Absolute configurational determination of an all-trans-retinal dimer isolated from photoreceptor outer segments

An all-trans-retinal (ATR) dimer (1) isolated from photoreceptor outer segments was found to have a stereogenic center at C13' flanked by tetraene (295 nm) and hexaenal (438 nm) chromophores. Analytical chiral HPLC (Chiralcel OD) revealed that the isolated retinoid had formed in 13% enantiomeric excess. Using a combination of (1)H-(1)H NOESY constraints, molecular modeling, and CD exciton coupling analysis, it was determined that the favored enantiomer was 13'(R). Three low-energy conformers of the 13'(S) model were found with MMFF/DFT and were used to calculate the CD spectrum of the ATR dimer (DeVoe method). The Boltzmann weighted spectrum was found to exhibit a positive exciton couplet, in excellent agreement with the experimental spectrum for the first eluted enantiomer. This further suggested that despite the large energy difference between the two interacting chromophores, the dominant source of optical activity in the CD spectrum is the nondegenerate exciton mechanism.     

Theoretical simulation of the electronic circular dichroism spectrum of calicheamicin

The aglycon, or so-called 'warhead' portion, of several potent 10-membered ring enediyne antitumor antibiotics contain dienonecarbamate and enediyne chromophores in an unusual bicyclic ring structure in which these two subunits are essentially orthogonal to each other. The circular dichroism (CD) spectra of the calicheamicin, esperamicin, and shisijimicin A families, all of which contain this bicyclic ring system, exhibit a characteristic negative exciton coupled CD at about 310 and 270 nm. This signature CD feature suggested the absolute stereochemical relationship between these chromophores as originally assigned and which was later confirmed by stereospecific total synthesis. Because of the unique nature of this chromophoric interaction and the importance of using this CD spectral feature in the assignment of the absolute stereochemistry of other related enediynes, we report here simulations of the CD spectra of the calicheamicin aglycon A, and of two other truncated models, B and C, by using density functional theory (DFT) and the DeVoe coupled oscillator approach. The DFT calculations provide a strong theoretical basis that the planar enediyne chromophore alone gives a negligible CD contribution, while that coming from the twisted dienonecarbamate is much more substantial. However, the shape and the largest part of the intensity of experimental CD spectrum can only be reproduced when the two unsaturated moieties are simultaneously present. Thus, the exciton coupling between the two chromophores provides the most important contribution to the experimental CD spectrum of calicheamicin. This conclusion is in full agreement with the results from the DeVoe calculation.     

Heme-heme interactions in tetramers and dimers of hemoglobin subunits: DeVoe theory calculations

Detectable exciton couplets arising from heme-heme interactions in the hemoglobin (Hb) tetramers of HbO(2) and deoxyHb were predicted by DeVoe theory. This prediction was supported by the observation of an exciton couplet in the CD difference spectrum between the Hb tetramer and the alphabeta dimer of HbCO. In this paper, DeVoe theory is used to calculate the heme-heme interactions in the CO complex of the Hb tetramer (alpha(2)beta(2)) and dimer (alphabeta), the systems studied by Goldbeck et al. The couplet strength of the resulting theoretical CD difference spectrum agrees well with experiment, thus confirming that heme-heme interactions contribute significantly to the CD of HbCO. Given that the heme-heme distances in HbCO are 25 A and more, it is highly likely that heme-heme interactions also contribute significantly to the CD of other multi-heme proteins, e.g., cytochrome c(3), cytochrome oxidase, cytochrome bc(1), etc., where the hemes are in closer proximity.     

Estimating the Strength and Direction of Functional Coupling in the Lamprey Spinal Cord

A method of estimating coupling strength between two neural oscillators based on their spikes trains (Kiemel and Cohen, J. Comput. Neurosci. 5: 267–284, 1998) is tested using simulated data and then applied to experimental data from the central pattern generator (CPG) for swimming in the lamprey. The method is tested using a model of two connectionist oscillators and a model of two endogenously bursting cells. For both models, the method provides useful estimates of the relative strength of coupling in each direction, as well as estimates of total strength. The method is applied to pairs of motor-nerve recordings from isolated 50-segment pieces of spinal cords from adult silver lampreys (Ichthyomyzon unicuspus). The strength and direction of coupling is estimated under control conditions and conditions in which intersegmental coupling between the two recording locations is weakened by hemisections of the spinal cords and/or chambers containing an inhibitory solution that blocks firing in postsynaptic cells. The relevance of these measures in constraining models of the CPG is discussed.     

