| Home | Positions Available | Graduate Study | List of Members | Ongoing Research | Publications | Labs | Related Links | Directions |
Major Findings from Recent Research Activities (2005-2006)
Low dimensional maps for gamma and theta oscillations. Postdocs Dmitri Pervouchine, and Tay Netoff , along with J. White and Kopell, finished a paper using 1-D and 2-D maps to describe how 3-cell networks taken from the hippocampus and entorhinal cortex can coordinate. One aim of the paper was to show how phase-response curve methods could be used for multicell networks of heterogeneous cells. Another was to show how the biophysical specifics of the cells affect synchronization in such networks. The paper is in press in Neural Computation.
Reductions of dimensions. Biophysical models of neurons and neural networks are typically high dimensional, and the variables evolve over many time scales. In some cases, the models are simple enough to be amenable to reduction to lower dimensional systems by making use of the time-scale separation between the different dynamic variables. This is the case for some Hodgkin-Huxley models (four-dimensional) that can be reduced to two dimensional models (Fitzhugh-Nagumo or Morris-Lecar type). By contrast, neural models with more currants can be high dimensional, and have complex dynamics (e.g., mixed mode oscillations, see below.) Research Asst Prof Rotstein, with Clewley and Kopell, showed that the interspike interval can be divided into subintervals inside which a 7-D entorhinal cortex stellate cell model can be reduced to a two- or three-dimensional systems that are amenable to geometric or analytic study. The reduction of dimension process makes use of the different times scales and the fact the some currents are inactive in some ranges of voltage.
Subthreshold oscillations (STOs). It was already known that the interaction between two non-standard intrinsic ionic currents, a persistent sodium and a hyperpolarization-activated (h-) currents, is enough to account for the generation of the STOs in Medial Entorhinal Cortex (MEC) Layer II Stellate Cells (SC). However, the mechanisms by which this phenomenon occurs and the specific role of each of these currents were still open questions. Rotstein, with Tim Oppermann, White, Martin Wechselberger and Kopell used reduction of dimension procedures to study mixed-mode oscillations (i.e., STOs and spikes) in the 7-D stellate cell model. They showed that the STOs and the onset of spikes are generated by a mechanism depending on a dynamic structure they call the “canard structure”. The main ingredients of this structure are the nonlinearities of the reduced model (represented by its nullsurfaces) and the time scale separation between the voltage and the h-current gating variables. This dynamic structure has the potential to produce the canard phenomenon (blowup). Both STOs and MMOs are closely related to the canard phenomenon. These phenomena can be reproduced in models in which the spike is replaced by a threshold and reset. Current work includes the relationship of this dynamical mechanism to other methods of producing STOs and MMOs and the role of each of the ionic currents in producing the resonance.
The same group are also working on mathematical aspects of the canard structure that emerges in this regime. Via an appropriate change of variables, they have brought the reduced 3D system to a form (transformed system) suitable for analysis. They have also built and are studying a toy model, consisting of a fast equation with a parabolic nullsurface, and two slow linear equations. It has the same qualitative features of the transformed system.
Subthreshold oscillations and resonance. Last year Rotstein, Kopell, T. Opperman and White submitted a paper on subthreshold oscillation in a kind of cell in the entorhinal cortex, now in press in Journal of Computational Neuroscience. The biophysical model gave rise to a new mechanism for the creation of such low amplitude oscillations, based on “canard” structures. This has been followed up with related work, almost finished, on resonance associated with such oscillators, with Tim Opperman of the lab of Andreas Herz. The work shows the time scales responsible for the resonance are related to the times to traverse the low amplitude oscillations, rather than any associated eigenvalues. More details are in the 2005 report.
Rhythms in entorhinal cortex. Postdoc Jozsi Jalics, PIN grad student Tilman Kispersky, and Kopell are working with Mark Cunningham and Miles Whittington (U. of Newcastle) to investigate the mechanisms underlying various neuronal rhythms and their role in the formation and coordination of neuronal ensembles in superficial layers of the entorhinal cortex, using numerical and analytical techniques. One current project almost completed concerns changes in rhythms in the presence and absence of kainate and NMDA receptor antagonists; modeling has led to an explanation of why NMDAR antagonists can cause a decrease in gamma power in the presence of kainate, but an increase in the absence of kainate. The model, which makes use of a structure involving stellate cells, pyramidal cells and two different kinds of interneurons, makes experimentally testable predictions about anatomy and synaptic kinetics. Jalics et al. have extended the above model to include multiple such modules , and have shown that theta and gamma rhythms can interact with focal inputs to produce ensembles of modules. Also, they have examined the role of inputs from the medial septum, which acts as a theta generator, in the creation of theta-nested gamma rhythms and the formation of ensembles. Some of this work has been presented at the 2004 and 2005 Society for Neuroscience meetings and multiple papers based on this work are in preparation.
