Major Findings from Research Activities of RTG Trainees
(2007-06-01 to 2008-05-31)
Nonlinear Dynamics and Pattern Formation
Interactions of vortices in viscous, incompressible fluid flows. Grad student David Uminsky, in collaboration with Wayne and with two faculty members (R. Nagem and G. Sandri) from Aerospace and Mechanical Engineering, has developed a generalization of the Helmholtz-Kirchhoff model of interacting vortices in two-dimensional fluid flows. The model systematically includes the effects of both viscosity and finite vortex core size and they have shown that it converges to the classical Helmholtz-Kirchhoff model when these parameters tend to zero. Furthermore, they gave conditions on the initial vorticity distribution which are sufficient to guarantee that their expansion converges for all time. A paper containing these results has been submitted to the SIAM J. Appl. Dynamical Systems.
Interactions of solitary waves in non-integrable, infinite dimensional Hamiltonian systems. In infinite dimensional integrable Hamiltonian systems (like the Korteweg-de Vries equation for example), 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. Postdoc Aaron Hoffman and Wayne are studying the collision of solitary waves in the Fermi-Pasta-Ulam model to understand exactly what sorts of behaviors can be expected. They have shown that there are open sets of initial conditions in this model for which the solution can be approximated by a pair of counter-propagating solitary waves for all time (i.e. not just for finite, but long, time intervals). The collision between the waves produces some radiation but this is shown to be small and localized with respect to the two main waves. A paper containing these results has been submitted to Nonlinearity.
Dynamical systems and metastability in parabolic partial differential equations. Recent grad student Margaret Beck, Wayne, and A. Bernoff from Harvey Mudd College have been studying metastable states in Burgers equation. They have proven that there exists an invariant, normally attractive, invariant manifold of finite dimension such that solutions with arbitrary initial conditions rapidly approach this manifold and then remain close to this manifold for very long times before approaching their final asymptotic state. The solutions on the invariant manifold are shown to coincide with the `diffusive N-waves' which Kim and Tsvaras had previously shown can be used to explain metastable phenomena in Burgers equation. In an extension of this work, postdoc Guillaume van Baalen and Wayne have been studying metastable behavior in the KdV-Burgers equation which displays an interplay between diffusive and dispersive phenomena.
Coherent structures in partial differential equations: Nonlinear analysis of breathers. With Kaper and Wayne, postdoc Stefanos Folias has examined a reductive approach, using an ODE approximation to facilitate the study of interacting breathers by analytical techniques. After careful scrutiny, the nonlinear analysis of the model was found to be in disagreement with numerical results of the full model, indicating that the ODE approach is inadequate to describe the dynamics necessary for studying the interaction of breathers. Consequently, he is currently pursuing a center manifold reduction for the full, infinite-dimensional model which, to our knowledge, has not yet been performed for this class of models. While the full model will be adequate to study the interaction, additionally, it may suggest how to augment the ODE approach to facilitate the analysis of the interaction of breathers.
Existence and stability of pulses in a novel three-component R-D system. Grad student Peter van Heijster (visitor at BU), Arjen Doelman (CWI, University of Amsterdam), and Kaper studied the existence, stability, and bifurcation of pulse solutions in a novel three-component system of reaction-diffusion equations modeling a gas-discharge system. Two papers have recently been accepted in PhysicaD and the Journal of Dynamics and Differential Equations. Three-species systems can exhibit far richer behavior than one or two species systems. They identified analytically the parameter regions in which single pulse and double pulse solutions exist, and they determined their stability using the Evans function and the NonLocal Eigenvalue Problem Method developed by Doelman, Gardner, and Kaper. The high dimensionality of the problem causes there to be interesting new mathematical features in the slow component of the Evans function. Finally, the various bifurcations these solutions undergo were identified analytically, including saddle-node bifurcations of pulse solutions, Hopf bifurcations to breathing pulses, and subcritical and supercritical bifurcations to traveling pulses. Presently, they are using renormalization group techniques due to Promislow, Doelman, and Kaper to determine the stability of pulses and fronts whose velocities and shapes vary in time.
Stability and convergence of iterative numerical schemes for finding slow manifolds. With Kaper, C.W. Gear (Princeton, NEC retired). Y. Kevrekidis (Princeton), and C. Vanderkerckhove (K.U. Leuven), recent grad student Antonios Zagaris (CWI and UvA) carried out the stability and convergence analysis on the iterative `constrained runs' numerical schemes that were developed earlier by Gear, Kevrekidis, Zagaris, and Kaper. These iterative methods identify slow manifolds in fast--slow systems and enable projection onto them. They are used by combustion engineers, mechanical engineers, chemical engineers, atmospheric scientists, and others to reduce the size of large systems that exhibit dynamics on multiple time and length scales. The stability and convergence analysis also includes a method to stabilize the iterative schemes when they are unstable. While Kaper was on sabbatical at the CWI (Amsterdam) in June-August, 2007, they submitted an article to the Philosophical Transactions of the Royal Society, A.