The Calculation of Frequency-Shift Functions for Chains of Coupled Oscillators, with Application to a Network Model of the Lamprey Locomotor Pattern Generator

Chains of coupled limit-cycle oscillators are considered, in which the coupling is assumed to be weak and only between adjacent oscillators. For such a system the change in frequency of an oscillator due to the coupling can be expressed, up to first order in thecoupling strength, by functions that depend only on the phase difference between the coupled oscillators. In this article a numerical algorithm is developed for the evaluation of these functions (the H-functions) in terms of a single oscillator and the interactions between coupled oscillators. The technique is applied to a connectionist model for the locomotor pattern generator in the lamprey spinal cord.An H-function so derived is compared to a function derived empirically(the C-function) from simulations of the same system. The phase lagsthat develop between adjacent oscillators in a simulated chain are compared with those predicted theoretically, and it is shown that coupling thatis functionally strong is nonetheless weak enough to behave as predicted.     

Multiple pulse interactions and averaging in systems of coupled neural oscillators

Oscillators coupled strongly are capable of complicated behavior which may be pathological for biological control systems. Nevertheless, strong coupling may be needed to prevent asynchrony. We discuss how some neural networks may be designed to achieve only simple locking behavior when the coupling is strong. The design is based on the fact that the method of averaging produces equations that are capable only of locking or drift, not pathological complexity. Furthermore, it is shown that oscillators that interact by means of multiple pulses per cycle, dispersed around the cycle, behave like averaged equations, even if the number of pulses is small. We discuss the biological intuition behind this scheme, and show numerically that it works when the oscillators are taken to be composites, each unit of which is governed by a well-known model of a neural oscillator. Finally, we describe numerical methods for computing from equations for coupled limit cycle oscillators the averaged coupling functions of our theory.Research partially supported by the National Science Foundation under grants DMS 8796235 and DMS 8701405 and the Air Force Office of Scientific Research under University Research Contract F 49620-C-0131 to Northeastern University     

The enduring legacy of Koji Nakanishi's research on natural products and bioorganic chemistry. Part 2. Inception and establishment of the ECD exciton chirality method in 1960s to 1970s: A marvel of Nakanishi's Japanese team

The electronic circular dichroism (ECD) exciton chirality method is very useful for determining the absolute configuration (AC) of chiral compounds. In the ECD spectroscopy, the chromophore-chromophore interaction, ie, exciton coupling, is very important. For example, Harada and Nakanishi first discovered in 1969 that chiral dibenzoates exhibit exciton split bisignate Cotton effects, from the sign of which the screw sense between two long axes of benzoate chromophores, ie, the AC of dibenzoate, can be determined. This method was named the dibenzoate chirality rule and has been successfully applied to various natural products to determine their ACs. During these studies, it was also found that this CD method was expanded to encompass other aromatic and olefin chromophores like naphthalene, diene, enone, etc. Therefore, the name of the dibenzaote chirality rule was changed to the CD exciton chirality method. In 1970s, there were heated controversies about the inconsistency between X-ray Bijvoet and CD exciton chirality methods, which was a shocking and serious problem in the community of molecular chirality research. Harada and coworkers synthesized the most ideal cage compound with two anthracene chromophores to connect X-ray Bijvoet and CD exciton chitality methods and proved that these two methods are consistent with each other.     

Two coupled neural oscillators as a model of the circadian pacemaker

Pittendrigh first found that the circadian rhythm of locomotor activity in nocturnal rodents split into two components. Hoffman then reported that the splitting phenomenon was even more reproducible in the small diurnal primate Tupaia. These “splitting” experiments and many other experiments suggest that two coupled oscillators may constitute the circadian pacemaker system. Pittendrigh proposed a phenomenological two-oscillator model. Daan and Berde developed a quantitative model assuming that the interaction between the two constituent oscillators is by instantaneous resets. Their model system can simulate several qualitative features in the experimental data. As the assumption of instantaneous resets seems to be unnatural, we study two limit cycle oscillators, which are coupled continuously to each other, as a model of the circadian pacemaker. We assume the following points, (i) One oscillator in a resting state does not affect another oscillator, (ii) Two oscillators are identical, (iii) The coupling is symmetrical. By the theory of Hopf bifurcation it is found that the general two-oscillator system has two stable periodic solutions. One is the in-phase solution where the two constituent oscillators oscillate in phase synchrony. Another is the anti-phase solution where the two oscillators oscillate 180 ° out of phase. The former corresponds to a single pattern of locomotor activity and the latter corresponds to a splitting pattern. Furthermore, we study specific two-neural oscillators, which are linearly coupled to each other. By the method of secondary bifurcation we find that the model shows simultaneous stability of the two alternative phase relationships and the hysteresis phenomena found in Tupaia. A natural period of the uncoupled constituent oscillator is longer than that of the in-phase solution but it is shorter than that of the anti-phase solution. This is in agreement with the data of Tupaia.     

