Research Areas
Nonlinear Dynamics and Pattern Formation
Pattern Formation in Reaction-Diffusion-Mechanics Systems. Grad student Matt Holzer has worked with Kaper and A. Doelman on Reaction-Diffusion equations coupled to finite deformation elasticity theory that arise in the modeling of cardiac tissues for which the medium is both excitable and contractible. They focus on one-dimensional versions of these models and study the role that the mechanical effects play in generating recurrent behavior, as well as role that deformation plays in the stability of traveling wave solutions.
Localized states in nonvariational PDEs. With Kaper, E. Knobloch (U. C. Berkeley), S. Houghton (University of Leeds), and J. H. P. Dawes, (University of Bath), postdoc J. Burke has been studying localized states in nonvariational PDEs. Localized structures are common in pattern forming systems, appearing in fluid mechanics, chemical reactions, and optics. The localized states that arise in these systems are often organized in what is called a snakes-and-ladders structure. Recent attention has focused on the simplest models that exhibit this structure, such as the Swift-Hohenberg equation. One drawback is that the simple models typically only contain stationary localized states. Burke and collaborators are systematically extending these results to more realistic models, resulting in a wider variety of localized states. They have shown that the snakes-and-ladders structure of stationary localized states exists in a particular nonvariational extension of the standard Swift-Hohenberg equation, which appears in chemical, biological, and optical systems. They have also shown that similar models contain localized states with more complicated time dependence, such as localized traveling pulses and breathers. Analysis of the existence, stability, and robustness of these states is underway.
Stability of interacting solitary waves in the Toda lattice. In infinite dimensional integrable Hamiltonian systems (like the Korteweg-de Vries equation for example), solitary waves (or solitons) possess the remarkable property of passing through each other and retaining the same shape they had after the collision as they did before. This is no longer expected to be the case in non-integrable systems, but postdoc Aaron Hoffman and Wayne showed that small, counter-propagating soliton-like interactions can occur in the nonintegrable Fermi-Pasta-Ulam (FPU) lattice model for certain initial conditions. Their proof uses the fact that a special case of FPU, the Toda lattice, is an itegrable system with interacting soliton solutions. Grad student Nick Benes joined Hoffman and Wayne in studying the stability of Toda 2-soliton solutions by using linearizations of the Backlund transformation. Understanding this stability may lead to proof of a wider range of soliton-like interactions for the FPU lattice.
Collision in the Fermi-Pasta-Ulam model. Postdoc Aaron Hoffman and Wayne have studied the interaction of solitary waves in the Fermi-Pasta-Ulam (FPU) model - a one dimensional infinite chain of oscillators with anharmonic nearest-neighbor coupling. This model plays a central role in the history of nonlinear science. It was one of the first differential equations to be numerically integrated (by Fermi, Pasta, and Ulam in a classic Los Alamos report), an investigation which demonstrated that solutions to nonlinear differential equations could have structure, as opposed to the randomness suggested by ergodic-type theorems and assumed in statistical mechanics. This work moreover inspired further numerical experiments by Zabusky and Kruskal which subsequently informed the now classical theory of solitons and their elastic interaction in completely integrable infinite dimensional Hamiltonian systems. As is often the case, perturbing away from a completely integrable Hamiltonian system is a nontrivial task, and even more so in infinite dimensions. Despite decades old success in integrable models, the long-time behavior of interacting solitary waves in FPU, which is typically not integrable, has remained an open question. In the near-integrable, long-wavelength, low-amplitude regime, they have established the existence of ``asymptotic two-soliton states'' that is, solutions whose difference from the linear superposition of two counterpropagating solitary waves, goes to zero as time goes to infinity. These ``nearly two-soliton solutions'' are asymptotically stable with respect to exponentially localized perturbations and are orbitally stable. A key idea in this work and proposed future work, which is quite distinct from classical KAM theory, is to leverage the algebraic structure of completely integrable systems to obtain analytical estimates for nearly-integrable systems.
Fronts in unidirectional lattices. Hoffman and Wayne have proved the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting 1 and 0 for a class of d-dimensional lattice differential equations with unidirectional coupling. They obtained a variational characterization of the critical wave speed. We also discuss coexistence of monotone and non-monotone waves and discuss the nature of waves with speed below the critical wave speed. When the coupling function is monotone, the fronts are well-characterized by the classic technique of monotone iteration. They use ideas from spatial dynamics to characterize these fronts even in the case when the coupling function is not monotone.
Crystallographic pinning. It is well known that scalar reaction-diffusion equations on the lattice, as opposed to the line, exhibit the phenomenon of pinning: the persistence of stationary fronts despite unequal energies in their asymptotic states. It is less well known that on the two-dimensional lattice, these equations also exhibit crystallographic pinning: the presence of privileged angles at which the fronts are severely pinned. Using a variety of techniques including singular perturbation, center manifold reduction, and transversality arguments, Hoffman and Wayne showed that crystallographic pinning occurs for a generic choice of bistable nonlinearity.
Navier-Stokes flows in exterior domains. Recent postdoc G. van Baalen has worked with Prof. P. Wittwer from the University of Geneva on Navier-Stokes flows in 3D exterior domains. Prior studies of both authors showed how stationary Navier-Stokes equations in 2D and 3D exterior domains and time-periodic equations in 2D domains could be interpreted as a dynamical system where the ``downstream'' variable plays the role of time. The present work is the culmination of 10 years of research in this domain. In particular, while previous results were mainly concerned with downstream asymptotics, complete asymptotic description of 3D flows are now available in the whole exterior domain. These theoretical results are of great practical importance, as they can improve the ratio accuracy vs. CPU time by several order of magnitude in numerical simulations of such flows.
Critical wave speeds for pushed and pulled fronts. Recent CBD postdoc Nikola Popovic has carried out a comprehensive study of pushed and pulled fronts in reaction-diffusion equations with cut-offs. These fronts exist for semi-infinite intervals of wave speeds, just as is the case for the classical Fisher-Kolmogoroff fronts. However, the critical wave speed, which marks the finite boundary of the interval, scales as a fractional power of cutoff parameter and is determined by a global condition, as opposed to a local condition. Popovic's work with Kaper and F. Dumortier (U. Hasselt, Belgium) gives the first rigorous proof of the existence of these waves, and it identifies the geometric and dynamical reasons why the fractional powers arise in the critical wave speed. The main method used is geometric desingularization.
Canards in a reaction-diffusion equation. Recent CBD postdoc Popovic has published a paper with Kaper and P. DeMaesschalck (U. Hasselt, Belgium) proving the existence of canards in a reaction-diffusion equation. This is thought to be the first such example in a PDE. Moreover, they have shown how the exit time (or buffer point) can be either spatially homogeneous or spatially inhomogeneous. This work appears to be cracking open an entire new area for exploration.