Neuronal synchronization and acetylcholine. Following the work of Netoff on neuronal synchronization, described last year, grad student Lisa Giocomo, postdoc Netoff, and BU faculty members Michael Hasselmo (Psychology) and White (BME) have examined the problem of how the neuromodulator acetylcholine changes synchronization properties. They find that the cholinergic agonist carbachol promotes excitation-based synchronization among layer III pyramidal cells in entorhinal cortex, but not among layer II stellate cells. Pharmacological results suggest that carbachol exerts its effects via the non-specific cation current INCM. This effect may be extremely important for ‘mode-switching’ in entorhinal cortex and hippocampus. They plan to submit this work for publication in fall 2006.
Mixed mode oscillations. Postdoc Jalics, Research Asst. Prof. Rotstein and Kopell are analyzing a biophysical model of an entorhinal cortex layer V pyramidal cell that includes a persistent sodium and a slow potassium current, which are active in the intervals between spikes. Using reduction of dimension techniques and bifurcation analysis, they are investigating the mechanisms that generate subthreshold oscillations, mixed mode oscillations, resonance, and rebound firing. Interestingly, they have found that the spiking currents, which are usually neglected, are important in the interspike interval. Also, in the mixed-mode oscillation regime, they play an important role in the analysis of a 3-d canard structure, in which trajectories remain in a neighborhood of an unstable manifold for a significant duration of time, that governs the model's dynamics. To study the mixed-mode regime, the six dimensional model has been reduced to a three dimensional model and transformed into a canonical form that exposes the canard structure and helps reveal a novel mechanism for the generation of mixed-mode oscillations.
Beta and gamma rhythms in the neocortex. M.Whittington, R.Traub and collaborators showed that superficial layers of the neocortex produce gamma rhythms in the presence of kainate. However, some cortical areas produce beta 1 (22-29 Hz) in the deep layers in the same slice. Traub has produced a detailed biophysical model of the deep layer beta, which depends on gap junctional connections among layer V cells. Postdoc Mark Kramer has collaborated with Kopell, Whittington and Traub to produce a reduced model of the beta 2 rhythm, consisting only of three compartments (a soma, axon, and dendrite), which exhibits the bursting activity observed in experimental recordings from deep cortical layers. Kramer and Kopell are now investigating the interaction of the rhythms in the deep and superficial layers.
Gamma and theta rhythms in the hippocampus. In a paper with Kopell, Whittington and other collaborators, T. Gloveli provided anatomical and physiological evidence that the prominent rhythmic network activities of the hippocampus, the behavior-specific gamma and theta oscillations, are seen predominantly along the transverse and longitudinal axes respectively. Modeling showed that this orthogonal relationship is the result of the axonal field trajectories and the differences in the two different kinds of slices in the interaction of the principal cells and major interneuron subtypes involved in generating each rhythm. Thus, the axonal arborization patterns of hippocampal inhibitory cells may represent a structural framework for the spatiotemporal distribution of activity observed within the hippocampus.
Multicompartmental models of hippocampal neurons. Postdoc Adriano Tort is working with Rotstein and Kopell on a more complex model of hippocampal CA1 and CA3 networks; the more complex model has more compartments, allowing one to investigate the role of differences in the h-current along the dendrites when that ionic current is modulated. They plan to collaborate with Gloveli on implications for epilepsy of changes in this current.
Neuronal metabolism and network response state. In a recent PNAS paper, Cunningham et al showed that rhythmic transitions between periods of high activity (up phases) and low activity (down phases) vary between wakefulness and deep sleep/anesthesia. Current opinion about changes in cortical response state between sleep and wakefulness is split between neuronal network-mediated mechanisms and neuronal metabolism-related mechanisms. This paper demonstrates that slow oscillations in network state are a consequence of interactions between both mechanisms: recurrent networks of excitatory neurons, whose membrane potential is partly governed by ATP-modulated potassium (K(ATP)) channels, mediate response-state oscillations via the interaction between excitatory network activity involving slow, kainate receptor-mediated events and the resulting activation of ATP-dependent homeostatic mechanisms. These findings suggest that K(ATP) channels function as an interface between neuronal metabolic state and network responsivity in mammalian cortex. The modeling for that paper was done by postdoc Pervouchine and Kopell.
Axonal plexus activity. Postdoc Stefanos Folias and Kopell are currently developing a project which explores the generation and effects of activity in the plexus of axons of pyramidal cells. Such activity is mediated by both chemical synapses as well as purported electrical gap junctions, and is believed to be centrally important for the creation of gamma oscillations that are induced by kainate. The aim of the project is to produce a model of this activity (less complex than the current model by Traub) and use this to explore the effects of the plexus activity on responses to afferent inputs. Others who have been involved are Roger Traub, Miles Whittington, and Costa Colbert.
Gain modulation in EC stellate cells. Previous work of Burdakov et al. studied the gain curves (changes in firing rate with input current) starting with different sets of ionic currents starting with the same baseline rate; the gain curves were shown to be different. PIN grad student Shirley Sanchez is carrying out a similar investigation for the EC stellate cells under the direction of Rotstein. They plan to study the consequences of this modulation for synchronization.
