Cortical and hippocampal neural rhythms: biophysics and dynamics

 Horacio Rotstein is continuing to work with Kopell on models of the theta rhythm (4-12 Hz), as produced in vitro in CA1 hippocampal slices by Miles Whittington using only inhibitory neurons.  Previous simulations that showed that the version of this rhythm seen in that in vitro data required the interaction of multiple inhibitory cells types. Building on this, with the help of White and grad student Corey Acker, they showed how the “ragged synchronization” seen in cells within a class can occur in large and small networks, and how the detailed timing of the noisy spiking can be explained from kinetic properties of the currents involved.  The mechanism involves networks of inhibitory neurons: fast‑firing interneurons (I) and oriens lacunosum moleculare (OLM) interneurons, which have non‑standard currents (hyperpolarization activated and persistent sodium) as well as standard ones (sodium, potassium and leak). The two types of interneurons have different times scales for intrinsic and synaptic currents.  Using numerical and analytical techniques, they dissected the various roles played by the inhibition-activated current I_h.  This work has led to experimental work of Matt Banks (in progress) to test the ideas using dynamic clamp technology, as built in the lab of John White.

Rotstein, Kopell and Rob Clewley continue to work on issues involving reduction of high-dimensional neural systems (single cells or networks) to lower dimensional systems and maps.  The central idea is that the relevant trajectories are divided into epochs such that, in each epoch, the number of relevant variables is much lower.  Rotstein has recently used this method to explain the existence of transient subthreshold oscillations in the theta frequency range in stellate cells of the entorhinal cortex.  The frequency is slower than that of the theta oscillations produced by these cells in spiking model, and the analysis explains why.  Work continues to determine why, in related models, noise enables such subthreshold oscillations to be much more robust. Also, they are currently exploiting this method to explain the synchronization properties in larger networks.

 Theoden Netoff has continued work with White and Kopell, applying phase response techniques in neurophysiological experiments, and comparing predictions from such techniques with results from “hybrid networks,” consisting of one or more biological neurons, coupled with real-time, in silico model neurons.  Netoff ‘s major findings in this project: (1) As predicted from past modeling work from that group (Acker et al., 2003), neurons with prominent slow currents give rise to synchronization via mutual excitation and anti-synchronization via mutual inhibition.  (2) Phase response results match those from hybrid networks well, even in the details, implying that the assumptions underlying the predictions hold.  (3) Results in studies thus far are largely independent of synaptic amplitudes or kinetics, implying that predictions remain valid even under changing conditions.  (4) Results are remarkably consistent within a cell type.  This result is somewhat surprising, given that results from models (Acker et al., 2003) are very sensitive to choices of parameters.  This result suggests that cells may tune their electrophysiological properties to achieve consistent synchronization. This work has been submitted.

Netoff’s more recent work, conducted with White, Kopell, and  Dmitri Pervouchine, focuses on more complex hybrid networks, consisting of as many as three cell types.  Netoff’s work confirms predictions from Pervouchine’s simulation studies (see below), and shows how such a network can exhibit either theta or gamma rhythms under slightly different conditions.  The inward rectifying current I_h seems particularly important in determining such behavior in both computational simulations and hybrid networks. An abstract has been submitted for the Soc. for Neurosci (SfN) meeting in 2004.

 Dmitri Pervouchine, Kopell, Miles Whittington and Mark Cunningham (a postdoc from the Whittington lab) have been working on mechanisms associated with nested rhythms in the in vitro entorhinal cortex (EC).  The work is a mixture of simulations and dynamical systems, to understand the origin of very slow rhythms (< 1 Hz), in which an active phase alternates with a silent period.  In the active phase, there is a nested rhythm of beta (~ 16 Hz) and theta (~ 8 Hz), involving several different cell types.  The recent work of Dmitri predicted the existence of some anatomical structures in the EC.  These structures have recently been found in the lab of Hannah Monyer.  An abstract on the modeling has been submitted for the 2004 SfN meeting.

The EC is especially interesting since it is the gateway between the neocortex and the hippocampus, where learning of associations is believed to take place.  The work with the Whittington lab on the physiology and dynamics of the EC and the hippocampus is informing other new work with Howard Eichenbaum on the creation of cell assemblies in learning paradigms.  Data from other labs (notably that of Clayton Dickson) has suggested that the gamma and theta rhythms in the EC have different synchronization properties, with gamma rhythms synchronous and coherent over a local region and theta coherent, but with regular phase lags, over a much larger region.   Joszi Jalics and grad student Tilman Kispersky are working with Kopell on a project involving both analysis and simulation: the aim is to understand how the gamma and theta rhythms control of the formation and coordination of the “neuronal ensembles”.  The current work focuses on the hypothesis that the entorhinal cortex is composed of spatially organized modules of stellate, interneuron and pyramidal cells, and looks at how intrinsic and synaptic currents affect how activity propagates throughout the EC.  An abstract has been submitted to the 2004 SfN meeting.  The analytical issues concern how the network switches among the different rhythms.