Nonlinear stability of evolving fronts in a three-component system. Graduate trainee P. van Heijster (U. Amsterdam) visited Kaper at the CBD for two extended periods in AY 08-09 to carry out research on a three-component system of reaction-diffusion equations. This model consists of a FitzHugh-Nagumo system for an activator and an inhibitor which both diffuse, coupled linearly to a second inhibitor, which diffuses over a longer length scale than the first inhibitor. This coupling makes it possible to have many more interesting patterns. Van Heijster completed an article with A. Doelman, K. Promislow (Michigan State) and Kaper proving the nonlinear stability of evolving N-front solutions in this system. The positions and speeds of the fronts change by order one amounts over algebraically long time scales, and hence classical stability theory for traveling waves (which have constant profiles in co-moving frames) does not apply. The Evans function was decomposed into fast and slow components, and one of the novel features was that the slow component was substantially more complex mathematically due to the presence of the two inhibitor fields. Popovic used the renormalization group stability technique that Doelman, Promislow, and Kaper had developed earlier for the interacting pulses in the generalized Gierer-Meinhart and Gray-Scott models. Several technical improvements were needed to make this theory work for a three-component R-D system.
New normal forms for nonautonomous ODEs from RG theory. Graduate student Holzer is completing a paper that follows up on his 2008 renormalization group paper in Physica D. In it, he shows how to derive normal forms for certain classes of nonautonomous ODEs using the CGO renormalization group theory, including systems with slowly-varying linear parts, and other systems traditionally analyzed using WKB and other disparate perturbation methods.
Neuroscience
Olfaction
Analysis of optical imaging data from the rat olfactory bulb. Postdoc Remus Osan is working with Kopell and with M. Wachowiak (BU, Biology). The collaboration is developing new analysis tools for optical recording data from awake olfactory bulb; it uses these results as an input for data-driven modeling of the neural computations of this region of the brain. The work so far indicates that the dynamics of neural representations depend non-linearly on odor identity and concentration as well as on breathing rhythms of the rats. Osan analyzed data sets of odorant-evoked responses representing activity in receptor neuron populations converging onto olfactory bulb (OB) glomeruli during different sniffing behaviors exhibited by the awake rodent. Using these population responses as inputs for subspace projection methods (Principal Component Analysis and Multiple Discriminant Analysis), they found that the response patterns evoked by different odorants can typically be projected onto distinct regions (odorant-specific clusters) of a low-dimensional encoding subspace. Osan is applying some of the data analysis methods developed in Sen's lab on neural encoding of song birds to this new type of data (namely the optical imaging data from rat olfactory bulb).
Computational modeling of information processing in the olfactory bulb. Postdocs Sherwood, Osan and grad student Ryan Carey from the Wachowiak lab are working with Wachowiak, Sen and Kopell, using the results from dynamics of optically imaged activity patterns in the rat OB in conjunction with computational modeling to gain insight into the early processing of olfactory signals. The efforts are directed in three modular directions: (I) Osan is working on an integrate and fire network model of the mitral cell layer as the output of the olfactory bulb processing network, where synchronization of a subset of the mitral cells during specific phases of an underlying gamma rhythm constitutes a code for recognition of a specific odor. That uses data from optical imaging as input to the model. The results suggest that the neural codes used in this model are too sensitive to the variation in the real data; they are now investigating if increased robustness would emerge when using biophysical neural models for the mitral cell layer. (II) Sherwood is developing detailed biophysical and network models for the peri-glomeruli layer, which is situated in between the olfactory receptor neurons and mitral cell layers. He is trying to fit the results of his model to single neuron recordings from this brain area in order to obtain en emerging theta rhythm generated in this layer. (II) Carey is characterizing the single mitral neuron modulations induced by changes in breathing, with a focus on multiple scale properties (rising time, amplitude, decay time) of the receptor neurons. These efforts, focusing on different aspects of the olfactory bulb network, are intended to lead to a combined computational model whose predictions can be tested in the Wachowiak lab.
Rhythm switches in olfactory learning. Postdoc Jorge Brea is working with Kopell in collaboration with Dr. Leslie Kay (University of Chicago). They model the mechanisms by which different gamma and beta oscillation emerge in the rat olfactory bulb while performing different odor discrimination learning tasks. One of the central questions in this work is how the piriform cortex (PC) and the olfactory bulb (OB) interact in order to switch from a predominant gamma (~30-90 Hz) activity to a higher power gamma rhythm in the OB or a predominant beta (~12-30 Hz) activity in the OB and PC as the rat successfully learns the task. The model they are constructing looks at how plasticity between the OB and PC together with the existing delayed feedback from the PC to the OB can generate switching from gamma to larger gamma power or beta frequencies of the local field potential in the OB. They have shown how these transitions can arise using different strategies depending on whether the switching is from gamma to beta or from low to high power gamma. They have also shown how graded inhibition can provide a mechanism for synchronization of the fast gamma rhythm, making use of the mitral cell subhreshold oscillations.
Interactions of inhibitory cells in the olfactory bulb. Also working with the Kay lab and Kopell, grad student Baldur Hedinsson has been investigating dynamics of the inhibitory granule cells of the olfactory bulb. The model is motivated by evidence that the low frequency gamma rhythm, not associated with respiration, is eliminated in a mouse without inhibitory connections to the granule cells. The dynamics of this model displays antiphase solutions even in the case when two identical cells receive the same input, in contrast to other models of similar inhibitory neurons; the difference has been tracked down to the properties of the K+ channel. Analysis of the antiphase and synchronous orbits have shown both to be stable in a large parameter regime, and a variety of perturbations can change the firing from synchrony to antiphase and vice versa. The frequency at which the cells fire in antiphase is greater than synchronous firing.
Audition
LTP in the presence of multiple gamma rhythms. Program in Neuroscience grad student, Shane Lee has been working with Kopell and Sen on models of how spike-time-dependent plasticity is affected when there are independent gamma rhythms (30-80 Hz) associated with both the presynaptic and postsynaptic cells. The models are motivated by effects of learning in the primary auditory cortex, for which there is evidence of independent control of a cortical gamma in the superficial layers, and another gamma coming from either the thalamus or the input layer in the cortex from the thalamus. Current models show that there can be potentiation or depression, depending on the relationship of the frequencies of the interacting rhythms; the time course of the potentiation is dependent on the decay time of the NMDAR mediated current. This work has given rise to a new collaboration with Ed Boyden (MIT) to look for the thalamic gamma in rodent. In related work, Lee and Sen have used spectral analyses to start investigating the role of rhythms in the auditory processing of natural complex songs in the primary auditory region called Field L of the zebra finch.
Natural variations in auditory stimuli. In a natural setting, no two occurrences of a sound are exactly the same. The natural variations present in auditory stimuli must be dealt with for an auditory system to effectively recognize different target sounds. Graduate student Ross Maddox and postdoc Cyrus Billimoria have been working with Sen in characterizing the invariance of neural discrimination of conspecific songs with variations in timing, speed, location in space and in the presence of specific kinds of noise. Maddox has been working in conjunction with Josh McDermott from NYU in developing noise maskers that contain varying numbers of statistics present in a multiple-bird song chorus to investigate the role these statistics play in auditory object recognition. The model system is the avian primary auditory cortex analog known as Field L in the zebra finch.
