and the determination of the mechanistic basis for allostery. These results can provide a foundation for applications including rational drug design and protein engineering. Here, we provide an introduction to the investigation of protein allostery using molecular dynamics simulation. We emphasize the importance of designing simulations that include appropriate perturbations to the molecular system, such as the addition or removal of ligands or the application of mechanical force. We also demonstrate how the bidirectional nature of allostery—the fact that the two sites involved influence one another in a symmetrical manner—can facilitate such investigations. Through a series of case studies, we illustrate how these concepts have been used to reveal the structural basis for allostery in several proteins and protein complexes of biological and pharmaceutical interest.     

Vectorial insertion of a β-helical peptide into membrane: a theoretical study on polytheonamide B

Spontaneous unidirectional, or vectorial, insertion of transmembrane peptides is a fundamental biophysical process for toxin and viral actions. Polytheonamide B (pTB) is a potent cytotoxic peptide with a β^6.3-helical structure. Previous experimental studies revealed that the pTB inserts into the membrane in a vectorial fashion and forms a channel with its single molecular length long enough to span the membrane. Also, molecular dynamics simulation studies demonstrated that the pTB is prefolded in aqueous solution. These are unique features of pTB because most of the peptide toxins form channels through oligomerization of transmembrane helices. Here, we performed all-atom molecular dynamics simulations to examine the dynamic mechanism of the vectorial insertion of pTB, providing underlying elementary processes of the membrane insertion of a prefolded single transmembrane peptide. We find that the insertion of pTB proceeds with only the local lateral compression of the membrane in three successive phases: “landing,” “penetration,” and “equilibration” phases. The free energy calculations using the replica-exchange umbrella sampling simulations present an energy cost of 4.3 kcal/mol at the membrane surface for the membrane insertion of pTB from bulk water. The trajectories of membrane insertion revealed that the insertion process can occur in two possible pathways, namely “trapped” and “untrapped” insertions; in some cases, pTB is trapped in the upper leaflet during the penetration phase. Our simulations demonstrated the importance of membrane anchoring by the hydrophobic N-terminal blocking group in the landing phase, leading to subsequent vectorial insertion.     

Vegetation dynamics in a coastal grassland of Hawaii

Vegetation development following goat removal in a tropical grassland with a Mediterranean rainfall seasonality on leeward Hawaii is reported from two permanent monitoring sites. The two sites are equipped with experimental exclosures against feral goats. The sites were monitored annually for a decade (1971–80) for changes in cover by species. The vegetation changes reported relate to both inside- and outside-exclosure developments.Four dynamic categories were recognized among the grassland species following goat removal. These are the decreasers, the increasers and the persistent species. The latter were divided into stable and oscillating persisters. Attention was drawn to the oscillating persisters, as exemplified by the endemic vine Canavalia kauensis, and to the absence of any correlation of its oscillation pattern to the variation in year-to-year rainfall. It was concluded that the oscillation pattern resides in the population it self and can be attributed to its life-cycle phases. It is suggested that synchronized life-cycle dependent death in local populations is an important dynamic phenomenon in certain plant communities. This phenomenon may be considered as separate from phenology and succession, but of similar significance in understanding the processes of vegetation dynamics.Nomenclature of plant names follows St. John (1973).     

Potentially complex biosphere responses to transient global warming

Feedback interactions between terrestrial vegetation and climate could alter predictions of the responses of both systems to a doubling of atmospheric CO₂. Most previous analyses of biosphere responses to global warming have used output from equilibrium simulations of current and future climate, as compared to more recently available transient GCM simulations. We compared the vegetation responses to these two different classes of GCM simulation (equilibrium and transient) using an equilibrium vegetation distribution model, MAPSS. Average climatologies were extracted from the transient GCM simulations for current and doubled (2×) CO₂ concentrations (taken to be 2070–2099) for use by the equilibrium vegetation model. However, the 2 × CO₂ climates extracted from the transient GCM simulations were not in equilibrium, having attained only about 65% of their eventual 2 × CO₂ equilibrium temperature change. Most of the differences in global vegetation response appeared to be related to a very different simulated change in the pole to tropic temperature gradient. Also, the transient scenarios produced much larger increases of precipitation in temperate latitudes, commensurate with a minimum in the latitudinal temperature change. Thus, the (equilibrium) global vegetation response, under the transient scenarios, tends more to a greening than a decline in vegetation density, as often previously simulated. It may be that much of the world could become greener during the early phases of global warming, only to reverse in later, more equilibrial stages. However, whether or not the world's vegetation experiences large drought-induced declines or perhaps large vegetation expansions in early stages could be determined by the degree to which elevated CO₂ will actually benefit natural vegetation, an issue still under debate. There may occur oscillations, perhaps on long timescales, between greener and drier phases, due to different frequency responses of the coupled ocean–atmosphere–biosphere interactions. Such oscillations would likely, of themselves, impart further reverberations to the coupled Earth System.     