 Brian Burton is working with White on two projects.  In the first project, Burton is studying how cellular oscillations develop in the entorhinal cortex around the time that rat pups’ eyes open.  Current experiments are exploring the mechanistic bases of these changes.  In the second project, Burton is studying oscillatory entorhinal neurons using techniques from communication theory.  His results show that cells respond preferentially to sequences of input that match the statistical properties of spike trains.  In the future, Burton will focus on the mechanisms underlying these spike train statistics.

Yu-Dong Zhou is working with White to understand the mechanistic basis of spike-time-dependent plasticity (STDP), a phenomenon by which synaptic weights change dynamically in some neuronal networks.  Zhou has demonstrated, for the first time, that STDP occurs in the entorhinal cortex.  His current experiments are elucidating how STDP is affected by spike width in postsynaptic neurons.  In future work, Zhou will work with White and Kopell to understand the cellular mechanisms of population oscillations in brain slices of entorhinal cortex.

Netoff and fellow  Rob Clewley have worked with White, studying how epileptiform behaviors arise in simulated neuronal networks with small-world connectivity.  Synaptic strength, the overall probability of connection between neurons, and the degree of small-world connectivity are all important for determining whether such networks “seize,” and the specific form such “seizures” take.  This work, which connects to the biological literature for hippocampal epilepsy, is currently under review.

Alan Dorval has worked with White to measure how membrane noise, generated by the stochastic flicker of voltage-gated ion channels, affects cellular oscillations in entorhinal cortex.  By mimicking ion channels using a real-time experimental control system, Dorval showed that membrane noise fundamentally alters the dynamics of entorhinal neurons.  Current work focuses on how such alterations affect the coding properties of the cells.  Dorval also examined how neuronal responses to natural “conductance” inputs differ systematically from those measured using the ubiquitous current-clamp technique.  Dorval defended his PhD in Spring 2004.  His work will be submitted for publication in Summer 2004.

With co-authors Kopell and White, Corey Acker published his work on phase response relationships in 2003.  His current work, mentored by White and Sen, focuses on mechanistic computational models of spike-time-dependent plasticity (STDP). This work complements the experimental studies of Zhou cited above.  Acker is also studying back-propagating action potentials in computational models.  He plans to take advantage of techniques developed by Rob Clewley to make firm mathematical statements regarding these simulations.

Tara Keck is working with White, focusing on how dendritic inputs and back-propagating action potentials (bAPs) interact.  Among her findings: (1) Dendritic inputs give rise to noticeably different phase response relationships, and hence synchronization properties, than somatic inputs.  (2) The neuromodulator acetylcholine affects neuronal synchronization properties.  (3) Properly timed bAPs obliterate excitatory inputs.  This effect depends critically on spike rate, and is probably important for determining how synchronization properties change with changing spike rate.

Sophie Desbiens, currently in her second year, is working with White to put together a dissertations prospectus (proposal), to be defended in late 2004.  Desbiens plans to perform calcium-imaging experiments in the deep layers of the entorhinal cortex.  Her initial hypothesis is that reported differences in synaptic plasticity, seen with different stimulation protocols, are related to calcium spikes in dendrites.

Jonathan Bettencourt has worked with White, Dorval, Netoff and others in White’s lab to create the next generation of the lab’s real-time experimental control system.  This system allows the user to interact with neurophysiological or other preparations in real time, at clock rates of up to 50 kHz.  This system is extremely useful for performing dynamical systems-inspired “wet” experiments.  The system is publicly available, and is being used by a number of laboratories, including those of Barry Connors (Brown), David McCormick (Yale), John Hugeunard (Stanford), Paul Manis (North Carolina), Matthew Banks (Wisconsin), and H. Steven Colburn (Boston University).

Ehud Sivan is working with Kopell on modeling data of the Laurent lab on slow patterning of activity, as well as the gamma oscillations, in the antennal lobe of the locust.  The slow activity, but not the oscillations, persists in the absence of GABA_A mediated inhibition. Earlier modeling work based the slow activity on non-GABa-mediated inhibition, though this has not been found.  Work of Sivan is showing that the slow patterns can be the result of four different sources; (i) intrinsic properties of the projection neurons, such as the existence of calcium dependent potassium channels, (ii) the input from the receptors (including its introduction/removal time constants), (iii) GABAergic input from local interneurons and (iv) input from centrifugal neurons. They argue that these simulations are consistent with all known data.

Rob Clewley has been investigating the effects of using shunting inhibition (conductance based coupling terms) in networks or neurons, as opposed to current-based inhibition.  Using simulations of excitatory‑inhibitory (EI) networks of cortical neurons Clewley has shown that the shunting inhibition is more robust.  Clewley also considered a chain of excitatory/inhibitory oscillators; he showed numerically and explained heuristically that transient input to only part of the chain could lead to a more permanent segmentation of the chain into subsets of cells, synchronous within a subset, but with phase differences between the subsets.  There is an associated 1-D map whose stability analysis relates to the domain of attraction of the segmented state.