Recognition of individual birdsongs. Graduate student Eric Larson and postdoc Cyrus Billimoria are working with Sen to develop biologically plausible model neural circuits that can recognize individual birdsongs. One discrimination model uses a network of integrate and fire model neurons to discriminate birdsongs, the results of which have been published in J Neurophys (Larson, Billimoria, Sen 2009: A Biologically Plausible Computational Model for Auditory Object Recognition). Preliminary results suggest that simple population codes can greatly improve accuracy of discrimination, and further work will be done to explore various methods of population coding, as well as other single-neuron classification and detection schemes.
Stimulus selectivity. Graduate student Ben Perrone has been working with Sen to investigate neural recordings in cM (caudal mesopallium), a downstream area of field L, and thus an area of interest for higher order stimulus selectivity. Specifically, Perrone has been investigating an effect of stimulus familiarity on spiking activity in the region, exploring a variety of recording techniques to optimize data yield in cM. Among these techniques are optimizing the design of the implants which allow for the recording of multiple chronic electrodes during awake, restrained recording sessions. In addition, Perrone has been using spectro-temporal receptive field (STRF) models to predict a neuron's ability to discriminate between natural stimuli.
Variation in natural songs. Postdoc Gilberto David Graña has published a paper (Graña, Billimoria, Sen 2009: Analyzing Variability in Neural Responses to Complex Natural Sounds in the Awake Songbird) summarizing the investigation of the stability of neural recordings in awake zebra finches in response to other zebra finch songs. Using three different metrics to investigate neural stability, it was observed that a majority of recording sites showed little variation in their neural output, and that all three metrics can be used to obtain a comprehensive understanding of the stability of neural recordings. Graña continues to work in training zebra finches to perform behavioral tasks. His goals are to train the zebra finches in a song generalization task. By varying the delay after which a bird is allowed to respond, he hopes to investigate how performance is affected by this delay.
Time-frequency representation. Tim Gardner and math grad student Genevieve Toutain are working on sparse time-frequency representation of bird song using methods that will reduce spectrally dense signals into sparse reassignments. After developing consensus of the nature of the signal across many songs, they will work on methods to re-synthesize the sounds. The methods will be useful for any system with spectrally dense signals, including EEG and MEG.
Taste
Characterization of the gustatory evoked cortical activity in rats. Working in collaboration with the Donald Katz group at Brandeis University, who provided the experimental data; postdoc Tort and Kopell have been analyzing local field potentials and spiking activity obtained from the gustatory cortex (GC) of rats after oral administration of tastants. The major findings include the presence of a gustatory evoked potential after taste delivery in GC followed by the emergence of prominent theta oscillations. Together, they observed increase of theta coherence within and between GCs (left and right), theta reset, changes in the theta peak frequency with time, and higher spike field coherence occurring following taste delivery. A manuscript reporting these findings is in the final stage of preparation.
Interaction of Rhythms
Rhythm switching in an in vitro model of somatosensory cortex. Miles Whittington, (Newcastle University), Roger Traub (SUNY Downstate), Nancy Kopell, and postdoc Mark Kramer continued developing mathematical models of rhythm generation through period concatenation, as observed in rat somatosensory cortex. Through a combination of experimental recordings and biophysical modeling, the research group has illuminated novel mechanisms of rhythm generation. The work has resulted in two conference presentations, and three manuscripts published in peer-reviewed journals.
Theta and gamma rhythms in hippocampal networks. Grad student Paola Malerba has been working with Kopell on developing a detailed understanding of the dynamic features of the theta-gamma rhythms that arise in the research of Gloveli et al. and Tort et al. After focusing on a two-cell network involving one O-LM cell and one fast spiking interneuron, which are mutually inhibitory, they are now addressing the role of the excitation provided by the pyramidal cells that is also known to be important. They have found that the level of excitation distinguishes two parameter regimes in which the interaction of the rhythms are regulated in distinct ways. Biological evidence has linked these regimes to properties of hippocampal plasticity. Current work focuses on bigger networks with modules in different excitation regimes.
Uncoupling of theta-gamma oscillations in interneuron selective GABA-A KO mice. Working in collaboration with the group of Hannah Monyer at University of Heidelberg, postdoc Tort and Kopell have constructed a biophysical network model of the hippocampus to better understand the uncoupling of theta-gamma oscillations seen experimentally in the knockout (KO) mice for the GABA-A receptor specifically in PV+ interneurons. Their work has suggested that intrahippocampal mechanisms involving connections among distinct interneurons subtypes may be responsible for the theta-gamma coupling seen in vivo and in vitro, and provided an explanation for the theta-gamma uncoupling observed in the KO mice. A paper reporting both the experimental findings and the simulation results has been recently published.
Theta-gamma coupling and associative memory in rats. Working in collaboration with Howard Eichenbaum lab at Boston University, postdoc Tort, supervised by Kopell, has been analyzing local field potentials recorded at the CA3 and CA1 regions of the rat hippocampus while animals were subjected to a conditional discrimination task in which animals have to learn to associate items to context. The analysis has focused in cross-frequency coupling (CFC) effects and the results have shown that CA3 and CA1 possess different theta-gamma CFC characteristics. In the CA1, theta modulates preferentially the high gamma subband, and this modulation was not related to learning. In the CA3, theta couple preferentially with low gamma and the strength of this coupling increases during learning sessions in a way positively correlated with the animals' performance on the task. Moreover, rats performing overtraining sessions were observed to present high levels of CA3 theta-gamma coupling since the first trials in the session. These results therefore suggest a role for hippocampal theta-gamma coupling in learning and memory. A manuscript reporting these findings has been written and is currently under review.
Pathological Rhythms
Pathological rhythms in Parkinson's disease. With Kopell, E.Boyden (MIT) and Xue Han (MIT), postdoc Michelle McCarthy has been investigating the origin of the pathological beta rhythm (23-30 Hz) associated with inability of PD patients to move fluently. McCarthy has created a computational model of the striatum that consisted of either the GABAergic medium spiny neurons (MSNs) or the MSNs and another class of GABAergic neurons known as low-threshold spiking interneurons (LTS cells). An interaction of inhibitory currents with the M-current in those cells helps to generate larger powers of the beta rhythm. The PD is modeled as a secondary effect of the loss of dopamine on the level of cholinergic modulation. The prediction that changes in cholinergic modulation change the striatal rhythm is now being tested by Xue Han. Modeling is also being used to understand how excitatory inputs from the cortex will affect the striatal dynamics in normals and PD patients, as well as the effects of striatal output on the rest of the basal ganglia components.
Rebound spiking and the dynamics of the M-current/inhibition interaction. In both the above work on beta oscillations in PD and in previous work of McCarthy and Kopell on beta oscillations due to low doses of propofol, the beta rhythm is produced by an interaction of GABA-A mediated inhibition with an M-current in some class of inhibitory cells. A central question is why that creates the observed rhythms. Computational work suggests this is arising as a population effect from an antiphase interaction of cells that normally spike at a much lower frequency, and that this interaction depends on rbound spiking. Other current work of McCarthy and Kopell includes a mathematical analysis of the conditions under which this rebound spiking occurs, and why either low does of propofol or cholinergic modulation can provoke this. The work uses dynamical systems techniques including reduction of dimension and bifurcation theory.