Discrimination of natural sounds. Graduate student Rajiv Narayan is extending his previous work on discrimination of natural sounds by auditory neurons in the songbird auditory cortex analog field L. Narayan previously worked on the analysis of neural discrimination of birdsongs, which has already resulted in two publications (one modeling and one experimental). He is now investigating how different forms of background noise affect neural discrimination. To do this he has been recording neural responses to songs embedded in different types of background maskers e.g., chorus of other birds. Ultimately, his results can be related to psychophysical results on the perception of sound mixtures by humans (in collaboration of Barbara Shinn- Cunningham’s lab at BU) and birds (in collaboration with Micheal Dent’s lab at SUNY, Buffalo) and may provide new insights into the neural substrates for understanding how the brain is able to separate auditory objects from complex noisy backgrounds, the so-called “cocktail party problem”.
Postdoc Cyrus Billimoria is investigating invariance of neural discrimination and recognition in field L by analyzing neural responses to song variations, which mimic natural variations e.g., songs at different intensities and different renditions of the same bird’s song. He has already learned the experimental techniques and starting to collect his own data. Billimoria’s preliminary data show the presence of neurons in field L that are surprisingly robust to song variations and may contribute towards invariant discrimination and recognition of individual songs. Billimoria is also planning to present his findings at the 2006 SFN Annual meeting.
Finite temporal resolution. Natural stimuli have a temporal structure; in many cases this temporal structure is represented by a time-dependent neuronal activity that is locked to certain features of the stimulus, which is suggestive of a temporal code. It is not clear how information may be coded temporally, especially since recent studies have suggested that the information content of the neuronal temporal response is severely limited due to temporal noise correlations. In contrast to these studies , postdoc Maoz Shamir, with Sen and Colburn, have recently found that information content of the temporal response scales linearly with the overall observation time of the response, enabling accurate sensory representation even in the presence of temporal noise correlations. Finite temporal resolution is sufficient for obtaining most of the information from the cell’s response. This finite time scale is related to the response properties of the cell. This work has been presented in the Hearing research seminar and the CoSyne 2006 workshop.
Plasticity in auditory receptive fields. Graduate student Gilberto Grana is continuing his work with Sen in awake songbirds. Grana has already obtained data from the awake experiments, which has contributed to a paper. His recent experiments have focused on rapid plasticity in spectral temporal receptive fields (STRFs) in awake birds. Rapid plasticity in STRFs has previously been demonstrated after training the animals over long periods on tone detection or discrimination tasks. Grana’s preliminary data suggest that it is possible to induce plasticity in neural receptive fields of awake male birds, without any prior training, by pairing a target tone with a behaviorally relevant stimulus i.e., the presence of a female bird. Grana is also planning to investigate state-dependent changes in EEG during these experiments.
Postdoc Gabriel Soto, who was working jointly with Kopell and Sen, left with a position in Argentina. Soto has already submitted a manuscript based on his previous modeling work on neuromodulation of auditory cortex and rapid plasticity in STRFs. His work also contributed to a research proposal on computational neuroscience in collaboration with Shihab Shamma’s laboratory at the Universtiy of Maryland and Norman Weinberger’s laboratory at UC Irvine. Soto is currently preparing two additional manuscripts based on his previous work on gamma oscillations and long-term plasticity in auditory cortex.
Olfaction Postdoc Ehud Sivan, math grad student Baldur Hedinsson and Kopell are working with Leslie Kay and her trainees on multiple rhythms in the olfactory bulb and pyriform cortex in intact behaving rats. The work centers on the origins of the different frequency rhythms that appear during different parts of a task (attentive waiting vs active discrimination), and in different states of learning for some tasks (beta rhythms, a lower frequency, appears when the rat has learned the task to criterion.) The modeling uses relatively detailed biophysical descriptions of different kinds of cell (mitral and granule in the bulb), based on physiological data; preliminary models have been constructed, and are now being used to investigate how various kinds of spatially and temporally patterned inputs are process by the pyriform-olfactory bulb loop.
STDP Working with White, postdoc Yu-Dong Zhou has published work (Zhou et al. 2005) on the mechanistic basis of spike-time-dependent plasticity (STDP), described in last year’s report. Zhou’s current work focuses on the relative contributions of multiple classes of NMDA receptors to signal processing in entorhinal cortex. He has found that postsynaptic action potentials diminish the signals from some NMDA receptors, but not others. They hypothesize that this effect is crucial for timing-dependent synaptic plasticity, on a time scale < 10 ms.
Backpropagation. Working with White, former grad student Corey Acker has continued studies of back-propagating action potentials on computational models. Since last year, he has extended his quasi-analytical approach to include studies of neurons with complex geometries. The major scientific conclusion of Acker’s work is that electrophysiological factors are more important than anatomical factors in determining whether action potentials fail. This work is under revision after initial reviews, and is expected to be accepted in late spring 2006.
Plasticity and glycine receptors. In last year’s report, we described the work of graduate student Tara Keck with White. This work focused on the modulation of glycine receptors in hippocampus, and the resultant effects on long-term synaptic plasticity. Since last year, Keck has defended her Ph.D. successfully and has moved on to a postdoctoral fellowship at Max- Planck-Munich. In new scientific developments, Keck, Lillis and White have discovered that the mechanism underlying this phenomenon involves retrograde messaging to presynaptic glycine transporters. This work is currently in review.
