Inferring the roles of individuals in collective systems using information-theoretic measures of influence.

In collective systems, influence of individuals can permeate an entire group through indirect interactionscom-plicating any scheme to understand individual roles from observations. A typical approach to understand an individuals influence on another involves consideration of confounding factors, for example, by conditioning on other individuals outside of the pair. This becomes unfeasible in many cases as the number of individuals increases. In this article, we review some of the unforeseen problems that arise in understanding individual influence in a collective such as single cells, as well as some of the recent works which address these issues using tools from information theory.

Isolated prosopagnosia caused by damage to the right inferior longitudinal fasciculus: a case report.

Prosopagnosia is a cognitive disorder in which facial recognition is severely impaired despite normal vision and intelligence. Prosopagnosia was first reported in the 1800s, but its cause remains unclear. Although other neurological symptoms are often present, some patients have pure prosopagnosia. The bilateral occipital lobes are believed to be associated with symptoms. Recent brain imaging techniques have identified the right fusiform gyrus (rFG), located at the junction of the right occipital temporal lobe, as the affected region. In this report, we present a case of associative prosopagnosia with no concomitant symptoms in a 76-year-old man. Brain magnetic resonance imaging detected a subcortical hemorrhage in the right temporal lobe. Using tractography based on diffusion tensor imaging, we visualized atrophy of the right inferior longitudinal fasciculus (ILF). This is the first time tractography has been used to show a clear association between associative prosopagnosia and ILF damage projecting from the rFG.

An encompassed representation of timescale hierarchies in first-order reaction network.

Complex networks are pervasive in various fields such as chemistry, biology, and sociology. In chemistry, first-order reaction networks are represented by a set of first-order differential equations, which can be constructed from the underlying energy landscape. However, as the number of nodes increases, it becomes more challenging to understand complex kinetics across different timescales. Hence, how to construct an interpretable, coarse-graining scheme that preserves the underlying timescales of overall reactions is of crucial importance. Here, we develop a scheme to capture the underlying hierarchical subsets of nodes, and a series of coarse-grained (reduced-dimensional) rate equations between the subsets as a function of time resolution from the original reaction network. Each of the coarse-grained representations guarantees to preserve the underlying slow characteristic timescales in the original network. The crux is the construction of a lumping scheme incorporating a similarity measure in deciphering the underlying timescale hierarchy, which does not rely on the assumption of equilibrium. As an illustrative example, we apply the scheme to four-state Markovian models and Claisen rearrangement of allyl vinyl ether (AVE), and demonstrate that the reduced-dimensional representation accurately reproduces not only the slowest but also the faster timescales of overall reactions although other reduction schemes based on equilibrium assumption well reproduce the slowest timescale but fail to reproduce the second-to-fourth slowest timescales with the same accuracy. Our scheme can be applied not only to the reaction networks but also to networks in other fields, which helps us encompass their hierarchical structures of the complex kinetics over timescales.

Comparison of particle image velocimetry and the underlying agents dynamics in collectively moving self propelled particles.

Collective migration of cells is a fundamental behavior in biology. For the quantitative understanding of collective cell migration, live-cell imaging techniques have been used using e.g., phase contrast or fluorescence images. Particle tracking velocimetry (PTV) is a common recipe to quantify cell motility with those image data. However, the precise tracking of cells is not always feasible. Particle image velocimetry (PIV) is an alternative to PTV, corresponding to Eulerian picture of fluid dynamics, which derives the average velocity vector of an aggregate of cells. However, the accuracy of PIV in capturing the underlying cell motility and what values of the parameters should be chosen is not necessarily well characterized, especially for cells that do not adhere to a viscous flow. Here, we investigate the accuracy of PIV by generating images of simulated cells by the Vicsek model using trajectory data of agents at different noise levels. It was found, using an alignment score, that the direction of the PIV vectors coincides with the direction of nearby agents with appropriate choices of PIV parameters. PIV is found to accurately measure the underlying motion of individual agents for a wide range of noise level, and its condition is addressed.

Dynamically induced conformation depending on excited normal modes of fast oscillation.