Characterizing Emergent Network Topology at Seizure Onset in Humans. Mark Kramer, in joint work with epileptologists Dr. Heidi Kirsch (UCSF) and Dr. Sydney Cash (MGH) and statisticians Eric Kolaczyk (BU) and Uri Eden (BU), has continued developing network analysis techniques to characterize cortical-level changes in the brain at the onset of epileptic seizures in humans. Network analysis of the brain's voltage data reveals a marked decrease in functional cortical connectivity, as well as an accompanying formation of apparent `communication hubs'. Kramer recently received a Burroughs Wellcome Fund Career Award at the Scientific Interface to support this interdisciplinary research.
The Role of an Axonal Plexus in Sleep and Epilepsy. Postdoc Erin Munro is working with Nancy Kopell to study the possible role of an axonal plexus (a network of axons connected by gap junctions) in slow-wave sleep, epileptogenesis and seizure initiation. Patients with temporal lobe epilepsy almost always have a brain lesion. After an induced brain lesion, animals undergo epileptogenesis - a period with heightened very fast oscillations (VFOs) while the seizure threshold slowly diminishes. Once epilepsy has developed, seizures are more likely to occur during sleep. Seizure initiation is also associated with higher amplitude VFOs.
Axons respond to lesions by sprouting many extra branches, which may drastically change the axonal plexus and its properties. In her doctoral work, Munro studied how an axonal plexus can produce VFOs. For this project, Munro is developing a realistic model of a normal neocortical axonal plexus and one next to a lesion involving axonal sprouting. These models can then be appended to a model of slow-wave sleep to study how the abnormal plexus affects slow-wave sleep and possible mechanisms for epileptogenesis and seizure initiation. Munro is also working with Lenore Cowen (Tufts University) on the graph theoretical aspects of modeling an axonal plexus in the neocortex and hippocampus.
Imaging epileptiform activity. Graduate student Kyle Lillis is using a recently developed laser-scanning strategy, Targeted Path Scanning (TPS), in conjunction with two-photon excitation of bath-applied, calcium-sensitive dye, Indo-1 AM, to image epileptiform activity in slices of hippocampal formation from GAD67-GFP (GIN) mice. In this way, he is simultaneously recording activity in populations of GABAergic interneurons (I-cells) and putative excitatory neurons (E-cells).
Network analysis of seizure-like events. Grad student Kyle Lillis is collaborating with postdoc Mark Kramer to develop cross-correlation-based network analysis techniques, used to distill intelligible information about network dynamics from the high-dimensional datasets generated by TPS. Time-windowed correlations are computed between calcium signals recorded from each pair of cells during seizure-like event (SLE). Each cell is represented as a node on a graph, and edges are drawn between sufficiently coupled pairs of nodes (i.e., strongly correlated pairs of cells). Three measures of network connectivity are calculated for each node: in-degree, the sum of correlations for which other cells lead the node (as determined by peak correlation); out-degree, the sum of correlations for which the node leads other cells; and a measure they term direction-degree, the difference between in-degree and out-degree. These measures are calculated in 1s windows at 100ms intervals over the course of 4min recordings. Sharp negative deflection in I-cell direction degree are observed at SLE onset, indicating that I-cells fire before E-cells at SLE onset. These data support a hypothesis that, in 4-AP-induced SLEs, I-cells fire hard enough to become depolarizing and alleviate the NMDA receptor Mg2+ blockade. Indeed, in zero-Mg2+-induced SLEs, no such I-E ordering exists.
Mechanism of transition from Normal to Hyperexcitable firing in entorhinal stellate cells. Studies in animal models of epilepsy have shown comparable levels of recurrent excitation among stellate cells (SCs) of the medial entorhinal cortex (mEC) and reduced levels of recurrent inhibition in epileptic networks as compared to control ones. Grad student Tilman Kispersky, with White and former postdoc Horacio Rotstein, have shown that the ability to generate epileptic-like hyperexcitable firing is intrinsic to recurrently coupled networks of SCs with inhibition playing a regulatory role in the transition from the normal to the epileptic state. Using biophysical (conductance-based) model networks including SCs and interneurons they found that the transition from normal to hyperexcitable firing is rapid and threshold like. These results persist in the absence of inhibition and for single, self-coupled SCs. They compared their theoretical results with in vitro SCs self-coupled with dynamic clamp. They found that the transition to hyperexcitable firing occurs at a threshold level of self excitation and that high frequency firing is burst-like with a duration modulated by the M-current. Using phase space analysis on a reduced version of the SC model they found that the transition between firing regimes is dependent on the decay kinetics of fast AMPAergic excitation, the h-current and the persistent sodium current. Overall, this paper supports the hypothesis that SCs have intrinsic and dynamic properties that endow them with the ability to display spiking activity in both the normal and hyperexcitable firing regime. In addition, they provide a mechanistic explanation for how such behavior might occur.
Mechanisms of anesthesia. Postdoc ShiNung Ching is working with Kopell and E. Brown (MIT) on the dynamical mechanisms underlying the workings of the anesthetic drug propofol, building on the previous work of postdoc Michelle McCarthy, Kopell and Brown. Work in Brown's lab has recently showed that doses of propofol adequate to induce loss of consciousness produces a rhythm close in frequency to the classical alpha (9-11 Hz) rhythm associated with closing of eyes, but distinct from the latter. Coherence studies of this rhythm suggests that the thalamus might be involved. Ching and collaborators are investigating thalamocortical models to understand the origin of this new propofol-induced rhythm.
Other neuroscience projects
Modeling transient amnesia, memory reconsolidation and extinction through Hopfield networks. Continuing their previous collaboration, postdocs Osan and Tort, with Dr. Amaral at UFRGS, have been adapting and applying Hopfield networks to gain further insights into some phenomena of memory impairments as well as normal learning. Experimental data suggest that contextual re-exposure can lead to either reconsolidation or extinction of learned memories, as amnestic drugs injected after reexposure can have opposite effects depending on behavioral parameters. Hypothesizing that reconsolidation represents updating of an existing attractor in a neural network, while extinction represents formation of a new attractor; they have built a network model in which one can observe retrieval, reconsolidation or extinction of a stored attractor upon presentation of a cue, depending on the similarity between the cue and the original memory. Such a model accounts for experimental data showing the effect of re-exposure duration in driving retrieval, reconsolidation or extinction, as well as for the effects of protein synthesis inhibitors in these three conditions. It also predicts that mismatch between an animal's perceived context and a stored memory is necessary for reconsolidation to occur, and that only attractors which are retrieved can be reconsolidated.
Parameter Optimization. As part of the development of the model for olfactory bulb, Sherwood has encountered issues involving appropriate parameter selection for the external tufted ET cell model; he has been exploring techniques for automated parameter search and parameter optimization for single and multiple compartment models of bursting neurons. This is joint work with Joe Tien (McMaster/OSU), who has extensive experience with smooth parameter optimization techniques for neuronal models.