Channel noise. Former graduate student Alan Dorval II (now a postdoc at Duke University) published one paper in 2005 and submitted a second in 2006. The published paper (Dorval and White 2005) shows that channel noise (i.e., electrical noise from thermally driven fluctuations in channel protein configurations) is necessary for the oscillatory activity seen in stellate cells of the entorhinal cortex. In the submitted paper, recently accepted by Chaos they show that the fact that synaptic inputs arrive as conductance changes is fundamentally important for neuronal function. This work calls into question the nearly ubiquitous technique of using applied current as a surrogate for synaptic inputs.
Sleep Rhythms. Math graduate student Cecilia Diniz Behn, working with Kopell and Emery Brown, modeled the dynamics of switches among sustained wake states , brief awakenings, non-REM sleep and REM sleep. The models involve the interaction of different nuclei in the brainstem, each described as a relaxation oscillator or an excitable system with more than one time scale. Multiple time scales were exploited to analyze the different kinds of switches , and how those could be altered in pathological circumstances, such as narcolepsy. Cecilia has defended her thesis and will be working next year at the Harvard Sleep Research Center .
Anesthesia. UCLA Applied Math graduate student Michelle McCarthy worked with Kopell and Emery Brown on the mechanisms associated with the anesthetic propofol. The central question is why low-doses of propofol induce a so-called “beta buzz”, an increase in power in the 12-25 Hz range of frequencies. Using analysis with small networks and simulations with larger ones, they have discovered that the extra power in the beta frequency band can arise from switches of power from both lower and higher frequencies when the kinetics of inhibition are changed by propofol. Dynamical systems methods are relevant to understanding the transformation of low to higher frequencies via switches from synchrony of cells to “clustering” at different phases.
Attention. Kopell, with S. Epstein and C. Borgers, has been working on mechanisms of specific attention. They have shown that coherent input to a target circuit (coherence associated with attention), can lead to locking with the target in such as way that other input is completely shut out. They have explained this phenomenon in terms of the kinetics of the inhibition in the target network. A paper is in progress.
Dynamics and schizophrenia. Grad student Dorea Vierling-Classen continued collaborative research on cortical rhythms in schizophrenia with Kopell, Steven Stufflebeam (Mass. General Imaging Center) and Peter Siekmeyer (McLean Hospital). They are studying pathologies in the rhythmic electrical responses of the auditory cortex of 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 the responses to auditory stimuli. The work was presented at the annual CBD symposium.
Encoding and recall. Graduate student Eric Zilli has worked with Prof. Michael Hasselmo to develop models of the role of theta rhythm oscillations in the encoding of retrieval of associations in the hippocampal formation. These models have been used to interpret electrophysiological data on the phase of action potential firing relative to the phase of theta rhythm oscillations during performance of odor delayed match to sample tasks and spatial delayed match to position tasks. This work has involved collaboration with researchers including James Hyman in the Hasselmo laboratory and Joe Manns in the Eichenbaum laboratory performing electrophysiological recording of unit activity in prefrontal cortex and hippocampus.
Rhythms in the hippocampus and behavioral tasks. With Dr. Randal Koene, Prof. Michael Hasselmo has been developing detailed models of the interaction of hippocampus and prefrontal cortex for performance of behavioral tasks including spatial alternation and spatial reversal in rats as well as an operant responding task in monkeys. This research uses the CATACOMB simulation package to develop spiking network models of goal directed behavior, focusing on the role of theta rhythm oscillations in hippocampal network function, and the interaction of hippocampal episodic retrieval mechanisms with goal-directed function mediated by prefrontal cortex.
Navigation. Graduate student Anatoli Gorchetchnikov completed his degree in 2005, working with Michael Hasselmo on the dynamical interaction of different hippocampal subregions in mediating goal-directed spatial navigation. He has taken a post-doctoral position in the Department of Cognitive and Neural Systems at Boston University.
Optical imaging in hippocampal and entorhinal cortex slices. Postdoctoral fellow Theoden Netoff and graduate student Tilman Kispersky have continued work with White on imaging coherent activity in brain slices of hippocampus and entorhinal cortex. In this work, they introduce calcium-sensitive dyes into neurons and glia, then image intracellular calcium concentration as a surrogate for electrical activity. Netoff’s efforts have focused on epileptiform activity, induced (e.g.) by the K+ channel blocker 4-aminopyridine. Kispersky has focused on coherent, non-epileptiform activity induced by the cholinergic agonist carbachol. They are investigating the induction, maintenance and propagation of the oscillation as mediated by different cellular components of the network. The large volume of data produced by the optical imaging studies has led the above group to develop novel techniques for extracting important features from out datasets. They are currently perfecting a method for extracting single cells from imaging data using independent component analysis. Further work on this project will aim to extract oscillatory network behavior, pinpoint the cellular components of the oscillation as they change over time and identify propagating wavefronts as they move through the imaging window. Preliminary work was presented at the 2005 Society for Neuroscience meeting. They are currently writing a methods paper, and hope to write the first scientific paper on epileptiform activity in summer 2006. Once the experimental data are mature, this work will spur collaborative modeling work with Kopell and others.