Grad student Amanda Serenevy has continued her Ph.D. work with Kopell on inhibitory networks with phase-dispersed periodic input.  She is using properties of strong inhibitory pulses to build mathematical tools capable of analyzing effects of distributed input. The work is motivated by earlier work of White and Kopell showing that, in some circumstances, periodic input to networks of inhibitory neurons could lead to higher power if the inputs to the different cells had a range of phases and amplitudes. 

 

Neural rhythms and behavior

With Dr. Randal Koene, Michael Hasselmo has been developing detailed models of the interaction of hippocampus and prefrontal cortex for performance of behavioral tasks including spatial alternation and spatial reversal in rats as well as an operant responding task in monkeys.  This research uses the CATACOMB simulation package to develop spiking network models of goal directed behavior, focusing on the role of theta rhythm oscillations in hippocampal network function, and the interaction of hippocampal episodic retrieval mechanisms with goal‑directed function mediated by prefrontal cortex.

Steve Kunec has been working with Hasselmo and Kopell on how biophysical properties of the cells that produce the theta rhythm can help in parsing that rhythm into epochs associated with encoding and retrieval.  The work builds on earlier work of Hasselmo, as well as on properties of cells in the CA3 part of the hippocampus that have been found in vitro (e.g. by the lab of Whittingon).  Prominent in that work are the O-LM cells, which are primed to fire by inhibition. This work will be submitted shortly.

With grad student Anatoli Gorchetchnikov, Hasselmo has also been working on models of the dynamical interaction of different hippocampal subregions in mediating goal‑directed spatial navigation.  This work includes modeling of the interaction of entorhinal cortical and region CA3 inputs to region CA1, as regulated by rhythmic input from the medial septum.

In work with Dr. Ali Atri, Hasselmo has tested predictions of computational models on the role of cholinergic modulation in cortical structures.  Recent work on the effects of the muscarinic antagonist scopolamine in human subjects support the prediction of the model that scopolamine should enhance proactive interference during the encoding of verbal paired associate stimuli.

With Steven Epstein, Kopell and Christoph Borgers are studying the role of gamma in attention.  This project, whose aim is to understand how gamma rhythms, which are so prominent in experimental paradigms involving attention, change network response to input with spatio-temporal structure. The work involves modeling different types of gamma rhythms in which the excitatory cells spike sparsely, and noise is an essential part of the drive.  It also involves reduction of very detailed compartmental models of Traub et al., which have rhythms created by a plexus of axons, to a much simpler description in which noise replaces much of the axonal complexity.

Ehud Sivan has been working with Kopell on a project associated with the olfactory system of insects, especially honeybees.  The aim of the project is to explain why oscillations appear to be important for identification of specific odors, but not for more general “clusters” of odors.  The work hypothesizes a division of Kenyon cells of the mushroom body into pre-wired “categories” associated with the interneurons of the lateral horn, and shows how this can account for a variety of data.  The role of the oscillations is to group the inputs to the Kenyon cells into small intervals of times. The ideas are supported by simulations showing the identification of specific odors (modeled by inputs into a small set of Kenyon cells) when there are oscillations, but only more general groups of odors when the input does not have this temporal structure.

Grad student Michelle McCarthy (of UCLA) has been working with Kopell and anesthesiologist/statistician Emery Brown on the effects of the anesthetic propofol on the EEG at different levels of anesthesia.  This complements experimental work of Brown, who is measuring the EEG of healthy individuals on propofol to understand the mechanisms by which this anesthetic removes consciousness.  The modeling is an attempt to bridge the known facts about the biophysical effects of propofol (notably the increase in the amplitude and the decay time of inhibition mediated by GABA_A receptors) with the measured, global EEG rhythms.

Grad student Cecilia Deniz Behn is working with Emery Brown and Kopell on the effects of the anesthetic clonadine, and adrenergic agonist that is believed to work through normal sleep-wake pathways.  Her modeling focuses on a network of neuronal nuclei in the brainstem and hypothalamus.  These nuclei are involved in the regulation of natural sleep and transitions between sleep‑wake states.   The rhythms here are ultradian and circadian, much slower than the EEG rhythms. The work is aimed at understanding some of the mechanisms of sleep disorders, such as narcolepsy. 

Dorea Claasen and Kopell have been part of a working group at BU on rhythms and schizophrenia with schizophrenia researchers from Mass. General Imaging Center and McLean’s Hospital.  The project involves pathologies in the rhythmic electrical responses of the auditory cortex of schizophrenic patients when given periodic stimuli.  The modeling is used to understand how different kinds of known deficits at the cellular and synaptic level might affect the reponses to auditory stimuli.