We present dynamical effects on conformation in a simple bead-spring model consisting of three beads connected by two stiff springs. The conformation defined by the bending angle between the two springs is determined not only by a given potential energy function depending on the bending angle, but also by fast motion of the springs which constructs the effective potential. A conformation corresponding with a local minimum of the effective potential is hence called the dynamically induced conformation. We develop a theory to derive the effective potential using multiple-scale analysis and the averaging method. A remarkable consequence is that the effective potential depends on the excited normal modes of the springs and amount of the spring energy. Efficiency of the obtained effective potential is numerically verified.

Dependence of DNA length on binding affinity between TrpR and trpO of DNA.

We scrutinize the length dependency of the binding affinity of bacterial repressor TrpR protein to trpO (specific site) on DNA. A footprinting experiment shows that the longer the DNA length, the larger the affinity of TrpR to the specific site on DNA. This effect termed "antenna effect" might be interpreted as follows: longer DNA provides higher probability for TrpR to access to the specific site aided by one-dimensional diffusion along the nonspecific sites of DNA. We show that, however, the antenna effect cannot be explained while detailed balance holds among three kinetic states, that is, free protein/DNA, nonspecific complexes, and specific complex. We propose a working hypothesis that slow degree(s) of freedom in the system switch(es) different potentials of mean force causing transitions among the three states. This results in a deviation from detailed balance on the switching timescale. We then derive a simple reaction diffusion/binding model that describes the antenna effect on TrpR binding to its target operator. Possible scenarios for such slow degree(s) of freedom in TrpR-DNA complex are addressed.

Flickering of cardiac state before the onset and termination of atrial fibrillation.

Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a "tug-of-war" between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.

Mechanism and Experimental Observability of Global Switching Between Reactive and Nonreactive Coordinates at High Total Energies.

We present a mechanism of global reaction coordinate switching, namely, a phenomenon in which the reaction coordinate dynamically switches to another coordinate as the total energy of the system increases. The mechanism is based on global changes in the underlying phase space geometry caused by a switching of dominant unstable modes from the original reactive mode to another nonreactive mode in systems with more than 2 degrees of freedom. We demonstrate an experimental observability to detect a reaction coordinate switching in an ionization reaction of a hydrogen atom in crossed electric and magnetic fields. For this reaction, the reaction coordinate is a coordinate along which electrons escape and its switching changes the escaping direction from the direction of the electric field to that of the magnetic field and, thus, the switching can be detected experimentally by measuring the angle-resolved momentum distribution of escaping electrons.

Spatio-temporal hierarchy in the dynamics of a minimalist protein model.

A method for time series analysis of molecular dynamics simulation of a protein is presented. In this approach, wavelet analysis and principal component analysis are combined to decompose the spatio-temporal protein dynamics into contributions from a hierarchy of different time and space scales. Unlike the conventional Fourier-based approaches, the time-localized wavelet basis captures the vibrational energy transfers among the collective motions of proteins. As an illustrative vehicle, we have applied our method to a coarse-grained minimalist protein model. During the folding and unfolding transitions of the protein, vibrational energy transfers between the fast and slow time scales were observed among the large-amplitude collective coordinates while the other small-amplitude motions are regarded as thermal noise. Analysis employing a Gaussian-based measure revealed that the time scales of the energy redistribution in the subspace spanned by such large-amplitude collective coordinates are slow compared to the other small-amplitude coordinates. Future prospects of the method are discussed in detail.

Measuring dynamical randomness of quantum chaos by statistics of Schmidt eigenvalues.