Geometric desingularization of some singularites in PDEs and of cusps in fast-slow ODEs. With Kaper and Peter de Maesschalck (Univ Hasselt, Belgium), recent postdoc Nikola Popovic started up a collaborative research project on the geometric unfolding of singularities in certain partial differential equations. They are presently completing a paper on the study of fold points. This project grew out of de Maesschaclck's visit to Boston University in 2007 (paid for in part by the CBD and by Kaper's NSF grant), and has continued through mutual visits in Amsterdam, Groningen (the Neth.), and Hasselt. Popovic also visited Boston University in Spring 2008 to work on this project. A related project has been the first geometric desingularization of the cusp singularity in ordinary differential equations which exhibit fast and slow dynamics. With Henk Broer (U. Groningen) and Martin Krupa (U. Twente), Kaper presented a complete geometric analysis of all the orbits in the vicinity of a cusp singularity and gave a precise identification of the boundary between smooth and nonsmooth returns for such orbits. Moreover, this treatment of cusp singularities completes the extension of Takens' work on singularities in constrained equations to all codimension one and two singularities in fast--slow systems of equations.
Renormalization group and normal form theory. Grad student Matt Holzer's paper showing the equivalence of renormalization group theory and normal form theory for systems of perturbed autonomous systems appeared in Physica D this year. He also showed that renormalization group theory yields a KBM-averaged normal form theory for systems with nonautonomous perturbations. This is joint work with former CBD trainees K. Josic (U. Houston), Lee DeVille (U. Illinois), and A. Harkin (R.I.T.). Matt has also shown how the RG approach recovers logarithm terms and fraction powers of small parameters in perturbed ODEs. Overall, his work has shed important new light on the mathematical underpinnings of this RG method.
Power geometry for asymptotics of solutions of Ordinary Differential Equations Grad student Oleg Mikitchenko completed his PhD thesis in mathematics under the supervision of Kaper and Wayne. Taking on a project of his own, he studied the method of A.D. Bruno known as the power geometry method for determining the asymptotic expansions of solutions of differential equations. This method is based on Newton polygons, and he first showed how it may be used to recover a broad array of asymptotical results for solutions of linear and nonlinear ordinary differential equations, including the classical Airy's equation, Bessel's equation, and other hypergeometric problems. Then, he showed how matched asymptotic expansions could be recovered and rigorously justified for nonlinear two-point boundary value problems with small parameters using this method. Finally, he applied this method to an equation that is singularly-perturbed near t=0 due to the presence of a factor of time in front of the highest derivative, rather than due to the more classical phenomena of a fixed, small parameter. He also showed how to match expansions for this nontraditional problem.
Neuroscience
Neural Rhythms
Rhythm switching in an in vitro model of somatosensory cortex. Working with M Whittington, (Newcastle University), R. Traub (SUNY Downstate) and Kopell, postdoc Mark Kramer developed a mathematical model of rhythm switching through period concatenation observed in rat somatosensory cortex. Observational data reveal a transition from coexistent gamma (30 Hz - 80 Hz) and beta2 (20 Hz - 30 Hz) rhythms in the deep and superficial cortical layers, respectively, to a synchronous beta1 (13 Hz - 20 Hz) rhythm in all cortical layers. To model this system, Kramer and Kopell have constructed a biophysical computational model of cells in rat somatosensory cortex and predicted which synaptic interactions and synaptic currents produce the transition to the beta1 rhythm. The work has resulted in two conference presentations, one manuscript published in a peer-reviewed journal, and another manuscript in preparation.
A cortical network model to study EEG phenomenology observed during anesthesia induced paradoxical excitation. Postdoc Michelle McCarthy completed the Ph.D. in Biomathematics at UCLA in June 2007, under the combined supervision of Nancy Kopell at Boston University and Emery Brown and Harvard/MIT. They constructed a cortical network model consisting of biophysical representations of cortical interneuron and pyramidal cells that is able to reproduce the EEG phenomenology observed during anesthesia-induced paradoxical excitation. It was shown that the state of paradoxical excitation correlated with an increase in beta frequency population spiking in our network models. This increase in beta frequency spiking in all instances is contingent on the presence of an M-current, a slow potassium current. In order to get one form of beta frequency spiking in their network models (interneuron antisynchrony), they showed that a single interneuron must be able to rebound spike after GABAa inhibition.
A dynamical systems approach to understanding current interactions for post-inhibitory rebound spiking. Postdoc Michelle McCarthy is working with Kopell to understand the interaction of the M-current and the GABAa current from a dynamical systems viewpoint in order to determine some of the quantitative constraints on post-inhibitory rebound spiking. They have taken a single Hodgkin-Huxley-type interneuron and have reduced it to a three-dimensional fast-slow system. Fixing the slow M-current gating variable, they show the system undergoes a saddle node bifurcation as the M-current conductance is decreased. Neuronal spiking is possible with M-current values below the bifurcation value. They also show that the addition of a GABAa current to the system results in a shift of the bifurcation point to lower values of M-current conductance. This decrease in the M-current bifurcation value changes linearly with increasing amounts of GABAa inhibition. In their full six dimensional model interneuron, GABAa inhibition decreases neuronal membrane voltage, which in turn decreases the M-current conductance. Thus, post-inhibitory spiking depends on the relative rates of decay of the GABAa and the M-current. Rebound spiking can occur only if the decay of the GABAa conductance is fast relative to the decay of the M-current conductance given their initial deviation from baseline.