New dynamics in neural systems. Mark Kramer, Postdoc John Burke, and grad students Anna Barry and Nick Benes have been working Kaper on the phenomena of torus canards in fast-slow systems. The standard canard phenomenon involves a family of stable orbits that track the unstable manifold of a fixed point of the fast subsystem for a surprisingly long time. Similarly, torus canards track the center-unstable manifold of a limit cycle of the fast subsystem. These were originally observed by Kramer, Traub, and Kopell (Phys. Rev. Lett. 101, 068103 (2008)) in a reduced five dimensional model of Purkinje cells. The current research effort is composed of two parts. The first is to investigate the biological significance of this behavior, which occurs at the transition from tonic spiking to bursting. The second part is focused on lower dimensional models, in an effort to study this phenomena in the simplest possible setting. They are exploring several models, including reduced versions of the original Purkinje cell model as well as more abstract (i.e., less biophysical) models. The goal is to identify and explain the aspects of torus canards which are distinct from standard canard behavior.
Dynamics of Oriens-Lacunosum Moleculare Interneurons. O-LM cells of the hippocampus have been implicated as theta frequency activity generators in hippocampal regions CA1 and CA3 in both models and experiments. However, precise measurements of the oscillatory properties of these cells have not been done. One hypothesis is that the O-LM cells do not form a pacemaker, but act instead as a resonator. Working with Kopell and White, grad student Kispersky did dynamic clamp experiments and modeling. He injected high frequency trains of excitatory and inhibitory synaptic inputs into O-LM cells in vitro, effectively mimicking the 'high-conductance' state experienced by cells in vivo. He modulated these input trains sinusoidally to mimic a rhythmic network state known to occur during network theta. Kispersky and collaborators plan to measure the response of O-LM cells to this input and what properties of the input train elicit theta resonance.
Gene Network Dynamics
Synthetic Biology
Synthetic gene networks that count. Synthetic gene networks can be constructed to emulate digital circuits and devices, giving one the ability to program and design cells with some of the principles of modern computing. A counter is one such device that would enable a new type of memory and allow for complex synthetic programming and novel behaviors. Grad student Ari Friedland, working with postdoc Xiao Wang, undergrad David Shi, and Jim Collins, report a synthetic genetic counter in E. coli that counts up to three identical induction events, expressing a unique protein species to signify each number. The counter is comprised of a transcriptional cascade in which transcription is de-coupled from translation by riboregulators, forming AND-gates. The modularity of this device permits counting of varied user-defined inputs and its open-ended architecture provides a potent biotechnology platform for counting higher numbers, which is supported by mathematical modeling.
Synthetic signaling pathways. Grad student Ellen O'Shaughnessy, in collaboration with Collins, Santhosh Palani and Casim Sarkar at the University of Pennsylvania, is working to explore the effects of topological variation on mitogen-activated protein kinase (MAPK) cascades. These essential signaling modules control a broad array of biological processes including growth, differentiation, stress response and apoptosis and are capable of producing a diverse set of system responses. The dynamics of MAPK activation is critical in determining cell-fate and therefore they aim to understand the biological mechanisms underlying different system responses. Using a combination of experimental and modeling methods they have built a basic, exogenous, MAPK cascade and applied perturbations such as scaffolding, concentration variation and negative regulation. Construction of these topological variants has enabled them to tune the threshold, set-point and ultrasensitivity of the MAPK system response over a biologically relevant range. Further, they have combined perturbations to successfully decouple the threshold and ultrasensitivity from the set-point achieved by the cascade. They are currently preparing a manuscript for submission to Nature Cell Biology.
Diversity-based, model-guided construction of synthetic gene networks with predicted functions. Postdocs Xiao Wang and Tom Ellis, with Jim Collins are combining molecular biology with mathematical modeling to construct novel synthetic gene regulatory networks in Xiao Wang yeast. This work has produced a library of synthetic gene networks acting as timers. Mathematical modeling guided the construction and successfully redict the network behaviors. This work has been published in May issue of Nature Biotechnology. Xiao also worked with Ari Friedland to use mathematical modeling help construct the first cellular counter. This work has been accepted by Science and will be published in May 2009.
Systems Biology
Increasing Antibiotic Efficacy Through Systems Biology Approaches. Antibiotics can be broadly categorized into two classes based on their phenotypic effects on bacterial cells. Bactericidal antibiotics result in bacterial cell death, while bacteriostatic antibiotics merely inhibit cellular growth. Using a combination of metabolic modeling and experimental approaches, grad student Jonathan Winkler is working with Jim Collins and postdoc Mark Brynildsen to trigger bactericidal activity from bacteriostatic drugs. In the process, they are identifying metabolic and transcriptional pathways that could lead to increased efficacy for all antibiotics.
Study of Bactericidal Mechanisms of Aminoglycoside Antibiotics and Transition Metal (Silver) Cocktails in Stationary and Exponentially Growing E. coli. The need for novel antibiotics and antimicrobial materials is a result of current concern among modern society regarding the development of multidrug resistance in various strains of bacteria. The development and synthesis of metallo-pharmaceutical drugs has played a significant role in therapeutic medicine, and in specific, the use of FDA approved silver compounds as antimicrobial agents. Postdoc Ruben Morones with Collins has found that antibiotic cocktails containing transition metals (silver) and aminoglycosides have a synergistic bactericidal effect on E. coli in both stationery and exponential growth phases. Therefore, through a systems biology approach, they are currently studying the bactericidal mechanism of the silver compounds and the mechanism of synergism with aminoglycosides. Through the understanding of novel bactericidal mechanisms of action there are potential applications in the development of potent and optimized antibiotic cocktails, as well as development of new drugs.
Sugar-Mediated Eradication of Persistent Bacteria by Aminoglycoside Antibiotics. Grad student Kyle Allison working with Postdoc Mark Brynildsen and Collins to develop methods to eradicate bacterial persisters. Antibiotic failure can result from multiple causes including genetic mutation, the spread of resistance-carrying plasmids, and bacterial persistence. Persistence is a phenomenon in which a subpopulation of bacterial cells (persisters) is tolerant to antibiotics while the overall population, which is genetically identical, is susceptible. Persisters are dormant bacteria formed on the transition between exponential growth and stationary phase and are believed to be responsible for recurrent infection. Though genes that play a role in persistence have been identified, the mechanism of persister formation remains to be elucidated and there is currently no approach for eradication. Here they report the rapid elimination of persistent E. coli through a sugar-mediated stimulation of aminoglycoside uptake. This phenomenon occurs by induction of cell elongation, which they show is necessary for uptake of aminoglycosides in both exponential and stationary phase cells. They further show that a similar mechanism of sugar-induced aminoglycoside uptake and subsequent elimination of persistent bacteria exists in the gram-positive pathogen S. aurues. This mechanism is specific for aminoglycosides and does not imply the awakening of persistent bacteria as the addition of mannitol does not potentiate killing by the quinolones or beta-lactams. This work provides insight into the long-studied but enigmatic bacterial uptake of aminoglycosides and may direct future therapeutic approaches to treating persistent infection.