A search for predictive understanding of plant responses to elevated [CO2]

This paper reviews two decades of effort by the scientific community in a search for predictive understanding of plant responses to elevated [CO₂]. To evaluate the progress of research in leaf photosynthesis, plant respiration, root nutrient uptake, and carbon partitioning, we divided scientific activities into four phases: (I) initial assessments derived from our existing knowledge base to provide frameworks for experimental studies; (II) experimental tests of the initial assessments; (III) in cases where assessments were invalidated, synthesis of experimental results to stimulate alternative hypotheses and further experimentation; and (IV) formation of new knowledge. This paper suggests that photosynthetic research may have gone through all four phases, considering that (a) variable responses of photosynthesis to [CO₂] are generally explainable, (b) extrapolation of leaf-level studies to the global scale has been examined, and (c) molecular studies are under way. Investigation of plant respiratory responses to [CO₂] has reached the third phase: experimental results have been accumulated, and mechanistic approaches are being developed to examine alternative hypotheses in search for new concepts and/or new quantitative frameworks to understand respiratory responses to elevated [CO₂]. The study of nutrient uptake kinetics is still in the second phase: experimental evidence has contradicted some of the initial assessments, and more experimental studies need to be designed before generalizations can be made. It is quite unfortunate that we have not made much progress in understanding mechanisms of carbon partitioning during the past two decades. This is due in part to the fact that some of the holistic theories, such as functional balance and optimality, have not evolved into testable hypotheses to guide experimental studies. This paper urges modelers to play an increasing role in plant–CO₂ research by disassembling these existing theories into hypotheses and urges experimentalists to design experiments to examine these holistic concepts.     

A Model for Representing the Dynamics of a System of Synfire Chains

Competitive synchronization among synfire chains may model the dynamics of binding and compositionality. Typically, such models require simulations of hundreds of thousands of neurons. Here we show that the behavior of such large systems can be numerically analyzed by representing the neuronal activity in a synfire chain as a wave. The position and velocity of waves are the only parameters needed to represent the neural activity within a synfire chain. With this wave model we describe how waves are generated, decay, interact within a single chain and among chains. The behavior of the wave model is compared to the behavior of detailed simulations of synfire chains with no qualitative difference. We show that interacting waves tend to become locked to each other (wave synchronization). Finally we prove that: (1) Within a system of many synfire chains with symmetric interchain connections, as long as waves do not fade away or become fully synchronized, the total synchrony among waves can only increase (or stay constant), but never decrease. (2) A wave that increases its speed during the synchronization process becomes more stable.     

Design of a set of probes with high potential for influenza virus epidemiological surveillance

An Influenza Probe Set (IPS) consisting in 1,249 9-mer probes for genomic fingerprinting of closely and distantly related Influenza Virus strains was designed and tested in silico. The IPS was derived from alignments of Influenza genomes. The RNA segments of 5,133 influenza strains having diverse degree of relatedness were concatenated and aligned. After alignment, 9-mer sites having high Shannon entropy were searched. Additional criteria such as: G+C content between 35 to 65%, absence of dimer or trimer consecutive repeats, a minimum of 2 differences between 9mers and selecting only sequences with Tm values between 34.5 and 36.5oC were applied for selecting probes with high sequential entropy. Virtual Hybridization was used to predict Genomic Fingerprints to assess the capability of the IPS to discriminate between influenza and related strains. Distance scores between pairs of Influenza Genomic Fingerprints were calculated, and used for estimating Taxonomic Trees. Visual examination of both Genomic Fingerprints and Taxonomic Trees suggest that the IPS is able to discriminate between distant and closely related Influenza strains. It is proposed that the IPS can be used to investigate, by virtual or experimental hybridization, any new, and potentially virulent, strain.     

Application of isotropic periodic sum method for 4-pentyl-4′-cyanobiphenyl liquid crystal

In future large-scale molecular dynamics (MD) simulations that will use parallel computing, the isotropic periodic sum (IPS) method is expected to effectively reduce the cost of interaction calculations while maintaining adequate accuracy. To assess the accuracy of this method in estimating low-charge-density polymer systems, we performed atomistic MD simulations of the bulk state of liquid crystal systems based on 4-pentyl-4′-cyanobiphenyl (5CB). In conditions of 270 K ≤ T ≤ 320 K and a normal pressure, the temperature dependence of the density, potential energy and order parameter was estimated using the IPS and Ewald sum method. The results of the IPS method and Ewald sum were consistent within the range of error. In conditions close to the phase transition point, however, the averaged values of potential energy and order parameter had a small difference. We concluded that the fundamental physical properties for the bulk state of 5CB systems are determined reasonably by using the IPS method, at least in conditions that are not close to the phase transition point.