Imaging of the olfactory bulb. Netoff is working with White and the group of Biology professor Matt Wachowiak on analysis of data from the olfactory bulb. In these experiments, Wachowiak collects data reflecting activity in olfactory receptors as they converge in the bulb. Netoff and White are employing techniques that have been used to study short-term synaptic plasticity to focus on adaptation in the olfactory system.
Imaging of axons. Netoff and White are also collaborating with the group of Irving Bigio (Boston University, BME). In this project, we are assessing the feasibility of recording neural activity strictly on the basis of changes in the optical properties of axons. Preliminary data suggest that the technique works, at least in isolated nerves. In future work, they will assess the technique in brain slices.
Imaging in a time-varying magnetic field. Kispersky, Netoff, and White are collaborating with the group of Professor Solomon Eisenberg (Boston University, BME) to study the feasibility of non-invasive magnetic stimulation of the brain. In the feasibility studies, we are using imaging techniques to monitor electrical activity in a brain slice that is exposed to a time-varying magnetic field. Preliminary data look promising.
Two-photon microscopy. Graduate student Kyle Lillis and White are collaborating with Professor Jerome Mertz (Boston University, BME) to study intracellular processing of calcium using two-photon microscopy. The first such project will focus on measuring the fine spatiotemporal characteristics of calcium signals related to synaptic plasticity. Two-photon techniques allow such measurements on a sub-micron length scale. White’s group has already published modeling work on this subject (Zhou et al. 2005). This project will lead to more modeling work in the near future.
FMRI and cholinergic blockade. Dr. Ali Atri has completed his work with Prof. Michael Hasselmo on tests of effects of cholinergic blockade on fMRI and memory behavior in human subjects. He is a staff neurologist at Mass General Hospital.
Scaling with population size. Postdoc Maoz Shamir has worked on properties of “Single Best Cell” readout for population cell. He has found that, although the SBC accuracy does improve when larger populations are considered, this improvement is extremely weak compared to other types of population codes. More precisely, he found that while the accuracy of a linear readout scales linearly with the population size, the accuracy of the SBC readout scales logarithmically with the number of cells in the population. These findings support the hypothesis of a SBC readout in cases where the psychophysical accuracy is comparable to information content of a single cell response. A paper has been accepted.
Neuronal diversity and population coding. In many cortical and subcortical areas neurons are known to modulate their average firing rate in response to certain external stimulus features. It is widely believed that information about the stimulus features is coded by a weighted average of the neural responses. Recent theoretical studies have shown that information capacity of such a coding scheme is very limited in the presence of the experimentally observed pairwise correlations. However, central to the analysis of these studies was the assumption of a homogeneous population of neurons. Experimental findings show a considerable measure of heterogeneity in the response properties of different neurons. In this study we investigate the effect of neuronal heterogeneity on the information capacity of a correlated population of neurons. With H. Sompolinsky, Shamir has shown that information capacity of a heterogeneous network is not limited by the correlated noise, but scales linearly with the number of cells in the population. This information cannot be extracted by the population vector readout, whose accuracy is greatly suppressed by the correlated noise. An optimal linear readout that takes into account the neuronal heterogeneity can extract most of this information. Simple on-line learning can generate readout weights with the appropriate dependence on the neuronal diversity, thereby yielding efficient readout.
Synthetic biology: engineered promotors. Grad student Nick Guido and Jim Collins, along with Tim Elston and Xiao Wang of the University of North Carolina at Chapel Hill, in the context of synthetic biology engineered a promoter to allow simultaneous repression and activation of gene expression in Escherichia coli, and studied its behavior, in synthetic gene networks, under increasingly complex conditions: unregulated, repressed, activated, and simultaneously repressed and activated. They developed a stochastic model that quantitatively captures the means and distributions of the expression from the engineered promoter of this modular system, and showed that the model can accurately predict the in vivo behavior of the network when it is expanded to include positive feedback. The model also revealed the counterintuitive prediction that noise in protein expression levels can increase upon arrest of cell growth and division, which was confirmed experimentally. This work shows that one can indeed use the properties of regulatory subsystems to predict the behavior of larger, more complex regulatory networks, and that this bottom-up approach can provide novel insights into gene regulation.
Synthetic biology: hybrid systems. Grad student Marius Kloetzer and Calin Belta use a hybrid systems approach to forward engineer and analyze synthetic genetic networks. Their approach is validated with two experimental systems. First, the steady state digital response of a transcriptional cascade is improved and the optimized cascades are used to build more robust toggle switches. Second, formal analysis of hybrid systems is used to fine-tune the dynamic behavior of a pulse generator that incorporates cell-cell communication and a feed-forward motif.