 

Dynamics of the auditory system

Rajiv Narayan has continued his work with Kamal Sen on discrimination of natural sounds by auditory neurons with Sen. Narayan has developed a computational model of auditory neurons in the songbird auditory cortex analog, field L. This work was presented at the annual meeting of the Society for Neuroscience and the midwinter research meeting of the Association for Research in Otolaryngology (a meeting focusing on research in auditory neuroscience). In his computational model, Narayan related the structure of experimentally observed receptive fields to the discrimination of natural sounds such as birdsongs. Narayan’s main findings are that key parameters of the receptive field that produce efficient discrimination are the relative timing and the balance of excitatory and inhibitory regions in the receptive field. A manuscript based on this work is now being prepared for submission. Over the last year, Narayan has also learned how to perform electrophysiological recordings from field L of the songbird. In his subsequent work, Narayan will combine electrophysiological recordings and computational modeling to characterize discrimination of songs in field L.

Two new members of the Sen lab are graduate student Gilberto Grana and Ayla Ergun. Grana has begun a project on characterizing correlations in firing between auditory neurons in response to natural sounds. He is implementing computational methods such as the cross-correlogram and the joint peri-stimulus time histogram and testing these methods on model circuits with known connectivity. He is planning to apply these techniques to characterize neural correlations in field L.  He is also developing a chronic recording set-up for recording neural responses in awake behaving songbirds. Ergun, a new student in PMCN, has begun a project on plasticity in the receptive fields of auditory neurons. She is currently working on a computational model to investigate the effects of Hebbian Spike Timing Dependent Plasticity (STDP) on the receptive field structure of auditory neurons.

Gabriel Soto has been working jointly with Kopell and Sen on a model of layer IV in auditory cortex investigating the relative roles of thalamocortical and intracortical circuits in shaping receptive field structure in auditory cortex and the effects of acetylcholine, a major neuromodulator of auditory cortex, on these circuits. Soto’s main findings: (1) the local average activity of neurons in a biophysical model constrained by anatomical and physiological data, is similar to experimentally recorded field potentials in auditory cortex and (2) Acetylcholine shifts the model network into a different state which shows three important differences: the ratio of thalamic vs. cortical contribution to the response is increased, the frequency tuning of cortical cells is sharpened, and cortical cells become more synchronized producing stronger gamma oscillations. Soto is submitting an abstract for the annual meeting of the Society for Neuroscience based on this work. Soto has also been attending the Sen lab meeting and interacting with the other graduate students in the Sen lab. In particular, Ergun has benefitted from interactions with Soto on computational models and may follow up on some of Soto's work.

Colleen Mitchell, mentored by Sen, Kopell and Steve Colburn continued her work with Mike Reed on early processing of auditory signals by the “octopus cell”.  The octopus cell (named for its morphology), is able to produce outputs that are an order of magnitude more synchronous than its inputs.  Mitchell has produced a biophysical model of the cell to complement her earlier work on the statistics of numbers of events in a given window of time.  She has also focused this year on parameter regimes in the statistical analysis that more closely match that of the biophysics. 

 

Pattern formation and dynamics of other excitable systems

Valmeek Kudesia has worked with White and Netoff to generate models of emerging ventricular fibrillation and defibrillation.  Kudesia has shown that “focal” defibrillators, with electrodes placed near the site of emergence of fibrillation, consume up to 98% less energy than traditional electrode placements.  This work will continue in Summer 2004.

Alexey Kuznetsov continued working with Kopell and Charlie Wilson on the dynamics of dopamine neurons of the substantia nigra .  These neurons are thought to be very important in the reward system, associated with goal‑directed behavior. The dopamine neuron ordinarily will not fire faster than about 10Hz when depolarized in slices. In vivo, much higher rates are briefly attained, for example after an unexpected reward. Using a physiologically based model, they suggest several mechanisms by which a burst may occur in vivo, but not in slices. The model represents the neuron as a number of electrically coupled compartments with different natural spiking frequencies, which correspond to the soma and parts of the dendrite. The primary hypothesis is that the soma is susceptible to loss of spiking due to inactivation of the Na channel, and the rapid activation of AHP currents in distal compartments is partly responsible for preventing this. They show that a difference in natural frequencies of the compartments is necessary for the transient oscillations to occur and propose two biophysically distinct mechanisms for obtaining the difference in natural frequencies. That difference does not by itself ensure a significant difference between transient and steady state frequencies, and they distinguish two dynamically different components contributing to the latter frequency difference.  They also investigate the consequences of a more realistic dendrite geometry, showing that both branching and the presence of long thin dendritic sections contribute to the high‑frequency transient. The work helps explain why spiking matters, and why cutting off parts of the dendrites, as occurs in vitro, can keep the transient response from happening.  A paper on this is almost complete, and an abstract has been submitted to the 2004 SfN meeting.

Steve Kunec and Josh Berke (of the Eichenbaum lab) are collaborating on analysis of field oscillations (gamma and beta range) in the striatum.  They have used ordinary and partial coherence analysis to show that the amount of coherence with another part of the brain (e.g. frontal cortex, piriform cortex) depends on the frequency band and the part of the brain.  They used wavelet analysis to construct triggered, averaged scalograms aligned on behaviorally significant events.  Kunec expects to model the biophysics underlying these data.