We study statistics of entanglement generated by quantum chaotic dynamics. Using an ensemble of the very large number (>/~10(7)) of quantum states obtained from the temporally evolving coupled kicked tops, we verify that the estimated one-body distribution of the squared Schmidt eigenvalues for the quantum chaotic dynamics can agree surprisingly well with the analytical one for the universality class of the random matrices described by the fixed trace ensemble (FTE). In order to quantify this agreement, we introduce the L(1) norm of the difference between the one-body distributions for the quantum chaos and FTE and use it as an indicator of the dynamical randomness. As we increase the scaled coupling constant, the L(1) difference decreases. When the effective Planck constant is not small enough, the decrease saturates, which implies quantum suppression of dynamical randomness. On the other hand, when the effective Planck constant is small enough, the decrease of the L(1) difference continues until it is masked by statistical fluctuation due to finiteness of the ensemble. Furthermore, we carry out two statistical analyses, the χ(2) goodness of fit test and an autocorrelation analysis, on the difference between the distributions to seek for dynamical remnants buried under the statistical fluctuation. We observe that almost all fluctuating deviations are statistical. However, even for well-developed quantum chaos, unexpectedly, we find a slight nonstatistical deviation near the largest Schmidt eigenvalue. In this way, the statistics of Schmidt eigenvalues enables us to measure dynamical randomness of quantum chaos with reference to the random matrix theory of FTE.

Nanosecond simulations of the dynamics of C60 excited by intense near-infrared laser pulses: impulsive Raman excitation, rearrangement, and fragmentation.

Impulsive Raman excitation of C(60) by single or double pulses of near-infrared wavelength λ = 1800 nm was investigated by using a time-dependent adiabatic state approach combined with the density functional theory method. We confirmed that the vibrational energy stored in a Raman active mode of C(60) is maximized when T(p) ~ T(vib)/2 in the case of a single pulse, where T(p) is the pulse length and T(vib) is the vibrational period of the mode. In the case of a double pulse, mode selective excitation can be achieved by adjusting the pulse interval τ. The energy of a Raman active mode is maximized if τ is chosen to equal an integer multiple of T(vib) and it is minimized if τ is equal to a half-integer multiple of T(vib). We also investigated the subsequent picosecond or nanosecond dynamics of Stone-Wales rearrangement (SWR) and fragmentation by using the density-functional based tight-binding semiempirical method. We present how SWRs are caused by the flow of vibrational kinetic energy on the carbon bond network of C(60). In the case where the h(g)(1) prolate-oblate mode is initially excited, the number of SWRs before fragmentation is larger than in the case of a(g)(1) mode excitation for the same excess vibrational energy. Fragmentation by C(2) ejection C(60) → C(58) + C(2) is found to occur from strained, fused pentagon/pentagon defects produced by a preceding SWR, which confirms the earliest mechanistic speculations of Smalley et al. [J. Chem. Phys. 88, 220 (1988)]. The fragmentation rate of C(2) ejection in the case of h(g)(1) mode excitation does not follow a statistical description as employed for instance in the Rice-Ramsperger-Kassel (RRK) theory, whereas the rate for a(g)(1) mode excitation does follow the prediction by RRK. We also found for the h(g)(1) mode excitation that the nonstatistical nature affects the distribution of barycentric velocities of fragments C(58) and C(2). This result suggests that it is possible to control rearrangement and subsequent bond breaking in a "nonstatistical" way by initial selective mode excitation.

Dynamical switching of a reaction coordinate to carry the system through to a different product state at high energies.

Questions of how the nature of a reaction coordinate that dominates the reaction ceases to exist and whether some new features emerge as an increase of total energy of systems are investigated for many degrees of freedom Hamiltonian systems. As a model system, a hydrogen atom in crossed electric and magnetic fields is scrutinized. It is shown that, when the total energy increases, the reaction coordinate no longer dominates the reaction as did at the lower energies. In turn, a new reaction coordinate emerges, connecting totally different reactant and product states. Furthermore, depending on which parts of the phase space the system traverses through the saddle, the system nonuniformly experiences the switching of the reaction coordinate leading to the different product state. The universal mechanism of the cessation and the switching of the reaction coordinate at high energy regimes above the saddle is investigated.

Bifurcation of no-return transition states in many-body chemical reactions.