Genetic mediators of disease. Grad students Ayla Ergun, Carolyn Lawrence, Michael Kohanski, and Tim Brennan, along with Jim Collins, showed that reverse-engineered gene networks can be used with expression profiles to compute the likelihood that genes and associated pathways are mediators of a disease. They applied the method to primary and metastatic prostate cancer data, and identified the androgen receptor gene (AR) among the top genetic mediators and steroid and lipid metabolism as highly enriched pathways, for metastatic prostate cancer; these results are consistent with a shift towards androgen independence in metastatic prostate cancers. They also found hemophilic cell adhesion as a significantly enriched pathway in the metastatic case, an indication of the spread and invasion of the cancer. Additionally they examined the chromosomal locations of the top genetic mediators, and find 8q and 18q, chromosomal arms implicated in metastatic prostate cancer, to be significantly enriched in the metastatic case. This work shows that a network biology approach can be used to identify the genetic mediators, mediating pathways and chromosomal abnormalities associated with a disease.
Variability in gene expression. Postdoc Will Blake, postdoc Gabor Balazsi, postdoc Farren Isaacs, grad student Kevin Murphy and Jim Collins showed that the level of variability in gene expression is affected by the sequence of the TATA box and identified transcription scaffold stability as a critical noise-mediating factor. They introduced mutations within the TATA region of an engineered Saccharomyces cerevisia GAL1 promoter and measured promoter response both at the single-cell and population levels, revealing general response types that can be characterized as being either highly variable and rapid, or steady and slow. They used a stochastic model of gene expression to illustrate how a stable transcription scaffold can result in bursts of gene expression, enabling a fast, variable response to a transcription- inducing stimulus. They also showed how bursts of gene expression can differentiate a rapidly responding subset of cells from the population, and experimentally demonstrate that such responses can confer a population-wide benefit after an acute change in environmental conditions.
Genomic normalization for microarrays. Grad student Hemali Patel, and Tim Gardner hypothesized that genomic DNA from E. coli could be used as a reference for normalizing gene expression on Affymetrix E. coli microarrays, as it would cancel out differences in hybridization efficiencies of genes and give a more quantitative estimate of transcript abundance in a sample when compared to normalization by RNA from a control condition. Measures of gene copy numbers can improve existing approaches taken for prediction of co-expressed genes, or operons; and estimation of promoter efficiency.
Transcriptional profiles during environmental perturbations. Patel and Gardner aim to uncover transcriptional regulatory networks controlling cellular pathways in E. coli. For maximal perturbation of the cellular dynamics, they are studying gene expression profiles of E. coli subjected to various environmental stresses such as starvation, osmotic stress, heat-shock, cold-shock, antibiotics, and nutrient shifts. they have preliminary results of transcriptional profiles of E. coli undergoing stringent response as a consequence of nutrient limitation. More studies, using Affymetrix microarrays for gene expression, are underway. From this collection of profiles, they will infer the transcriptional regulatory networks using algorithms and methods developed in the Gardner lab.
Mapping regulatory gene networks. Grad student Mike Driscoll, with Collins and Gardner Gardner are combining network inference tools and high-throughput experimental assays to investigate the metal-reducing bacterium Shewanella oneidensis MR-1. Using a custom microarray platform they designed for Shewanella, they have systematically generated over one hundred genome-wide expression profiles of the organism under a range of environmental conditions. This work of elucidating the regulatory networks governing metal reduction are critical first steps in our goals of optimizing Shewanella for applications in bioremediation and biologically-based fuel cells.
Shotgun mapping of transcriptional regulation from a compendium of expression profiles Trainees Jeremiah Faith, Boris Hayete, Joshua Thaden, Ilaria Mogno, with Simon Kasif, Collins and Gardner, have developed a genome-scale approach for mapping transcriptional regulatory networks in microbes. The approach uses information theoretic analysis of a compendium of 445 Escherichia coli gene expression profiles to identify the gene targets of transcription factors.
Dynamical analysis of combinatorial regulation. Ilaria Mogno and Gardner are identifying combinatorial regulations in E. coli using time series data. The analysis started with steady states data they collected in the M3D compendium. For that data nonlinear regression analysis has been applied to identify the genes that are regulated by two TFs. In order to better identify the relationship at the promoter region, Gardner has developed a tool that uses the Extended Kalman Filter to identify the parameters of the regulation (thresholds, cooperativity, etc). This approach needs time series data that will be generated by using GFP as a reporter for gene expression. Experimental work has been done to clone the promoters of interest in front of a gfp gene.
Reverse engineering metabolic networks. Trainees Julien F. Penders, J. Faith, B. Hayette and M. Driscoll, with David Byrne and Gardner, are developing a novel method to iteratively learn metabolic networks from experimental data. The algorithm searches all biochemically feasible metabolic networks, and learns an optimal network by iterative comparison of experimental data with flux balance analysis simulations.
Drug target prediction. Grad student Jasmine Zhou is 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, uses sparse inference methods (e.g., the LASSO) to infer network structure, and implements outlier detection tests with false discovery rate principles to rank candidate genes potentially affected by external compounds. Initial work in this direction has developed a prototype version of the methodology and validated it by reproducing the findings of the MNI methodology. In addition to this work, Zhou is also working on related theory and methods developing an L1- penalized version of total least squares. Lastly, she is finishing up a second paper with Murad Taqqu on the effect of random permutations on stationary processes. A first paper in this area is nearing publication.