Inhibitory rhythms in the olfactory bulb with periodic inputs. Working with Kopell, in collaboration with the Kay lab (Univ. Chicago), grad student Baldur Hedinsson has constructed a single compartment model of the (inhibitory) granule cells (GC) of the mammalian olfactory bulb. He uses parameters from detailed biological models. 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 in the presence of mild heterogeneity, in contrast to other models of similar inhibitory neurons; the difference has been tracked down to the properties of the K+ channel. Specifically the magnitude of activation and the time constant of the activation variable. Exciting the GCs with phasic input (as a signal from the piriform cortex) makes synchrony more robust for certain frequency ranges. While for other frequencies the oscillating input entrains the cells in antiphase. Nullcline analysis for the differential equations that describe the inhibitory neurons explains this. The oscillating input modifies the nullclines in a time dependent way based on the frequency of the oscillation. When the frequency of the oscillation is close to the natural frequency of cells and the amplitude of the oscillation is above a critical value the synchrony is more robust.
Rhythm switching in an in vivo olfactory system. Postdoc Jorge Brea is working with Kopell and in collaboration with Prof. Leslie Kay's Lab at the 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. These experiments where carried out by Jennifer Beshel and Claire Martin working in Dr. Kay's Lab. 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 predominant beta (~12-30 Hz) activity in the OB 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 beta frequencies of the local field potential in the OB. They have shown how these transitions can arise using different strategies depending if the switching is from gamma to beta or a switching from low to high power gamma. (The work builds on the work of recent postdoc Ehud Sivan.)
Neuronal intrinsic oscillations and the representation of time-varying external stimuli. Postdoc Maoz Shamir has worked with Kopell, Dr. Ghitza, and Steve Epstein to investigate the possible computational role of neuronal intrinsic oscillations on the representation of time-varying stimuli. They find that the intrinsic oscillations generate a temporally-sparse code for the external stimuli. In this code, every cell may fire a single spike during a network intrinsic cycle, depending on its tuning properties and on the temporal structure of the specific input. Thus, the identity of the stimulus is coded by the list of excitatory cells that fired during each cycle. They quantify the properties of this representation in a series of experiments and find that in the range of 10-20% the sparseness of the code makes it robust to changes of the overall time-scale. They also find that resetting of the oscillation phase at stimulus onset is important for a reliable representation of the stimulus, and that there is a tradeoff between the resolution of the neural representation of the stimulus and the robustness to time-warp.
Theta and gamma rhythms in two-cell networks of O-LM cells and interneurons. 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, as in the work of Gloveli et al., they are now addressing the role of the excitation provided by the pyramidal cells that is also known to be important, see Tort et al. In this model, they are also investigating how the interaction of the h-current and the A-current in the O-LM cells can regulate the theta modulation of a nested gamma rhythm.
Cellular mechanisms of excitability: Mechanisms of action potential initiation. With Kopell, postdoc Stefanos Folias has been refining the development of a multicompartmental model of a single pyramidal cell that describes and elucidates some of the mechanisms of action potential initiation, which up until now have not been adequately addressed. With this model, he is investigating (1) differences in the firing properties of the cell, including its response to oscillatory drive, (2) the effects of synaptic depolarization by axo-axonic cells converging on the axon initial segment, which is the locus of action potential generation, and (3) the interaction of the soma-initial segment region with the axon proper under the condition of high frequency activity known as very fast oscillations (VFOs) which are believed to arise from a network of axons connected by gap junctions called the axonal plexus.
Data analysis of cortical rhythms. Postdocs Mark Kramer and Adriano Tort, in collaboration with Kopell, performed a detailed analysis of frequency comodulation measures in current use in the neuroscience literature. They determined that rapid increases or decreases in observational data can produce spurious frequency co-modulation in all established measures. They recently reported these results in a peer-reviewed journal.
Assessment of cross-frequency couplings in rat striatum and hippocampus during performance of a T-maze task. Working in collaboration with the Ann Graybiel group at MIT, who provided the experimental data, postdocs Tort and Kramer, supervised by Kopell, have developed and applied cross-frequency couplings measures to the analysis of local field potentials of rat striatum and hippocampus while the animals were subjected to a T-maze paradigm. Their data analysis revealed the emergence of rhythmic cross-frequency co-modulations occurring dynamically within the T-maze task. The strongest coupling occurred between the theta phase and the amplitude of fast rhythms (gamma and high frequency oscillations (HFO)) during the choice period of the maze. The observed cross-frequency coupling tended to disappear when the rat reached the goal. The analysis also evidenced important distinctions between the low gamma, high gamma and HFO frequency bands and their relations to the theta rhythm, supporting different biophysical origins and functions for these fast oscillations. This work also described for the first time the existence of HFO modulated by theta phase in the hippocampus, which appear to originate from different process than the sharp-wave associated ripples oscillations. A manuscript describing these findings is at the final stage of preparation.