Network biology approach to bacterial persisters. Persistence is a phenotypically induced state of cellular senescence, which allows a sub-population of genetically identical cells (persisters) to survive diverse environmental stresses, such as nutrient limitation, heat shock or antibiotic treatment. Persisters are thought to be formed through a stochastic, epigenetic mechanism which results in the observed population heterogeneity. Grad students Mike Koeris, Mike Kohanski and Kyle Allison, postdoc Diogo Camacho, and Collins focused on determining the underlying mechanisms - stochastic and deterministic - that are responsible for the formation of persistent cells during the transition from exponential to stationary phase, using a network biology approach to guide their experimental approach. These analyses revealed possible roles played by quorum sensing and shifts in polyamine metabolism.
Antibiotic-mediated reactive oxygen species formation leads to heteroresistance and multidrug cross-resistance. Antibiotic resistance continues to be a growing problem, leading to a reduction in effective therapeutic options. Efforts to combat drug resistance have been confounded by heteroresistance, that is, different levels of resistance to specific antibiotics within clinical isolates, as well as multidrug cross-resistance. Recently, oxidative stress has been implicated as one of the mechanisms whereby bactericidal antibiotics kill bacteria. Grad student Mike Kohanski with Collins has shown that sub-lethal levels of bactericidal antibiotics can induce mutagenesis via oxidative DNA damage, leading to heteroresistance and multidrug cross-resistance. They demonstrated that antibiotic-induced increases in mutation rate are directly related to the formation of reactive oxygen species. They also showed that treatment with low levels of bactericidal antibiotics, which induce oxidative stress and allow for the accumulation of mutations, can result in heterogeneous increases in the minimum inhibitory concentration (MIC) for a range of antibiotics. These effects lead to mutant strains that are sensitive to the applied antibiotic but resistant to other classes of antibiotics. This work establishes a molecular mechanism whereby sub-lethal levels of antibiotics can lead to the emergence of both heteroresistance and multidrug cross-resistance, which has important implications for the widespread use and misuse of antibiotics.
Bactericidal Antibiotics Induce Nitric Oxide Production and Signaling in Escherichia coli. The initial drug targets of antibiotics are known, as are some of the lethal consequences of these reactions. However there is still much to be discovered about the response pathways antibiotics invoke in bacteria, and how these responses contribute to cell death. Nitric oxide is a ubiquitous signaling molecule in both eukaryotic and prokaryotic organisms, and a key part of host defense responses against invading pathogens. In E. coli, nitric oxide is generated as a byproduct of reactions catalyzed by anaerobic respiratory enzymes. Grad student Carrie Lawrence, with postdoc Dan Dwyer, grad student Mike Kohanski and Collins, took a systems approach to investigate nitric oxide production and signaling in aerobically growing E. coli treated with bactericidal antibiotics. They results indicate that antibiotic-induced nitric oxide has a dual role in the bacterial response to antibiotics - intracellularly produced nitric oxide acts in a cytotoxic manner by disrupting the normal function of target proteins, while diffused nitric oxide acts in a cytoprotective manner by signaling to nearby cells and inducing protective responses.
Identification and functional characterization of small RNA regulatory networks in E. coli. Small, non-coding RNA molecules regulate a vast array of processes, from transcription to translation, in all kingdoms of life. In the bacterium Escherichia coli, small RNAs have been extensively studied and several approaches have been used for their identification and characterization. However, these methods have mostly relied on sequence homology with other bacterial organisms, leading to a number of challenges and difficulties. Postdoc Diogo Camacho, grad students Sheetal Modi, Mike Kohanski and Collins introduced a network approach for identifying small RNA targets, using a compendium of gene expression arrays. With this approach, they identified and validated a large number of novel targets, as well as correctly identify known targets for several small RNA molecules. By studying the effect of small RNAs on their targets, they also characterized and validated the functional role of these molecules in the cell.
Machine-learning algorithms for systems biology. Postdoc Mike Molla, with Professors Simon Kasif and Collins, makes use of machine learning and other computational methods to perform central tasks in high-throughput biology. These tasks include gene-chip design, detection of genomic variation, and the interpretation of gene-expression patterns. Recently, they have used machine-learning algorithms to build models of gene-target potentiation of antibiotic sensitivity based on the results of knockout screening. Molla has also helped to complete a first-of-a-kind survey of repeat-length polymorphisms (RLPs) in human genomes. Currently, he is developing an improved version of the gene network finder CLR that can make use of diverse data sources — not just gene-chip expression — to build gene-network models. He is also helping to use gene chips, sequencing and computational methods to chart the mutational path to antibiotic resistance in E. coli.
Network biology approach to T cell regulation. Grad student Ayla Ergun with Collins is studying regulatory T cells (Treg cells), which are key mediators of immune tolerance to both self and non-self antigens. These cells have wide ranging immunosuppressive abilities and it is hoped that they can be used to curb autoimmune diseases and prevent rejection of transplanted organs. It has often been stated that Foxp3 acts as a master regulator for Treg cells. However, recent studies have suggested that Foxp3 might not have such a central role in the Treg cell lineage. Ergun and collaborators use a network approach in order to elucidate the different components of the Treg signature and identify a set of regulators which influence the Treg signature genes.
Prediction of Protein Function. Former postdoc David Gold has worked with Kolaczyk and with Simon Kasif (Bioinformatics), and grad student Xiaoyu Jiang, on the prediction of protein function using integrated sources of information and Bayesian statistical tools. They have published one paper and have a second under invited revision.
Drug target prediction. Grad students Shu Yang, Elissa Cosgrove, and Lisa Christadore are working with Kolaczyk and Schaus (Chemistry) to develop a statistical framework for drug target prediction from inferred gene regulatory networks, based on microarray measurements. The new framework uses sparse statistical inference methods (namely Lasso regression) to infer network structure, and implements outlier detection tests to rank candidate genes potentially affected by external influences (e.g. drug compounds or genetic mutation or dysregulation in cancer or disease). Yang has developed mathematical justification for the method; Cosgrove has explored methodological issues relating to relative information gain in experiments; and Christadore is pursuing the question of the effect of experimental conditions on model training and prediction.
Fundamental properties and biological applications of a multi-phenotype genetic interaction map. The work of graduate student Evan Snitkin (Bioinformatics Program), in the group of Daniel Segrè, has been focused on performing genome-scale simulations of the effects of single and double gene deletions of metabolic enzyme genes in the yeast S. cerevisiae. The goal of the project is to study how the cell responds to genetic perturbations, and how perturbations combine with each other to affect phenotype. In addition to demonstrating the validity of model predictions, through a large-scale comparison with experimental data (work published recently in Genome Biology), Evan employed this approach to compute a comprehensive network of epistatic interactions between any two gene deletions relative to all metabolic flux phenotypes in the model. This work has yielded insight into the nonlinearities of the network's response to perturbations, relevant for the study of metabolic diseases and drug effects (manuscript submitted). Evan received his Ph.D. in April 2009.