Protein function prediction. Grad student Xiaoyu Jiang is working with Kolaczyk, and colleague Simon Kasif (Bioinformatics), to do protein function prediction in worm. The focus of the quantitative work is on data integration, for which kernel-based methods are being employed. Jiang has implemented a kernel logistic classifier and tested it on a subset of the worm proteome, using PPI network information. Efforts are now being put into scaling the underlying software implementation, incorporating additional measurements (e.g., BLAST scores), and developing a recursive Bayesian strategy for post-processing protein/GO-term specific predictions down a given DAG in the GO hierarchy to refine intitial raw predictions. In addition, Jiang is conducting a theoretical analysis of the statistical risk inherent in a certain class of kernel integration estimators.
Reaction-diffusion equations. Postdoc Nikola Popovic has continued working with Kaper and Freddy Dumortier (University of Hasselt)) on critical wave speed phenomena in a class of scalar reaction-diffusion equations with polynomial nonlinearity that includes the Fisher- Kolmogorov- Petrowskii- Piscounov equation. They considered the regime when the degree m of the nonlinearity becomes large and derived a rigorous asymptotic expansion for the critical wave speed that separates waves of exponential structure from those which decay only algebraically in the limit as m goes to infinity. Moreover, they proved that the critical speed is regular as a function of 1/m. The analysis is based on geometric singular perturbation theory in general and on the blow-up technique in particular.
Hyperbolic phenomena and damping. Postdocs Nikola Popovic and Guillaume Van Baalen have been working with Wayne to develop a dynamical systems approach to understand the interplay between hyperbolic phenomena and damping. In particular they have been studying systems of damped hyperbolic partial differential equations. Prior work by Hsaio and Liu, Nishihara and others proved that solutions of such systems tend asymptotically to solutions of an associated parabolic equation and Popovic, Van Baalen and Wayne are attempting to give a more geometric interpretation of this result. In particular they hope to prove that there are finite dimensional manifolds in the infinite dimensional phase space of this system on which the motion is governed by the limiting parabolic equation and that solutions of the full system corresponding to a general class of initial conditions will approach these manifolds.
Scalar viscous conservation laws. Grad student Margaret Beck has been working with Wayne on the behavior of solutions of scalar viscous conservation laws. She has shown that if one considers perturbations of traveling wave solutions of equations like Burgers equation one can decompose the solution into “near field” and “far field” parts and construct invariant manifolds which allow one to give very precise descriptions of the evolution of both parts of the perturbation. She is also working with Wayne to attempt to give a geometric, “fast-slow” picture of the changeover from hyperbolic to diffusive behavior in such systems. This would involve constructing invariant “slow” manifolds in the phase space which describe both the long-term diffusive behavior of these equations as well as the very slow, metastable approach to these asymptotic states, and also identifing a “fast” approach to these manifolds which would correspond to the hyperbolic part of the motion.
2-D Navier Stokes equations. Postdoc Van Baalen has been working with Wayne to attempt to understand the long time behavior of solutions of the Navier-Stokes equations on the twodimensional torus in the small viscosity limit. While one can prove that such solutions tend asymptotically to zero numerical experiments indicate that the rest state is approached via a sequence of very long-lived metastable states. Van Baalen and Wayne are attempting both to identify these metastable states analytically and to give a rigorous explanation for their metastability.
Small viscosity corrections. Grad student David Uminsky has begun working with Wayne recently. In the past year he has successfully completed his qualifying exams and begun to study the evolution of vortex solutions of the two-dimensional Navier-Stokes equations in the weak vorticity limit. He and Wayne have recently begun a collaboration with two faculty members in the Aerospace and Mechanical Engineering department (G. Sandrini and R. Nagem). They will investigate both theoretically and numerically the small viscosity corrections to the common models of inviscid point vortex motion.
Rigorous asymptotics. Grad student Oleg Mittichenko has continued to work with Kaper, Wayne and with postdoc Popovic to develop new applications of Brujno's method of power geometry. In the past year he has shown how this method can be used to give a new, rigorous and algorithmic derivation of the classical asymptotics of solutions of equations like Airy's equation. He is now studying whether the method can be used to derive asymptotic explansions for the solutions of two-point, singularly perturbed boundary value problems. Forced network of oscillations. In previous work, J. White and Kopell showed numerically that a network of heterogeneous oscillators can react with more power to input in which the phases to different oscillators are dispersed, rather than homogeneous. The reasons why had been mysterious. Grad student Amanda Serenevy and Kopell came up with a proof showing why and how this works in some parameter regimes. The proof reduces the very highdimensional network behavior to a 1-dimensional “timing map”, dependent on the particular drives to the cells, that contains the information about what percentage of the cells will fire in response to the drive.
Canard phenomenon and oscillatory patterns in chemical and biochemical systems. In recent years the canard phenomenon has emerged as a common mechanism underlying various chemical, biochemical and biological phenomena in which they are interactions between more than one "cell". Examples are localized (some cells oscillating at low amplitude or silent, while others oscillate at high amplitude) and mixed-mode oscillation in calcium coupled two-pool model, localized and mixed mode oscillatory cluster patterns in the globally coupled Belousov- Zhabotinsky reaction. In a set of projects, Rotstein, Rachel Kuske, Martin Krupa and Kopell have investigated the above mentioned phenomena in terms of the local canard phenomenon and the global properties of the various systems studied.