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, postdocs Tort and Kramer, supervised by Kopell, have been analyzing local field potentials obtained from the gustatory cortex (GC) of rats after oral administration of tastants. The data analysis revealed that the peripheral administration of tastes caused an evoked potential response in GC (i.e., gustatory evoked potential), along with the emergence of theta oscillations in this cortical region lasting 1.5 s after taste delivery. High frequency oscillations were also observed to increase during the same period as the theta oscillations. The data analysis also revealed the phenomenon of oscillatory reset at the theta band locked to the taste delivery. Their current analysis is now focusing on the study of the spiking units related to the field oscillations.
Forced rhythms in the auditory system of normal and schizophrenic subjects. Working with S. Stufflebeam (Mass General Hospital/Martinos Center for Biomedical Imaging) and Peter Siekmeier (McLean Hospital/Harvard Medical School), postdoc Dorea Vierling-Claassen has continued study of the dynamics of the rhythmic electrical responses of the auditory cortex of normals and persons with schizophrenia when given periodic stimuli. The modeling is used to understand how known deficits at the cellular and synaptic level, in particular, alterations to cortical fast spiking interneurons, might affect responses to auditory stimuli. Mathematical analysis of the models using discrete dynamic maps has provided insight into how inhibitory changes can impact drive response in the gamma/beta range. The network model publication is in press at Journal of Neurophysiology, and a paper regarding the dynamical analysis is in preparation for SIAM Journal on Applied Dynamical Systems (SIADS).
Auditory coding
Biologically plausible models for song discrimination. Graduate student Eric Larson and postdoc Cyrus Billimoria have been working with Sen to develop biologically plausible model neural circuits that perform song discrimination. They have devised a simple model for discrimination inspired by a spike distance metric using a network of integrate and fire model neurons. They applied this model to the birdsong system in the context of song discrimination and recognition, and showed that the model circuit is effective at recognizing individual songs based on experimental input data. Preliminary results suggest that simple population codes can greatly improve accuracy of discrimination, and further work will be done to explore population coding using this scheme.
Invariance to timing variations. Natural stimuli, such as sentences or birdsong, vary with each presentation, but are still recognized as having the same content. Graduate student Ross Maddox and postdoc Cyrus Billimoria have focused with Sen on time-warped stimuli and the zebra finch's ability to categorize songs, both behaviorally and neurally. A phase vocoder was used to change the playback speed of zebra finch songs in a range from half-speed to double without altering spectral content. Behavioral experiments showed that the birds are able to discriminate better than chance at time warps well outside the natural range. Neural recordings were made in field L that using our normal spike distance metric (SDM) were shown not to be invariant. However, with two modifications to the metric, they showed that the information for a high level of invariance was present. The first modification involves a realignment of the spike trains in time. The second modification involves adjusting the time constant of the exponential filter in the SDM proportionally to the warp factor.
Awake neural recordings and behavioral experiments. Graduate student Gilberto Grana continued his work with Sen in recording neural responses in field L of awake birds. Previously, Grana had obtained data from the awake experiments, which has contributed to two papers. He also performed experiments that focused on assessing the stability/variability of spectral temporal receptive fields (STRFs) of field L neurons in awake birds, which indicated diverse levels of STRF stability and would allow identification of candidate neurons that would be well suited for plasticity and learning experiments. His recent work focused on implementing a behavioral paradigm for the training of songbirds in a generalization task to test invariance to intensity and time-warping. The results indicate that, like humans, the zebra finch can generalize over a range of intensities and speeds of playback.
Song memory and recognition in higher order areas. New graduate student Benjamin Perrone has started with Sen to perform awake neural recordings in cM and Field L. The area cM is a major output of Field L, and thus it is a place to look for invariant discrimination and higher order stimulus selectivity. Perrone is looking for post stimulus neural activity in Field L which has not previously been well characterized. Perrone is now designing a wide range of stimuli to fully probe this higher level area.
Plasticity in auditory fear conditioning. Graduate student Shane Lee, working with Sen and Kopell, has investigated the specificity of plasticity in auditory fear conditioning via a simplified biophysical model of primary auditory cortex (AI) constrained by anatomical and experimental data. Using spike timing dependent plasticity (STDP) as a mechanism for the thalamocortical plasticity, they are investigating properties of the simultaneous frequency-dependent potentiation and depression of the tone frequency-specific inputs. They found that optimal potentiation may depend on the length of the tone-shock pairing, with evidence that this is coupled to the decay time for the NMDAR mediated currents in AI pyramidal cells. They also found that inserting pauses in the thalamocortical input carrying tone-frequency specific information can prolong the potentiation, only if the pause length corresponds to the NMDAR mediated current decay time. In conclusion, their model provides a mechanism for learning specificity of tone information and suggests a role for the NMDAR mediated current in regulating optimal plasticity.
Coding of time-varying stimuli. Postdoc Maoz Shamir has studied the coding of time-varying natural stimuli, such as speech. by the dynamic response of nerve cells. In collaboration with Prof Colburn and Dr Sen, he analyzed the information content of the cell dynamic response and investigated the effect of noise correlations on the accuracy of the code. They have shown that the information content of the neural dynamic response scales linearly with the overall observation time of the response - in contrast to conventional claims, thus, enabling accurate sensory representation even in the presence of temporal noise correlations. They also found that finite temporal resolution is sufficient for extracting most of the information. This finite time scale is related to the response properties of the cell. This work was published in peer-reviewed journal and Shamir was invited to international meetings to present the results.