Rotstein has been working with Rachel Kuske and Kopell on the role of the canard phenomenon in the mechanism of localization in diffusively coupled, heterogeneous calcium oscillators. Localization here means that some oscillators in the network display only small amplitude rhythms, while others have large amplitude oscillations. These models are usually more complex than globally coupled BZ models, which were analyzed by this group in the past. In the latter, localization is mainly due to the global coupling term while in the former the local coupling created by diffusion is the main source of localization. For single oscillators, suitable transformations are necessary in order to calculate the values of the parameters for which the canard explosion occurs. In addition, diffusive coupling, due to its local character, acts as a forcing term on each oscillator dynamically moving at least one of its nullclines and complicating the analysis.

Rotstein is also studying propagation failure in chemical front models. These models are based on different ways of achieving non‑local feedback in chemical (and biological) systems.  The effects this type of coupling exerts on the dynamics of fronts may give hints about similar effects on different dynamical structures such as fronts separating different oscillatory clusters; i.e., oscillatory domains with different phases, relevant in chemical, biological and neurobiological studies.

Kaper and former grad student Dave Morgan published an article concerning annular ring solutions of the Gray‑Scott model. In the monostable regime, annular rings are far‑from‑ equilibrium patterns supported on annuli inside of which the activator is concentrated. The diffusive flux of inhibitor over long length scales toward such an annulus feeds the production of activator there, and the interaction is semi‑strong. Numerical and experimental observations show that annular rings often split into spots, and the main result presented in this article is a method to predict the number of spots that an annular ring, unstable to angular disturbances, will split into. This method is an extension to 2‑D circular geometries of the NonLocal Eigenvalue Problem (NLEP) method developed for pulse solutions of the 1‑D Gray‑Scott problem, in which the full eigenvalue problem ‑‑ a pair of second‑order, nonautonomous coupled equations ‑‑ is recast as a single, second‑order equation with a nonlocal term. They also continue the results for the monostable regime into the bistable regime of the Gray‑Scott model, where target patterns exist and their rings are observed to destabilize into rings of spots, as may be shown using a classical Turing/Ginzburg‑Landau analysis. Thus, for these 2‑D circular geometries, the NLEP method is to the instability of annular rings in the monostable regime what the Turing analysis is to the instability of target patterns in the near equilibrium regime. It is an important new tool that they have exploited on many activator‑inhibtor systems, especially in the works with Doelman, Eckhaus, Peletier and Gardner.

Grad student Margaret Beck is working with Kaper on bioremediation, i a promising technology for cleaning contaminated groundwater and soil. They study an idealized, 1‑D PDE model for pollutant, microorganism, and nutrient concentrations. The model is known (see Murray and Xin) to posses a traveling wave solution, which loses stability to a periodic traveling wave. They use matched asymptotics to construct the leading order traveling wave and to study how the bifurcations it can undergo depend on the key physical parameters.

Ehud Sivan is working in collaboration with H. Parnas and L. Segel to understand the underlying mechanism of a bursting behavior observed in a four-dimensional system constructed to model the neurons in the cardiac ganglion of the lobster (Av‑Ron et al. 1991, 1993).  They focus on the initiation and termination of the burst and seek the "inertia" mechanism they believe exists at those borders. This inertia must overcome the tendency of the system to recross the border immediately after it was crossed the first time. The work focuses on the role of calcium in closing the channels and the drop in its concentration at the end of the burst.

 

Sensorimotor Dynamics

Grad student Attila Priplata, postdoc Ben Patritti, Jim Collins and colleagues from Afferent Corp. and Harvard Medical School) examined the effects of noise input to the somatosensory system on posture control in patients with balance deficits.  They hypothesized that the postural sway of patients with diabetic neuropathy and patients with stroke during quiet standing can be significantly reduced by applying mechanical noise to the feet using vibrating insoles.  To test this hypothesis, they conducted a series of quiet‑standing experiments on 15 subjects with diabetic neuropathy and 15 subjects with stroke. They found that applying applying subsensory mechanical noise to the feet, via the vibrating insoles, significantly reduced the postural sway of both patients groups.  individuals during quiet standing. These results suggest that noise‑based devices, such as randomly vibrating shoe inserts, could ameliorate diabetic and stroke impairments in balance control.

Undergraduate Audrey Rosengarten, grad student Attila Priplata, and Jim Collins also examined the effects of subsensory mechanical noise applied at the ankle on quiet‑standing balance control.  Fifteen healthy young subjects were and fifteen elderly subjects were included in the study.  They found that applying subsensory mechanical noise to the ankles, via vibrating tactors, significantly reduced the postural sway of both young and elderly subjects.  These results suggest that noise‑based ankle wraps may be effective in improving balance control in young and elderly people.