Canards in a multi-compartment model. Popovic, Martin Krupa (New Mexico State University), Kopell and Rotstein have continued analyzing the so-called Wilson-Calloway model, which has been proposed to explain the firing patterns observed in dopaminergic neurons in the mammalian brain stem, in the limit of strong electrical coupling among compartments. More recently, they have focused on the formulation of a model problem which, though simpler analytically, still reproduces the salient qualitative features of the full problem. One of the main characteristics of the "toy model" is the presence of three different time scales (fast, slow, super-slow). This separation of scales allows them to access the underlying nearintegrable structure of the problem, to interpret the dynamics as a "slow passage through canard explosion", and to show that this canard phenomenon causes the occurrence of socalled mixed-mode oscillations (MMOs). The relative simplicity of the model problem enables them to derive explicit asymptotic formulae for the associated return map, and to systematically identify the corresponding bifurcation (Farey) sequences. Finally, they also show how the full Wilson- Callaway model can be fit into the above framework via a global center manifold reduction.
Traveling waves in neural networks. Jozsi Jalics is studying traveling waves with Jonathan Rubin and Bard Ermentrout (U. of Pittsburgh). They have used functional analytic techniques to prove the existence of stimulus-locked traveling waves in a firing rate model with a general firing rate function of a one-dimensional excitatory neuronal network modeled by a nonlocal integraldifferential equation. They are working to extend the results to a network which includes inhibition and are planning to study the stability of the waves.
Reduction dimension and diffusion. Popovic has been working with Kaper, Hans Kaper (ANL), Leonid Kalachev (University of Montana), Antonios Zagaris (CWI), and Michael Davis (ANL), on Michaelis-Menten-Henri (MMH)-like kinetics in the presence of diffusion. For the basic MMH mechanism, it is well-known that a dimension reduction can be achieved by exploiting conservation relations between the species, as well as by making use of the underlying separation of time scales. They are investigating under what circumstances a dimension reduction is still possible if the species are allowed to diffuse, and are examining a broad spectrum of diffusivities (very large, very small, and moderate). The main tool used in the analysis is the method of matched asymptotic expansions.
Other reduction dimension. PhD Candidate Christophe Lecomte, working jointly with AME faculty Paul Barbone and J Greg McDaniel, has been studying the problem of projecting high dimensional dynamical systems onto low dimensional subspaces. The linearized eigenvalues of the reduced order problem (so called Ritz values) approximate a some of the eigenvalues of the full problem. Christophe derived highly accurate error bounds on Ritz values and Ritz vectors that approximate eigenvalues of a high dimensional system. This is currently being written up into a paper.
Swarms and hybrid systems. Grad student Marius Kloetzer and Belta focused on both continuous and discrete abstractions for robotic swarms. For continuous abstractions, they investigated the problem of mapping the very large control system describing the swarm to a small control system, capturing its essential features of interest. In the discrete abstraction problem, they studied several types of environment partitions and vector fields for which the finite dimensional discrete abstractions exist. The main tools in both types of abstractions are equivalence relations such as simulations, bisimulations, and language equivalences. The results include the development of discrete abstractions for multi-affine systems, an algorithm for reachability analysis of such systems, a fully automated framework for control of linear systems from LTL formulas over linear predicates, and a fully automated framework for planning and control of fully actuated swarms from temporal logic formulas over their position and shape.
BME PhD candidate Michael S. Richards, expects to finish this summer his PhD thesis on quantitative 3D elasticity imaging, with intended applications to breast imaging. His thesis examines mathematical uniqueness of the 3D problem, computational methods to solve the problem, and experimental evaluation of the techniques. He has recently accepted a postdoctoral research position at the Medical School, University of Michigan, Ann Arbor. There he will have the opportunity to apply many of the imaging methods developed during his PhD within new and ongoing to clinical studies.
AME PhD candidate Nachiket Gokhale, working jointly with AME faculty Assad Oberai and Paul Barbone, has solved a nonlinear inverse problem to measure the nonlinear hyperelastic properties of soft tissue, noninvasively. A particular challenge was dealing with the incompressibility constraint in a stable manner. Nachiket overcame this difficulty by two different methods. His techniques have so far been tested with simulated data, and are currently being written up for publication in a series of papers.
PostDoc Ricardo Leiderman has developed both theoretical and computational models for the mechanics of highly vascularized soft tissue. He's presenting his recent work in two talks at the Spring Meeting of the Acoustical Society of America.
Undergraduate researcher Alexis Mason, under the supervision of faculty advisor Barbone and postdoc Ricardo Leiderman, last summer developed a testing protocol for calibrating the mechanical properties of gelatin tissue mimicking phantom materials. She presented this work at the Annual Biomedical Research Conference for Minority Students (ABRCMS) in Atlanta.
Click here to view our old research page