Epileptiform Activity
Characterizing Emergent Network Topology at Seizure Onset in Humans. Postdoc Mark Kramer, in joint work with Dr. Heidi Kirsch (UCSF) and Kolaczyk, has used techniques from network analysis to characterize cortical-level changes in the brain at the onset of epileptic seizures in humans. Network analysis of ECoG data reveals a marked decrease in functional cortical connectivity, as well as an accompanying formation of apparent `communication hubs'. They proposed targeting these communication hubs for treatment of intractable epilepsy. The results of their work were recently published in a peer-reviewed journal.
Mathematical modeling of a neuronal network exhibiting seizure-like events. Grad Student Kyle Lillis is also collaborating with postdoc Mark Kramer and White to apply advanced mathematical techniques to evaluate changes in the correlation structure of the neuronal network leading up to seizure-like events. He has also recently begun to investigate cell-type specific firing motifs during epileptiform activity.
Miscellaneous neuroscience
Modeling transient amnesia, memory reconsolidation and extinction through Hopfield networks. Postdocs Osan and Tort, in collaboration with Drs. Amaral and Roesler at UFRGS, have been adapting and applying Hopfield networks to gain further insights into the understanding of some phenomena of memory impairments as well as normal learning. A first project concerned the phenomenon of transient amnesia following disruptions of memory consolidation and reconsolidation. They showed how memory recovery might be explained within a framework of systems consolidation, persistent synaptic reinforcement, and multiply memory traces. Their current research is aimed in understanding the mechanisms underlying memory extinction and reconsolidation blockade. Motivated by recent experimental findings, emphasis is being given to studying the influence of NMDA activation, protein synthesis and degradation, and the strength of the memory traces on these two phenomena.
Analysis of optical imaging data from the rat olfactory bulb. Postdoc Remus Osan is working with Kopell and with Matthew Wachowiak (BU, Biology) towards developing data analysis techniques applied to optical imaging data from rat olfactory bulb, as well as network models aimed at understanding processing of odor information in this region of the brain. They employ subspace analysis techniques to identify and monitor distinct spatio-temporal patterns of olfactory bulb neural activity that are evoked by presentation of different odors in the awake, behaving animal. Investigations into how the coding properties and network dynamics are altered by sampling behavior (sniffing) of the animal will be used augment the neural network models and render them more biologically plausible. This project is part of a larger collaborative effort investigating the same sensory system, with fellow postdoc Erik Sherwood. They are incorporating detailed biophysical properties of the different types of neurons from the olfactory bulb network (periglomeruli, externally tufted cells, short axons and mitral cells) into the network models. The project also involves CBD faculty member Sen (BME), and they are 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).
Biophysically-detailed models of juxtaglomerular neurons in olfaction. Postdoc Erik Sherwood begun in January 2008 and started working on a project with Kopell and Matt Wachowiak on early processing of odors. He is developing biophysically detailed models of three species of juxtaglomerular neurons (external tufted, periglomerular, and short axon) and their intra- and inter-glomerular connections; most prior work on odor discrimination has focused on the mitral cell layer. However, recent electrophysiological studies indicate that endogenous rhythmic oscillations in the glomerular layer rapidly entrain to sniffing activity and play a significant role in the spatiotemporal encoding of odors. The combined modeling and experimental study with Kopell and Wachowiak focuses on elucidating mechanisms by which the glomerular and mitral layers discern the novelty of an odor coincident with encoding its neural representation.
New mathematics in Purkinje cells. Postdoc Mark Kramer, in collaboration with Kopell and R. Traub (SUNY Downstate), developed a simple --- yet biophysical --- mathematical of a cerebellar Purkinje cell. They find in the simple model a new type of dynamics: limit cycle canards. Similar dynamics appear to occur in more realistic models of Purkinje cells, and in in vitro recordings from Purkinje cells. They recently submitted a manuscript describing these results for publication in a peer-reviewed journal.
Analysis of limit cycle canards. New grad students Anna Barry and Nick Benes are working with postdoc Kramer, Kaper,and Kopell to analyze the new phenomena of limit cycles of canards discovered by Kramer, Kopell, and Traub. They are first considering a simple, low-dimensional system of ODEs with attracting and repelling limit cycles that depends on a slowly evolving parameter. Fenichel theory applies away from the saddle-node of limit cycles and gives the existence of families of invariant, normally hyperbolic cylinders. They are presently extending these families of invariant cylinders to the neighborhood of the saddle-node point, and using geometric desingularization theory to blowup the dynamics in this region. The by-now classical theory of canards created in the Hopf bifurcation to relaxation oscillations in oscillators such as the van der Pol equations is serving as a useful guide for understanding this new phenomenon.
Targeted path scanning. Grad student Kyle Lillis's research with White is focused on two-photon imaging of calcium sensitive dyes in rat hippocampal slices. We developed a technique, which we call Targeted Path Scanning, for quickly scanning the laser across a sample. This provides a means to sample calcium dynamics in dozens of spatially extended cells at rates exceeding 100Hz. Specifically, they have been imaging 4-aminopyridine-induced epileptiform activity.