A new method is presented to study bifurcation of no-return transition states (TSs) at potential saddles for systems of many degrees of freedom (dof). The method enables us to investigate analytically when and how the no-return TS bifurcates. Our method reveals a new aspect of bifurcation for systems of many dof, i.e., the action variables of the bath dof play a role of control parameters as long as they remain approximately conserved. As an illustrative example, we demonstrate our new method by using a three atomic exchange reaction. The bifurcation of no-return TSs gives rise to a short-lived intermediate state at the saddle, which results in the overestimation of the reaction rate. Hence, the understanding of the bifurcation of the no-return TS is crucial to capture the complexity in kinetics and dynamics of the reactions. The definability of no-return TSs in many-body chemical reactions is also addressed under the occurrence of bifurcation above the reaction threshold.

Exact formula of the distribution of Schmidt eigenvalues for dynamical formation of entanglement in quantum chaos.

The exact formula of the one-level distribution of the Schmidt eigenvalues is obtained for dynamical formation of entanglement in quantum chaos. The formula is based on the random matrix theory of the fixed-trace ensemble, and is derived using the theory of the holonomic system of differential equations. We confirm that the formula describes the universality of the distribution of the Schmidt eigenvalues in quantum chaos.

Fractional behavior in nonergodic reaction processes of isomerization.

We present numerical evidence of fractional behavior in reactions for a prototype model of three-degree-of-freedom isomerization. The survival probability in the well exhibits two distinct ranges of time scales: one where it decreases with a power law, and the other where it decreases exponentially. Trajectories corresponding to power law decays exhibit 1/f spectra and subdiffusion in action space, and those with exponential decays exhibit Lorentzian spectra and normal diffusion. The existence of these two types of behavior is explained on the basis of nonergodicity in the network of nonlinear resonances (Arnold web) in the well, and connection between the saddle and the Arnold web. Implications of the fractional dynamics are discussed in terms of Maxwell's demon in molecules.

Fractional behavior in multidimensional Hamiltonian systems describing reactions.

The fractional behavior is presented for a minimal Hamiltonian system of three degrees of freedom which describes reaction processes. The model has a double-well potential where the Arnold web within the well is nonuniform. The survival probability within the well exhibits power law decay in addition to exponential decay. Moreover, the trajectories of the power law decay exhibit 1/f spectra and subdiffusion in the action space, while the trajectories of the exponential decay show Lorentzian spectra and normal diffusion. Transient features of these statistical properties reveal the dynamical connection, i.e., how trajectories approach to (depart from) the Arnold web from (to) the region around the potential saddle. In particular, a wavelet analysis enables us to extract transient features of the resonances. Based on these results, we suggest that resonance junctions including higher-order resonances are important for understanding the dynamical origins of the fractional behavior in reaction processes.

Definability of no-return transition states in the high-energy regime above the reaction threshold.

No-return transition states (TSs) defined in multidimensional phase space, where recrossing trajectories through the commonly used "configuration" TS pass only once, robustly exist up to a moderately high-energy regime above the reaction threshold, even when nonlinear resonances among the bath degrees of freedom perpendicular to the reaction coordinate result in local chaos. However, at much higher energy when global chaos appears in the bath space, the separability of the reaction coordinate from the bath degrees of freedom starts to lose locally. In the phase space near the saddles, it is found that the slower the system passes the TS, the more recrossing trajectories reappear. Their implications and mechanisms are discussed concerning to what extent one can define no-return TSs in the high-energy regime above the reaction threshold.

Phase-space reaction network on a multisaddle energy landscape: HCN isomerization.

By using the HCN/CNH isomerization reaction as an illustrative vehicle of chemical reactions on multisaddle energy landscapes, we give explicit visualizations of molecular motions associated with a straight-through reaction tube in the phase space inside which all reactive trajectories pass from one basin to another, with eliminating recrossing trajectories in the configuration space. This visualization provides us with a chemical intuition of how chemical species "walk along" the reaction-rate slope in the multidimensional phase space compared with the intrinsic reaction path in the configuration space. The distinct nonergodic features in the two different HCN and CNH wells can be easily demonstrated by a section of Poincare surface of section in those potential minima, which predicts in a priori the pattern of trajectories residing in the potential well. We elucidate the global phase-space structure which gives rise to the non-Markovian dynamics or the dynamical correlation of sequential multisaddle chemical reactions. The phase-space structure relevant to the controllability of the product state in chemical reactions is also discussed.