Inference and integration of regulatory dynamics in metabolic network models. Understanding the principles that underlie metabolic regulation, and identifying approachable computational strategies for integrated modeling of metabolic and regulatory networks constitute an important open challenge. Some new approaches to this challenge are being pursued in the lab of Daniel Segrè by three graduate students. Hsuan-Chao Chiu (Ph.D. candidate, Bioinformatics Program) has developed a data-driven method based on linear optimization to infer time- or condition-dependent metabolic objectives, in the form of dynamically changing biomass compositions (results published in the journal Genome Informatics). William Riehl (Ph.D. candidate, Bioinformatics Program) and Eduard Reznik (Ph.D. candidate, Biomedical Engineering) have been developing a new mathematical method for predicting the regulatory network that controls a metabolic pathway, based on optimality criteria similar to the ones used in Flux Balance Analysis. Preliminary results from this work have been published in a Genome Informatics paper. A poster by Hsuan-Chao Chiu and Bill Riehl has been recently awarded a prize and selected for an oral presentation at a meeting organized by the Department of Energy.
Combinatorial genetic and nutrient modifications for metabolic engineering applications. Metabolic engineering of microbes is increasingly used for the production of renewable chemicals and energy sources. The research of David Byrne (Ph.D. candidate, Bioinformatics Program) in the group of Daniel Segrè, and in collaboration with the group of Jim Collins, has been focused on understanding how metabolic pathways may be modulated to increase the production of bioenergy or other useful natural products. Multiple engineering objectives are considered: maximization of productivity, yield, and/or purity, minimization of economic cost, and combinations thereof. Associated trade-offs and pareto-optimal sets are determined for different formulations. Optimal predictions indicate that significant improvements in Escherichia coli lactic acid synthesis and Shewanella oneidensis reducing power and biohydrogen generation are attainable. David's poster on this topic has been chosen for an award, and selected for an oral presentation at a recent meeting organized by the Department of Energy.
Mathematical models of microbes within complex microbial ecosystems. Communities of microorganisms are found nearly ubiquitously and play important roles in human health, the environment and industry. Niels Klitgord (Ph.D. candidate, Bioinformatics Program) in the group of Daniel Segrè is developing and applying mathematical models to simulate the growth of different microbial species in a community, to predict the metabolic interactions that occur between them, and to predict environments that will lead to stable community structures. Varun Mazumdar (Ph.D. candidate, Bioinformatics Program) jointly advised by Daniel Segrè and Salomon Amar (BU School of Dental Medicine) has developed a mathematical model for the oral pathogen Porphyromonas gingivalis. The model is an important step towards understanding the role of microbial metabolism in human diseases. This work has been published in the Journal of Bacteriology, and featured on the issue cover. Further work to study the interaction of P. gingivalis with other oral bacteria is currently being performed by Lina Faller, a Ph.D. candidate in the Bioinformatics Program who recently joined the Segrè lab.
Revealing the metabolic and regulatory strategies of an environmental microbe. The bacterium Shewanella oneidensis possesses unique respiratory and metal-reducing abilities that pose intriguing evolutionary questions, and provide the opportunity for useful bioremediation and bioenergy applications. The experimental research activity of Qasim Beg, postdoctoral fellow in the group of Daniel Segrè, is aimed at gaining insights into the global regulatory process during different phases of Shewanella growth. mRNA levels at different time points were measured using Affymetrix microarray. The mathematical analysis of the data collected is being performed by Mattia Zampieri, a graduate student from Italy (SISSA, Trieste), who spent a semester in the Segrè lab.
Mathematical modeling of M. tuberculosis. Grad student Chris Garay is working with James Galagan on incorporating gene expression information into genome-scale metabolic models of Mycobacterium tuberculosis. The goal of this work is to use high-throughput measurement of gene expression and flux balance analysis models to develop a better understanding of how changes in M. tb metabolism, and changes in mycolic acid synthesis in particular, contribute to the virulence of the organism during infection.
Engineering a transcriptional regulatory network for biofuel production. One of the promises of biofuel projects is the ability to use existing biological systems to produce massive quantities of a desired biofuel, through some synthetic biology techniques. The integration of multiple genetic circuits into a single microorganism which is well characterized (most commonly yeast or a bacterium) is seen as the ideal approach, though it may come at the expense of a non-optimal organism and, therefore, non-ideal production of the biofuel. Grad student Alex Fichtenholtz, postdoc Diogo Camacho and Collins developed a system biology approach to devise a comprehensive transcriptional and metabolic model of the bacterium Escherichia coli. Using parameter estimation, they pursued the set of optimal changes that should be made at the transcriptional level that would have the biggest impact in the metabolic outcome, measured as production of ethanol by the bacterium. The set of transcriptional changes effectively means altering the strength and, ultimately, the direction in which a transcription factor regulates its targets, in order to obtain an optimal production of the desired product with minimal impact in the cell's biology.
Other Statistical and Dynamical Systems Projects
Dyson-Schwinger equations in Quantum Field Theories. Postdoc G. van Baalen and graduate student D. Uminsky have worked together with Prof. D. Kreimer and Graduate Student K. Yeats on various questions in Quantum Field Theories, more precisely on QED and QCD. Former work of Kreimer and Yeats show how to reduce these theories to the study of one ordinary differential equation (the Dyson-Schwinger equation) for an anomalous dimension, and a set of functions related to successive derivatives of the anomalous dimension (the Dyson-Schwinger recursion). In this work, dynamical systems ideas are used to study the anomalous dimension's equation. In particular, the existence of ``physical'' solutions is shown, together with their asymptotic properties in the strong or weak coupling limits. Criteria for the existence/non-existence of so-called Landau Poles in the theory are also given. They establish that the theory must have asymptotic freedom beyond perturbation theory and also investigate the low energy regime and the possibility for a mass gap in the asymptotically free theory.
Mathematical modeling of efficacy rates of an HPV vaccine. The HPV infection caused by the Human papillomavirus is responsible for 70 percent of cervical cancer in the United States. Recently, a vaccine, Gardasil, was approved for use to defend against the HPV infection and consequently cervical cancer. To date, models addressing the efficacy of the vaccine have assumed full immunity provided by the vaccine after one injection. However, Gardasil is administered in three doses over a six-month period. A Markov model is used to determine the affects of the three dose structure on overall instances of HPV and cervical cancer in the United States, specifically how it affects the variance of HPV cases as transmission rates vary across injection states. HPV cases are found to decrease substantially and cervical cancer is expected to be eliminated with any vaccine, but curtailed less in a three dose structure. Furthermore, how many women are vaccinated initially and the percentage of those who complete the series, is found to have a greater affect of the HPV outcomes than expected. This is joint work of Uminsky with Angela Gallegos.
Infinite logconcavity of the binomial coefficients. Uminsky and Karen Yeats recently made significant progress on a conjecture by Victor Moll regarding the infinite logconcavity of the binomial coefficients. They were able to show, for the first time, the existence of a large set of infinitely logconcave symmetric sequences, using a technical hyperplane argument to establish the result. Most recently, Peter McNamara and Bruce Sagan have re-proved that result using a stronger condition of logconcavity, which results in a much simpler proof. Uminsky and Yeats plan to use this new approach to prove Moll's original conjecture that the binomial coefficients are infinitely logconcave.
Invariant manifold theory and the long time behavior of chemotaxis. In collaboration with Nick Benes, Anna Barry, and C. Eugene Wayne, Uminsky considered the Cauchy problem for the parabolic Keller-Segel model (KS) for chemotaxis. For the regime of initial data which produce bounded solutions, they are applying invariant manifold theory to KS to improve existing asymptotics and to better understand the dynamics of solutions.