Gene Regulation
Cellular apoptosis induced by antibiotic treatment in E. coli. Programmed cell death in multicellular organisms is an active, gene-directed process that plays a critical role in development and homeostasis. The most common physiological mode of programmed cell death is apoptosis, which is characterized by a stereotypical set of biochemical and morphological hallmarks. Apoptosis induction has been shown to occur upon integration of diverse intrinsic and extrinsic signals, including mitochondrially-generated reactive oxygen species. Recently, reactive oxygen species generation was observed in prokaryotic cells treated with bactericidal antibiotics. Postdoc Dan Dwyer, grad student Mike Kohanski, grad student Carrie Lawrence, and Collins discovered that Escherichia coli also exhibit several characteristic markers of apoptosis following bactericidal antibiotic treatment. They showed that chromosomal condensation, DNA fragmentation, phosphatidylserine translocation and decreased membrane potential are all detectable upon drug application. In addition, they provided evidence for the drug-dependent induction of a protease with caspase-like substrate specificity. These novel findings illustrate that prokaryotic organisms possess the biochemical machinery sufficient to insure cell death in response to diverse noxious stimuli, and suggest that genetic regulation evolved to manage apoptotic biochemistry and harness its deadly potential.
An engineered, tunable genetic switch to regulate the expression of EGFP in mouse and human cells. Grad student Tara Deans, Charles Cantor, and Collins developed an engineered, tunable genetic switch that couples repressor proteins and an RNAi target design to effectively turn any gene off. They used the switch to regulate the expression of EGFP in mouse and human cells, and found that it offers more than 99 percent repression as well as the ability to tune gene expression. To demonstrate the system's modularity and level of gene silencing, they used the switch to tightly regulate the expression of Diphtheria Toxin and Cre Recombinase, respectively. They also used the switch to tune the expression of a pro-apoptotic gene, and show that a threshold expression level is required to induce apoptosis. This work establishes a system for tight, tunable control of mammalian gene expression that can be used to explore the functional role of various genes, as well as to determine whether a phenotype is the result of a threshold response to changes in gene expression.
Controlling and reducing noise in eukaryotic gene expression. Precision and reliability are two important aspects of information processing that are vitally important in natural cellular gene networks. Likewise, researchers aim to experimentally regulate and control gene expression, either in inducible gene expression systems or in completely synthetic gene networks and devices. However, such control and fidelity of genetic information is countered by the inherently stochastic or noisy nature of gene expression. Synthetic biologists must account for this noise or unpredictability in gene expression in order to construct artificial gene circuits and devices that operate reliably within the cell. In order to do this, noise controlling mechanisms must be incorporated within the designs of these genetic devices. Ideally, such mechanism would be simple to include, allow for variation in the control of noise levels, and be free of undesirable secondary affects. Grad student Kevin Murphy, postdoc Gabor Balazsi, and Collins developed such a mechanism for controlling and reducing noise in eukaryotic gene expression. Their method combines the noise properties observed in two previous studies from the Collins lab, namely the transmission of noise in cascades, as well as the reduction of noise levels by TATA box mutations. In this study, four different mutations were introduced into the TATA box of the upstream regulatory GAL10 promoter controlling expression of the TetR repressor in Saccharomyces cerevisiae. Importantly, these TATA box mutations in the upstream GAL10 promoter resulted in significant reductions in gene expression noise from the downstream tet-regulated GAL1 promoter, as measured by flow cytometric analysis of yEGFP reporter expression. Overall, this allows for an improved technique whereby several TATA box mutations are utilized to differentially reduce extrinsic noise transmission in a gene regulatory cascade, which results in significant attenuation of gene expression noise in the downstream gene of interest, without loss of repression or promoter strength.
The role of introns in gene expression noise. Noise or variability is an inherent property of the biochemical reactions that facilitate gene expression in living cells. Numerous studies have examined the underlying mechanisms involved in gene expression in order to determine how these specific processes contribute to the overall level of noise. Extensive analysis has revealed key contributing factors such as transcription, translation, chromatin remodeling and others in both prokaryotic and eukaryotic settings. Often overlooked have been post-transcriptional mRNA processing events, such as splicing in eukaryotic gene expression. Mostly due to their fast and efficient nature, splicing and other post-transcriptional events have been marginalized and lumped into a generic transcriptional process within mathematical stochastic models. However, such a generalization may be inappropriate, especially in developmentally complex eukaryotes where the presence of an intron can have dramatic affects on gene expression at a variety of levels (transcription, translation efficiency, polyadenlyation, mRNA export and stability). Grad Student Kevin Murphy and Collins experimentally examined the potential contribution to gene expression noise by introns and their splicing in Saccharomyces cerevisiae. Both intron-containing and intronless fluorescent fusion constructs were expressed from an inducible GAL1 promoter and analyzed in terms of gene expression and noise levels. Initial examination of two native S. cerevisiae genes revealed slight differences in the onset of increased noise levels, but overall no significant difference in the amplitude of gene expression noise due to the presence or absence of an intron. The results of this simple case in yeast appear to be in agreement with models that choose to neglect splicing as a significant contributor to noise levels. In the future, it may be worthwhile to examine more complex splicing processes, such as those found in developmentally complex eukaryotes, or even other post-transcriptional processes, such as mRNA editing, to determine other possible contributions to gene expression noise.