 

Gene Dynamics

Hideki Kobayashi, Mads Kaern, Michihiro Araki, grad student Kristy Chung, Tim Gardner, Charles Cantor and Jim Collins demonstrated how an engineered genetic circuit can be used to construct cells that respond to biological signals in a predetermined and programmable fashion. They employed a modular design strategy to create Escherichia coli strains where a genetic toggle switch is interfaced with: (i) the SOS signaling pathway responding to DNA damage, and (ii) a transgenic quorum sensing signaling pathway from Vibrio fischeri. The genetic toggle switch endowed these strains with binary response dynamics and an epigenetic inheritance that supports a persistent phenotypic alteration in response to transient signals. These features were exploited to engineer cells that form biofilms in response to DNA damaging agents and cells that activate protein synthesis when the cell population reaches a critical density. This work represents a step toward the development of "plug‑and‑play" genetic circuitry that can be utilized to create cells with programmable behaviors.

Postodcs Alexey Kuznetsov and Mads Kearn, working with Kopell, built on previous work on the toggle switch to figure out how to construct a coherent oscillation in a population of cells.  They constructed a robust, hysteresis‑based genetic relaxation oscillator and provided a theoretical analysis of the conditions necessary for single‑cell and population synchronized oscillations. The oscillator is constructed by coupling two subsystems that have previously been implemented experimentally. The first subsystem is the toggle switch, which consists of two mutually repressive genes, and can display robust switching between two expression states and hysteresis. The second subsystem is an intercell communication system involved in quorum‑ sensing. This subsystem drives the toggle switch through a hysteresis loop in single cells and acts as a coupling between individual cellular oscillators in a cell population. They demonstrated the possibility of both population synchronization and suppression of oscillations, depending on diffusion strength and other parameters of the system and proposed an optimal range of the parameters and small variations in the architecture of the gene regulatory network that substantially expand the oscillatory region and improve the likelihood of observing oscillations experimentally.  A paper is almost completed and a second paper is in progress, addressed to a more biological audience and focusing on stochastic issues

Farren Isaacs, grad student Dan Dwyer, Dmitri Pervouchine, Chunming Ding (BU Bioinformatics), Charles Cantor and Jim Collins developed a post‑transcriptional regulation system in Escherichia coli that uses RNA to both silence and activate gene expression.  They inserted a complementary cis sequence directly upstream of the ribosome binding site in a target gene.  Upon transcription, this cis‑repressive sequence causes a stem‑loop structure to form in the mRNA that interferes with ribosome binding, silencing gene expression.  A small activating mRNA thiat is expressed in trans targets the cis‑repressed RNA with high specificity, causing an alteration in the stem‑loop structure that dramatically increases expression.  These engineered riboregulators, which lend insight into mechanistic actions of RNA‑based processes, could serve as scalable components of biological networks, able to function with any promoter or gene to directly affect gene expression.

Hideki Kobayashi, Michihiro Araki, Mads Kaern and Jim Collins the developed and successful applied an engineered, enzymatically active bacteriophage T7 to eradicate mature biofilm formed by Escherichia coli. The engineered phage was designed to employ a two‑pronged attack strategy: (i) its enzymatic activity targets and degrades the extracellular matrix of the biofilm, thus exposing the biofilm‑embedded cells, and (ii) the phage infect and kill the exposed cells, releasing additional enzymatic phage in the process.  Bacterial biofilms are associated with many human health and environmental issues. For instance, bacteria form biofilms on implanted medical devices (e.g., catheters, heart valves, joint replacements) and damaged tissue, such as the lungs of cystic fibrosis patients. Because bacteria in biofilms are highly resistant to antibiotics and host defenses, they are persistent sources of infection.  The present work could form the basis for a novel, effective treatment for dispersing and eliminating biofilms.

Mike Thompson and Jim Collins studied interacting networks of proteins and genes, and explored the hypothesis that the magnitude of the global cellular response to a perturbation is positively correlated with the network connectivity of the perturbed gene product. They found that the connectivity in the protein‑protein interaction network in Saccharomyces cerevisiae is not well correlated with the magnitude of the response, measured as genome‑wide expression changes following the deletion or over-expression of a gene. When the network model is extended to include genetic regulatory interactions and protein complex interactions, and when the cellular response is measured under the environmental conditions in which the perturbed gene normally operates, the correlation between connectivity and response improves, but remains low.  These results point to the limitations of global analyses of biological networks, which are based on static network models composed of homogenous nodes and edges. Despite such limitations, they showed that the analysis of outliers can provide substantial biological insight. For example, highly connected proteins whose perturbation generates a small cellular response are generally components of redundant pathways or have been perturbed outside the environmental context of their activity; whereas poorly connected proteins that generate a large response upon perturbation, such as the ergosterol metabolic enzymes, likely elicit cellular responses through diffuse channels.

Jonathan Mason, Paul Linsay (Superior Methods, Inc.), Jim Collins and Leon Glass (McGill University) constructed and experimentally analyzed an electronic circuit that is based on a class of ordinary differential equations that model genetic networks. Networks in this system can display a variety of dynamics, including steady states, limit cycles and chaos.  They focused on limit cycles and showed that it is possible to evolve networks that display stable oscillations of a specified cycle length.  By analyzing the fitness landscape, they demonstrated that there is an optimal evolution rate for obtaining such dynamics.  This work showed how mutations in model gene networks can lead to the evolution of dynamic behaviors.