Asymptotic Methods. Holzer, Kaper, RE Deville, A Harkin and K Josic have worked on renormalization group methods for differential equations. RG methods have been proposed as a unifying asymptotic method generalizing other asymptotic methods such as matched asymptotic, multiple scales and averaging. They have shown that for a large class of systems, the RG method is equivalent to normal form theory. Among the advantages of the RG method is that it naturally derives the appropriate gauge functions required for the asymptotic approximation. They have studied this property in the context of logarithmic switchback and blow up methods, where terms involving the logarithm of the small parameter arise unexpectedly.
Work in Dr. Shinn-Cunningham's laboratory focuses on exploring how the brain processes the acoustic information reaching the ears. Both behavioral experiments and computational models are employed to elucidate how acoustic features in sound are extracted and processed by the human listener. Current projects include studies of directional and distance perception, the effects of echoes and reverberation on auditory perception, the influence of spatial cues and other source attributes on acoustic source segregation, auditory and cross-modal attention, and short-term plasticity and perceptual learning in spatial hearing.
Barbone lab: Subsystem Representation in Dynamics Simulations. Paul Barbone uses tools from applied mathematics to study forward and inverse problems in (bio)mechanics, (bio)acoustics, medical imaging, and other areas. He has studied and made contributions in the areas of structural acoustics; waves in elastic media, piezoelectric media, layered media, periodic media, and in media with microstructure; vibration of infinitely complicated structures, hybrid asymptotic/numerical methods, optimal finite element methods, algebraic eigenvalue problems, nonlinear acoustic propagation, multiphase (bubbly) flow and ultrasound imaging.
Belta Lab: Role of Obesity in Infection, with S. Amar. Their main objective in this project is to identify genetic differences between obese and lean organisms that are involved in the response to infection. In particular, they focus on mouse cell lines and infection with P.gingivalis. Their ultimate goal is to identify genetic modifications bringing the response to infection in obese cells close to the response of lean cells. Students from Belta lab involved in this project: Guilhem Richard(Bioinformatics) and Niraj Trivedi (Bioinformatics)
Hierarchical Abstractions for Planning and Control of Robotic Swarms. In this project, they develop theoretical and computational tools to describe, control, and analyze large collection of identical agents (swarms). They bring together tools from geometric control and formal verification to develop swarm abstractions at different levels. Students from Belta lab involved in this project: Boyan Yordanov (Biomedical Engineering)
Gardener lab (Bio). Signal processing: Continuous edges, or contours, are powerful features for object recognition, both in neural and machine vision. Similarly, most auditory signals include continuous edges in the time-frequency plane, suggesting that a contour representation of sound could be relevant for auditory signal processing. However, the mathematical foundations of a general contour representation of sound have not been established. Sinusoidal representations of voiced speech and music have been explored, but these approaches do not capture broadband signals.
In the last year, they have constructed a contour representation of sound that is generally applicable to any time series. This representation is perfectly invertible - by simply adding together the amplitudes of the contours, the original signal is resynthesized. Polynomial fits to the contours lead to signal compression — with speech compression meeting or surpassing current technologies. They are currently applying this method to produce probability densities for the structure of songbird vocalizations, and essential part of their experimental work. This work was done with Yoonseob Lim, a student in CNS department, coadvised by Tim Gardner and Barbara Shin-Cunningham.
Neuroscience: Since Joining BU in January 2009, they have assembled an experimental laboratory for the study of vocal learning in songbirds. The lab's focus is on developing new tools for quantification of vocal behavior, application of selective perturbations to song control system, and chronic neural recordings in singing birds. The questions they are addressing can be described in more detail as follows: How do songbirds memorize the songs of other birds, and how do these memories influence their own vocal learning? Many songbirds sing fairly normally when reared in isolation, but in the right circumstances, they may also imitate external models. Song learning is therefore the result of a self-organized innate program that provides a basic outline for song, and an auditory-memory based learning that builds on the innate program. The laboratory is currently investigating the process that builds and maintains the core sequence of the song behavior.
What mechanisms underly the self-organization of song and what are the geometric properties of the resulting circuit? Song behavior is reminiscent of a dynamical system that hops among well defined basins of attraction. They are interested in understanding the mechanisms of this switching behavior. In this pursuit they ask what homeostatic mechanisms maintain the circuit dynamics, and what may be the role of spontaneous neural activity in sleep, in the process of tuning these attractor states. A postdoc joining the laborotory, Bob Agate, will be dedicated to developing optical genetic perturbation (Chr2, and Halorhodopsin) in songbirds, which will allow them to address some of these questions in a refined manner.
Bradham lab: Their research is focused on understanding secondary (dorsal-ventral) axis specification and patterning in the sea urchin. They are interested in producing a systems-level description for this series of events that occur during the first 48 hours of development following fertilization. Sea urchin, a non-chordate deuterostome, is an ideal model organism for systems-level developmental studies. Genomic analysis has revealed that sea urchins share the diversity of signaling and transcriptional molecules with vertebrates, including humans, but lack the complexity associated with a duplicated genome. Further, sea urchin larvae are morphologically quite simple, being composed of approximately 15 cell types, and thus are accessible to detailed analysis of cell specification and cell-cell communication mechanisms. Finally, the use of gene regulatory networks to model developmental processes was pioneered in urchin, providing a strong precedent for this work. The lab is focused primarily on two projects: understanding how the peripheral nervous system is specified, and how the larval skeleton is patterned.
Isaacson: Systems Biology. Isaacson worked on the influence of spatial chromatin distribution on the time required for regulatory proteins to find specific DNA binding sites. Participants in this project included, D McQueen (Courant Institute) and C. Peskin (Courant Institute). Using fluorescence imaging data, a three-dimensional stochastic reaction-diffusion model was constructed to study the question of how the time required by gene regulatory proteins to ?nd specific DNA binding sites is affected by subcellular structure within the nucleus of cells. A new numerical method for incorporating potentials into the reaction-diffusion master equation was developed to model volume exclusion due to chromatin. Using this numerical method computational simulations suggest that, from the point of view of a protein searching for a DNA binding site, chromatin dense regions posing a weak barrier are more helpful than if the chromatin has no volume exclusion effects or strong volume exclusion effects. A manuscript based on this work is in preparation.
Isaacson also worked on a statistical systems project: Relationship between the Reaction-Diffusion Master Equation and Diffusion Limited Reaction Models. This project included D. Isaacson (Rensselaer Polytechnic Institute), and graduate student I. Agbanusi. Te mathematical relationship between the reaction-diffusion master equation (RDME) and diffusion limited reaction models was investigated by both analytical and computational studies. Two relevant publications from 2009 are listed below. It was shown that the RDME may be interpreted as a divergent asymptotic approximation to diffusion limited reaction models. The accuracy of the approximation for biologically relevant parameter values was also investigated. Graduate student I. Agbanusi is now involved in two ongoing projects trying to improve the accuracy of the approximation, and develop numerical methods for simulating stochastic reaction-diffusion models on three-dimensional surfaces within cells.