Mediation of immune tolerance by regulatory T cell. With Collins, postdoc Ayala Ergan studies regulatory T cells (Treg cells) that 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. Ergan and collaborators use a network approach in order to elucidate the different components of the Treg signature. They first identify the set of genes that have similar expression with Foxp3 but which are not necessarily regulated by Foxp3. Then, they use conditional mutual information (cMI) in order to identify a set of master regulators that might be driving the Treg signature.
Bacterial persister formation via quorum sensing-mediated DNA replication inhibition. Grad student Michael Koeris, postdoc Diogo Camacho, and grad student Mike Kohanski are working with Collins on bacterial persister formation. Persistence is a phenotypically-induced state of cellular senescence which allows a subpopulation of genetically identical cells to survive diverse environmental stresses, such as antibiotic treatment or heat shock. Persisters are thought to be involved in the resistance of biofilms to antibiotic treatment, leading to chronic infection. The rate of persister formation peaks during late exponential phase and early stationary phase, coinciding with the activation of quorum sensing systems; however, to date, there is no known association between quorum sensing and persister formation. The Collins group has shown that the AI-2 quorum sensing system of Escherichia coli significantly influences persister formation. Knockouts of the lsr operon, which is involved in AI-2 update and degradation, reveal that cells with increased lsr-mediated AI-2 levels are more likely to become persisters. Using a network biology approach, they identified a novel regulatory interaction between the repressor LsrR, the regulator of the lsr operon, and CspD, a DNA replication inhibitor, and demonstrated that this interaction affects persister formation. They also showed that overexpression of lsrR inhibits cell division and decreases persister formation. This work established a quorum-sensing mediated mechanism whereby imported AI-2 inactivates lsrR which de-represses cspD, leading to DNA replication inhibition and the controlled completion of cell division, enabling cells to become persisters.
Dynamical analysis of regulation of catabolic genes. Postdoc Ilaria Mogno and Gardner are identifying combinatorial regulations in E. coli using time series data. The analysis focused on sugar metabolism genes, which are known to be expressed only when the external media contains the correct sugar. However, their data showed that these genes are activated by a major regulator upon carbon starvation. The roles of the major activator and of the sugar-specific regulators are investigated, as well as the role of the Feed Forward Loop often regulating these genes. This approach uses time series data generated through GFP as a reporter for gene expression. Experimental work has been done to clone the promoters of interest in front of a gfp gene.
Transcriptional regulatory networks in E. coli stringent response. Grad student Hemali Patel with Gardner aim to study the transcriptional regulatory networks controlling the stringent response in E. coli. Stringent response is an adaptation to starvation and involves global reprogramming of gene expression. Combining gene expression profiles collected using Affymetrix microarrays and machine-learning algorithms, we are able to predict the transcriptional regulatory networks that are activated during stringent response in E. coli. We provoked stringent response by multiple induction pathways and identified the core transcriptional profile that is characteristic of the cellular response to ppGpp accumulation. By comparison of wild type and ppGpp-deficient mutant strains, we identified the expression changes that are specifically dependent upon ppGpp.
Reverse- and forward-engineering metabolic networks. Graduate student David Byrne, working with Daniel Segre and Ionnis Paschalidis, is developing algorithms and methods to facilitate the design of novel biosynthetic pathways, and to predict the outcome of genetic, media and feedstock changes on biosynthesis. Regulatory logic is inferred using high-throughput experimental data and integrated with metabolic models. This work includes machine learning algorithms for metabolic model validation and refinement, and metabolic flux analysis and optimization.
Detection of drug target compounds using statistical techniques on gene regulatory data. Grad students Shu Yang (Stats), Elissa Cosgrove (BME), and Melissa Dominguez (Chemistry) are working with Kolacyzk, Gardner, Simon Kasif (BME), and Scott Schaus (Chemisty) on the development and validation of novel statistical techniques to help in the automated detection of drug target compounds, primarily from gene regulatory data. Methods in development are network-based, relying on sparse inference techniques to extract relevant information from high-dimensional microarray experimental output. They are being developed and tested on a combination of curated public data and data generated by the Schaus lab.
Evolution of Topology, Function, and Regulation in Biochemical Networks. Graduate student William Riehl (Bioinformatics Program) in the Segrèroup, has been using an artificial chemistry model for predicting expected topological and dynamical features of an optimally evolved metabolic network. Model results have been compared with corresponding real metabolic networks from multiple species. This work is the result of a collaboration with Prof. Sidney Redner (CBD and Physics at BU). Similar ideas are now being extended to studying metabolic regulation.
Inference of gene regulatory networks Postdoc David Gold has worked with Kolaczyk and with Simon Kasif (Bioinformatics) on problems in the inference of gene regulatory networks and the use of those inferred networks for higher-level tasks, such as drug target prediction, with an emphasis on Bayesian statistical tools. They are presently preparing a paper.
Bottom-up construction of synthetic networks in eukaryotic cells. Postdoc Xiao Wang and Tom Ellis, with Jim Collins are combining molecular biology with mathematical modeling to construct novel synthetic gene regulatory networks in yeast. This work has produced a synthetic toggle switch and various feed forward loops in yeast. Mathematical modeling also revealed the mechanisms for stochastic cell differentiation, which could be applicable for natural systems.