Modeling the dual pacemaker system of the tau mutant hamster

Circadian pacemakers in many animals are compound. In rodents, a two-oscillator model of the pacemaker composed of an evening (E) and a morning (M) oscillator has been proposed based on the phenomenon of "splitting" and bimodal activity peaks. The authors describe computer simulations of the pacemaker in tau mutant hamsters viewed as a system of mutually coupled E and M oscillators. These mutant animals exhibit normal type 1 PRCs when released into DD but make a transition to a type 0 PRC when held for many weeks in DD. The two-oscillator model describes particularly well some recent behavioral experiments on these hamsters. The authors sought to determine the relationships between oscillator amplitude, period, PRC, and activity duration through computer simulations. Two complementary approaches proved useful for analyzing weakly coupled oscillator systems. The authors adopted a "distinct oscillators" view when considering the component E and M oscillators and a "system" view when considering the system as a whole. For strongly coupled systems, only the system view is appropriate. The simulations lead the authors to two primary conjectures: (1) the total amplitude of the pacemaker system in tau mutant hamsters is less than in the wild-type animals, and (2) the coupling between the unit E and M oscillators is weakened during continuous exposure of hamsters to DD. As coupling strength decreases, activity duration (alpha) increases due to a greater phase difference between E and M. At the same time, the total amplitude of the system decreases, causing an increase in observable PRC amplitudes. Reduced coupling also increases the relative autonomy of the unit oscillators. The relatively autonomous phase shifts of E and M oscillators can account for both immediate compression and expansion of activity bands in tau mutant and wild-type hamsters subjected to light pulses.     

Estimation of the transmission time of stimulus-locked responses: modelling and stochastic phase resetting analysis

A model of two coupled phase oscillators is studied, where both oscillators are subject to random forces but only one oscillator is repetitively stimulated with a pulsatile stimulus. A pulse causes a reset, which is transmitted to the other oscillator via the coupling. The transmission time of the cross-trial (CT) averaged responses, i.e. the difference in time between the maxima of the CT averaged responses of both oscillators differs from the time difference between the maxima of the oscillators' resets. In fact, the transmission time of the CT averaged responses directly corresponds to the phase difference in the stable synchronized state with integer multiples of the oscillators' mean period added to it. With CT averaged responses it is impossible to reliably estimate the time elapsing, owing to the stimulus' action being transmitted between the two oscillators.     

Simple models for excitable and oscillatory neural networks

 Chains of coupled oscillators of simple “rotator” type have been used to model the central pattern generator (CPG) for locomotion in lamprey, among numerous applications in biology and elsewhere. In this paper, motivated by experiments on lamprey CPG with brainstem attached, we investigate a simple oscillator model with internal structure which captures both excitable and bursting dynamics. This model, and that for the coupling functions, is inspired by the Hodgkin–Huxley equations and two-variable simplifications thereof. We analyse pairs of coupled oscillators with both excitatory and inhibitory coupling. We also study traveling wave patterns arising from chains of oscillators, including simulations of “body shapes” generated by a double chain of oscillators providing input to a kinematic musculature model of lamprey.. Received: 25 November 1996 / Revised version: 9 December 1997     

Photoselection and circular dichroism in the purple membrane.

The transient dichroic ratio D = delta A parallel/delta A perpendicular has been measured in the visible absorption region of bacteriorhodopsin in purple membrane by a flash photolysis method. D is found to be wavelength independent throughout the visible absorption band, and reaches a maximum value of 2.75 +/- 0.15 on reduction of the excitation intensity. This value is close to that expected for a single nondegenerate transition dipole moment and is incompatible with the strong exciton coupling model used to explain circular dichroism (CD) spectrum of purple membrane. A time-dependent analysis of the exciton interaction and consideration of the coupling strength suggests an explanation of these observations. It is concluded that excitation interaction between retinals in purple membrane is of the weak or very weak type defined by Förster.     

Phase Resetting Curves Allow for Simple and Accurate Prediction of Robust N:1 Phase Locking for Strongly Coupled Neural Oscillators

Existence and stability criteria for harmonic locking modes were derived for two reciprocally pulse coupled oscillators based on their first and second order phase resetting curves. Our theoretical methods are general in the sense that no assumptions about the strength of coupling, type of synaptic coupling, and model are made. These methods were then tested using two reciprocally inhibitory Wang and Buzsáki model neurons. The existence of bands of 2:1, 3:1, 4:1, and 5:1 phase locking in the relative frequency parameter space was predicted correctly, as was the phase of the slow neuron's spike within the cycle of the fast neuron in which it occurred. For weak coupling the bands are very narrow, but strong coupling broadens the bands. The predictions of the pulse coupled method agreed with weak coupling methods in the weak coupling regime, but extended predictability into the strong coupling regime. We show that our prediction method generalizes to pairs of neural oscillators coupled through excitatory synapses, and to networks of multiple oscillatory neurons. The main limitation of the method is the central assumption that the effect of each input dies out before the next input is received.     