Collaborator Diego di Bernardo, Tim Gardner and Jim Collins developed and successfully demonstrated an algorithm that can identify the genes and proteins that mediate a cell's response to drug treatment.  The algorithm enables the use of unstructured gene expression data to estimate a linear dynamic model of the gene regulatory network underlying drug response.  The model is estimated using a recursive multiple regression scheme combined with singular value decomposition for de‑noising and dimensional reduction.  The estimated model is subsequently applied to new data measuring a cell's response to drug treatment.  The model acts as a filter that separates the genes that are initial mediators of drug response from those genes that are only secondary responders to the drug.  The method was successfully applied in simulations and to a yeast data set consisting of 6000 genes measured in 300 experiments.  In the yeast study, the gene mediators of common antifungal drugs were correctly identified.

Grad student Matt Holzer and Tasso Kaper are working on the deterministic and stochastic mathematical modeling of genetic regulatory networks, in particular the modeling of DNA transcription.  In the literature, the complex sequence of reactions involved in transcription is usually condensed into a single reaction step obeying Michaelis‑Menten type kinetics.  They are  appling mathematical reduction techniques to a multi‑step description of DNA transcription to determine whether the Michaelis‑Menten framework is mathematically consistent with the model. 

 

Cell Cycle Dynamics

Visiting wetlab scientist Dr. Cornelio Caday and Baltazar Aguda carried out perturbation experiments on the PI3K/Akt survival signaling pathway to determine how the trigger for apoptosis is controlled in a human cancer cell line (chronic myeloid leukemic cell line K562).  The perturbations involved an Akt inhibitor purchased commercially.  As the theoretical and computational models developed in our lab show, a sharp, reproducible and robust switching behavior was observed for the induction of apoptosis.  A PhD rotation student Chang-Jiun Wu participated in the computer simulations of the threshold properties of the PI3K/Akt pathway.

G. Craciun (postdoc at Ohio State Univ), Avner Friedman (Director of the Math. Biosciences Institute at Ohio State Univ), and Baltazar Aguda, carried out a detailed mathematical analysis of the proposed Aguda-Algar model for the coordination of the cell cycle and apoptosis.  It was shown that the modularity of the model and the module-module interactions are surprisingly accurate in explaining experimental results.  A very interesting result of the analysis is the prediction that apoptosis could be induced by proliferative transcription factors with or without going through the cell cycle.

Yang Su and Mary Wong (PhD students in Bioinformatics at Boston University) are progressing in their projects on linking chromosomal aberrations to perturbations in cellular pathways, mentored by Aguda.  Yang Su carried out statistical analyses on a set of chromosomal aberrations in chronic myeloid leukemia patients (from the Mitelman Database) and showed that there is a non-random tree-like progression of chromosomal instability.  Mary Wong created a database and a suite of programs that link chromosomal gene loci, microarray gene expression data, and the gene ontology annotation of biological processes.  Yuan Cheng, a database programmer, is actively involved in this project; he has recently created a pathway database and knowledgebase focusing on chronic myeloid leukemia.

G. Craciun, R. Cetin-Atalay, and Baltazar Aguda are currently collaborating on finding methods of automating the generation of models of gene regulatory networks from bioinformatics databases; the ideas will be discussed in an upcoming invited review chapter.

 

 

Mechanics, fluid and solid

Working with Kaper and Nadim (formerly of CBD, now at Harvey Mudd), ex-CBD student Anthony Harkin worked on one of the most fundamental problems for a single gas bubble in a Newtonian liquid:  the coupling of the volume/breathing mode (in which the bubble undergoes radially‑symmetric oscillations) with the shape deformation modes (spherical harmonics).  Until now the modeling of these interactions has been almost exclusively based on a  linearization of the governing equations. They propose one of the first models that is nonlinear and that accounts for the energy transfer in both directions, from the dominant volume mode to the shape modes as well as the subdominant back transfer. This model will be useful for many other simulations, especially in sonoluminesence, and it helps to point out the limitations of the linearized analysis.

Sunil Ahuja has finished his MS Thesis on ``Low dimensional representations of flow past a cylinder," under the direction of Paul Barbone, with help from Tasso Kaper. The work demonstrates shortcomings of the POD, when used in conjunction with the Galerkin discretization method.  A novel space‑time Petrov Galerkin method is developed to address the shortcomings of the standard technique.

Christophe Lecomte, working with Paul Barbone and J Greg McDaniel has extended his work on low dimensional representations of structural dynamic systems. This resulted in a journal paper published, and another submitted.  Lecomte  won a fellowship to attend and present his work at the 7^th  US National Congress on Computational Mechanics, in Albuquerque, NM.