Inference Kinetic models for nitric oxide synthesis in endothelial cells. Grad student Christopher Garay is working with Collins and in Joseph Loscalzo's lab at Brigham and Women's Hospital (Harvard) to develop kinetic models that describe the dynamics of nitric oxide synthesis in bovine endothelial cells. They are using these models to predict behavior that can be verified via time course measurements of metabolite concentrations.
Integrating gene regulatory networks into metabolic flux models. New postdoc Michael Molla has recently begun to apply his skills in machine learning, software design, and gene expression analysis to the study of gene regulatory networks and their integration with metabolic flux models. He will be mentored by Collins and Simon Kasif (Bioinformatics). An African-american, he comes to the CBD and Boston University with a Phd in Computer Science, as well as with five years work experience at IBM, two years at the Whitehead Institute, and consulting for Nimblegen Systems. He will help extend the RTG interactions into the computer science community at BU.
Bacterial quorum sensing. With Steve Lory (Harvard Medical School), grad student Josh Thaden has been studying the quorum sensing, or cell density signaling, transcriptional regulatory network in the pathogenic bacterium Pseudomonas aeruginosa. Quorum sensing is important in P. aeruginosa virulence as this signaling network controls the release of exotoxins, extracellular proteases, hydrogen cyanide, and other disease-causing agents in response to high cell density. We are trying to understand the molecular interactions that govern the quorum sensing response in order to better understand and perhaps better treat Pseudomonal infections.
Drug target prediction. Grad students Jasmine Zhou and Elissa Cosgrove are working with Kolaczyk and Gardner to develop a statistical framework for drug target prediction from inferred gene regulatory networks, based on microarray measurements. The new framework recasts the MNI framework of Gardner and Collins and colleagues in the context of sparse simultaneous equation models (SSEMs), uses a sparse inference method, namely Lasso regression, to infer network structure, and implements outlier detection tests with false discovery rate principles to rank candidate genes potentially affected by external influences (e.g. drug compounds or genetic mutation or dysregulation in cancer or disease). Cosgrove has assembled a new compendium of 962 yeast Affymetrix microarray experiments. She has used this dataset and an Affymetrix E. coli dataset to test the performance of the SSEM-Lasso approach in comparison to the MNI algorithm and a null approach using compendium-based z-scores. In both Affymetrix datasets, the investigators have observed superior performance by the SSEM-Lasso method in identifying the known targets of genetic perturbations, and also some promising, though less consistent, results when the algorithm is applied to identify known targets of drug perturbations. They are currently applying the algorithm to an Affymetrix human cancer dataset.
Optimality criteria for the prediction of metabolic fluxes in yeast mutants. Graduate student, Evan Snitkin (Bioinformatics Program) has been working in the group of Daniel Segrèperforming 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 a study recently submitted for publication, we integrated experimentally measured growth phenotypes of 465 S. cerevisiae gene deletion mutants under 16 metabolically relevant conditions with the corresponding flux balance model predictions. We found that the quality of the model is good enough to allow identifications of errors in the experimental data set, and to gain significant biological insight on how the cell utilizes specific metabolic pathways.
Determination of time-dependent objectives in metabolic flux models. Flux Balance Analysis (FBA), is a constraint-based method for studying cellular metabolism at steady state. Graduate student Hsuan-Chao Chiu (Bioinformatics Program), in the group of Daniel Segrèhas been working on extending current FBA models, which capture the average behavior of steadily growing cell populations, to the time-dependent analysis of dynamically changing single cells or cell populations. Preliminary results have been obtained for the dynamics of cell cycle in yeast.
TRAINING AND DEVELOPMENT
Seminars
CBD Faculty member Daniel Segrè has been the main organizer of a new research seminar series in Systems Biology at Boston University (http://sysbio.bu.edu), meant to bring together people from many different departments. The event has been very successful, with active participation from Biology, Bioinformatics, Physics, Computer Science, Biomedical Engineering, Chemistry.
Collins, Kopell, and Sen each again ran weekly meetings of students and postdocs, with attendance in each group ranging from 10 to over 25. Gardner also ran a weekly seminar during the Summer of 2007, before leaving BU for a job in industry. All of these weekly meetings, attended mainly by the trainees working with a particular faculty member, were open to all the members of the other groups, and frequently had attendees from other groups. Our new postdocs have found these to be indispensable for selecting research topics.
Kaper and Wayne each ran working groups in this year, Kaper on pattern formation with four graduate students and Wayne on integrable Hamiltonian PDEs with eight graduate students and postdocs.
Grad students Paola Malerba and Erin Munro (Tufts) took over organization of a research group specifically for graduate students and early postdocs working in computational neuroscience. The group this year had 7 participants, some from outside BU. The group focuses on identifying specific paths for developing their individual research projects and on using their combined knowledge of mathematics and neuroscience to solve problems that may come up in individual projects.
Grad students Matt Holzer and David Uminsky have again organized the weekly graduate student seminar in dynamical systems, which this year involved twelve regular participants, mostly from math, but some from engineering.
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