Exciton coupling between enones: Quassinoids revisited

The electronic circular dichroism (ECD) spectra of two previously reported quassinoids containing a pair of enone chromophores are revisited to gain insight into the consistency and applicability of the exciton chirality method. Our study is based on time‐dependent Density Functional Theory calculations, transition and orbital analysis, and numerical exciton coupling calculations. In quassin ( 1 ) the enone/enone exciton coupling is quasi‐degenerate, yielding strong rotational strengths that account for the observed ECD spectrum in the enone π‐π* region. In perforalactone C ( 2 ) the nondegenerate coupling produces weak rotational strengths, and the ECD spectrum is dominated by other mechanisms of optical activity. We remark the necessity of a careful application of the nondegenerate exciton coupling method in similar cases.     

Pulse coupled oscillators and the phase resetting curve

Limit cycle oscillators that are coupled in a pulsatile manner are referred to as pulse coupled oscillators. In these oscillators, the interactions take the form of brief pulses such that the effect of one input dies out before the next is received. A phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike in an oscillatory neuron depending upon where in the cycle the input is applied. PRCs can be used to predict phase locking in networks of pulse coupled oscillators. In some studies of pulse coupled oscillators, a specific form is assumed for the interactions between oscillators, but a more general approach is to formulate the problem assuming a PRC that is generated using a perturbation that approximates the input received in the real biological network. In general, this approach requires that circuit architecture and a specific firing pattern be assumed. This allows the construction of discrete maps from one event to the next. The fixed points of these maps correspond to periodic firing modes and are easier to locate and analyze for stability compared to locating and analyzing periodic modes in the original network directly. Alternatively, maps based on the PRC have been constructed that do not presuppose a firing order. Specific circuits that have been analyzed under the assumption of pulsatile coupling include one to one lockings in a periodically forced oscillator or an oscillator forced at a fixed delay after a threshold event, two bidirectionally coupled oscillators with and without delays, a unidirectional N-ring of oscillators, and N all-to-all networks.     

Dynamics of energy transfer and trapping in the light-harvesting antenna of Rhodopseudomonas viridis.

By low intensity picosecond absorption spectroscopy it is shown that the exciton lifetime in the light-harvesting antenna of Rhodopseudomonas (Rps.) viridis membranes with photochemically active reaction centers at room temperature is 60 +/- 10 ps. This lifetime reflects the overall trapping rate of the excitation energy by the reaction center. With photochemically inactive reaction centers, in the presence of P+, the exciton lifetime increases to 150 +/- 15 ps. Prereducing the secondary electron acceptor QA does not prevent primary charge separation, but slows it down from 60 to 90 +/- 10 ps. Picosecond kinetics measured at 77 K with inactive reaction centers indicates that the light-harvesting antenna is spectrally homogeneous. Picosecond absorption anisotropy measurements show that energy transfer between identical Bchlb molecules occurs on the subpicosecond time scale. Using these experimental results as input to a random-walk model, results in strict requirements for the antenna-RC coupling. The model analysis prescribes fast trapping (approximately 1 ps) and an approximately 0.5 escape probability from the reaction center, which requires a more tightly coupled RC and antenna, as compared with the Bchla-containing bacteria Rhodospirillum (R.) rubrum and Rhodobacter (Rb.) sphaeroides.     

Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators

Gamma oscillations can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices. How synchronization can take place over long distances in a stable manner is considered an open question. The phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike, depending upon where in the cycle it is received. We use PRCs under the assumption of pulsatile coupling to derive existence and stability criteria for 1:1 phase-locking that arises via bidirectional pulse coupling of two limit cycle oscillators with a conduction delay of any duration for any 1:1 firing pattern. The coupling can be strong as long as the effect of one input dissipates before the next input is received. We show the form that the generic synchronous and anti-phase solutions take in a system of two identical, identically pulse-coupled oscillators with identical delays. The stability criterion has a simple form that depends only on the slopes of the PRCs at the phases at which inputs are received and on the number of cycles required to complete the delayed feedback loop. The number of cycles required to complete the delayed feedback loop depends upon both the value of the delay and the firing pattern. We successfully tested the predictions of our methods on networks of model neurons. The criteria can easily be extended to include the effect of an input on the cycle after the one in which it is received.