John Bailliul is working with many grad students and postdocs.  With Grace Kessenich, he is working on multi‑agent localization for mobile robots.  Hani Sallum is working on user interfaces for motion programming of groups of mobile robots.  Adam C. Smith is modeling the control of boundary flow separation.  Keyong Li is coding for feedback control using rate‑limited information channels.  Jeremy Grace is working on search and surveillance algorithms for multi‑agent systems.

Slava Krigman, working with Gene Wayne, studied the control theory for Maxwell's equations in damped media.  While there is an extensive literature on the control of solutions on Maxwell's equations in lossless media, Slava studied the more difficult (and more physically realistic case) in which the material disipates energy.  Somewhat surprisingly this makes many of the mathematical tools which were developed to treat the case without dissipation much less effective.  Slava studied in detail the case of a cube of material and was able to prove that if controls are applied to one side of the cube the fields cannot be exactly controlled but can be approximately controlled (and he gave estimates on the degree of approximation.)  In the course of this work he discovered and corrected a significant error in a well known paper on control theory for wave equations.  He will give an invited talk on his work at the 5th AIMS Conference on Dynamical Systems and Differential Equations next month in Pomona, CA.

 

Soft- tissue imaging

Nachiket Gokhale's course project in AM580, Theory of Elasticity, taught by Paul Barbone, has recently appeared in the journal Inverse Problems. Nachiket extended Barbone's uniqueness result for two displacement field measurements to four displacement field measurements.

Graduate students Nachiket Gokhale and Mike Richards, working with faculty Assad Oberai, Paul Barbone (BU AME) and Marvin Doyley (Dartmouth College), developed an elastic image registration method which allows two medical images to be aligned in a manner consistent with known laws of mechanics, even if the physical parameters inthose laws are unknown at the time.  The alignment procedure thereby obtains those physical parameters which are often of themselves of primary interest. Nachiket won a fellowship to attend and present his work at the 7^th  US National Congress on Computational Mechanics, in Albuquerque, NM. Related work was also presented IEEE Int Symp Biomedical Imaging, and published in its proceedings.

Adi Dwitama continues his PhD work with Paul Barbone to develop new continuum models for the mechanical behavior of well‑vascularized soft tissue.  These account for fluid exchange among the extravascular and microvascular compartments in the tissue, as well as percolation through the microvasculature, and coupling to the elastic response of the solid phase. The models are derived by asymptotic homogenization. The model is now being coded to test its predictions in various scenarios.

In his PhD work with Paul Barbone, Mike Richards has begun a collaboration with a team from MGH to investigate the feasibility of measuring breast tissue mechanical properties from 3-D x‑ray tomosynthesis images.  Mike has so far analytically determined the conditions necessary for the method to work and will soon be evaluating those predictions in the lab.

 

Network analysis

With graduate students Pu Chen and Federico Vasquez, Redner has been studying the dynamics of opinion formation in populations that are driven by the competing influences of compromise and incompatibility.  These systems are described in terms of interacting spin system that contain a ferromagnetic interaction (representing the natural tendency of reasonable people to develop consensus) and, for certain models, an anti‑ferromagnetic interaction (representing contrarians).  These simple models have been found to display a wealth of unexpected behaviors.  For the example of evolution by a pure majority rule, it appears that the upper critical dimension is infinite.  The time for consensus grows as a power law of the system size for finite spatial dimension, and logarithmically for infinite spatial dimension.  For a threshold dynamics model in which agents compromise if their opinions are sufficiently close and do not interact otherwise, a rich set of bifurcations of opinion occurs as a function of the threshold.      

 

Multiscale analysis

Antonios Zagaris and Kaper wrote a series of papers on the asymptotics of singular perturbed systems.  In the first two papers (Zagaris, Kaper, Kaper 1 and 2), they use geometric singular perturbation theory to examine the asymptotic accuracy of the Computational Singular Perturbation (CSP) method, which has been successfully used to model complex systems of chemical reactions. Developed by Lam and Goussis, it relies on the presence of a range of time scales, such as is common in most combustion problems, in many enzyme kinetics problems, and also in air pollution studies. The goal of the method is to exploit the separation of time scales to reduce the dimensionality and hence also the complexity of the problems.  The  principal findings are that successive iterations of the two‑step method generate, order by order, the asymptotic expansions of a slow manifold and of a linear approximation to the family of fast fibers along which solutions approach the slow manifold. They also show that a one‑step method suffices to find the slow manifold. In paper 3 with Bill Gear and Yannis Kevrekidis, a new reduction method is presented, that works with legacy codes and on the fly.  This method also exploits the separation of time scales and is motivated by the properties of matched asymptotic expansions of solutions to these singularly perturbed systems. It is shown to be computationally much less expensive than a number of other existing methods, and preliminary analytical work (for an eventual part II of this paper) shows that the method will find the slow manifolds in singularly‑perturbed problems. In papers 4 and 5 with Mike Davis, Zagaris has shown, in the context of two very elementary (and admittedly low‑dimensional) systems, how to carry out reduction in the presence of advection and diffusion. These papers are essentially for toy models, but nevertheless they serve as a good starting point for generalization to more realistic problems.