Biomedical Simulations Resource (BMSR)

Core Project #4

Nonlinear Model of the Hippocampus

Theodore W. Berger, Ph.D.
Project Leader

The research objectives of Core Project #4 are to further develop and apply methodologies based on principles of nonlinear systems analysis for experimentally-based mathematical modeling of neurons and neural systems. A nonlinear systems analytic approach provides the basis for an “external” or “input/output” model, and as such, is particularly well-suited to study of neural systems found in the mammalian brain, i.e., neural systems comprised of multiple populations of neurons, with neurons of each population expressing functional dynamics that are strongly nonlinear and of high order. Of the multiple mechanisms underlying nonlinearities, only some are known; of those that are known, only some are experimentally observable. The particular neural system to be studied is the hippocampus, which is composed of five subsystems (entorhinal cortex, dentate gyrus, CA3 and CA1 pyramidal cell regions, and the subicular cortex) necessary for the formation of new memories. The hippocampus is an ideal brain region to subject to a systems analysis; because the relative simplicity of its anatomical organization permits experimental manipulations that allow its major subsystems and their principal neurons to be studied in the context of progressively simplified network structures. Such an experimental decomposition of the network, when coupled with a theoretical decomposition, allows a determination of the contribution made by each population of neurons to the dynamics of the global system. Moreover, because the processes which determine the activity of a single hippocampal neuron can be subjected to a similar analysis, the impact of subcellular processes on system dynamics can be investigated. Third, afferents to all of the principal neurons in hippocampus are highly laminated, with each afferent terminating on only selective portions of the dendritic tree. Because anatomical studies of this lamination have been extensive, the hippocampus is ideally suited to studying nonlinear interactions among multiple afferents. Finally, the synapses interconnecting hippocampal neurons exhibit several forms of use-dependent plasticity, making it possible to study the same neuronal system as it exists in different functional states. With respect to the “input/output” or “nonparametric model” of hippocampus, our specific aims are the following:

Specific Aim #1

Like virtually all other mammalian CNS neurons, hippocampal granule and pyramidal cells receive synaptic inputs from multiple other neurons which are known to fire both synchronously and asynchronously. All nonlinear systems analytical methods developed and applied to date have involved synchronous activation of hippocampal afferents, i.e., the single input-single output condition. Although the theoretical basis for kernel estimation in the dual input-single output condition has been outlined previously, it has not been applied extensively to neurobiological preparations and not at all to hippocampus. Using newly developed silicon-based multi-site stimulation/recording arrays that now provide a practical experimental means for such simultaneous, selective activation of multiple afferents, we propose to use random impulse train stimulation of the in vitro hippocampal slice to characterize and model:

#1A: nonlinear input/output properties of dentate granule cells in response to microstimulation of (i) medial perforant path fibers, and (ii) lateral perforant path fibers (asynchronous activation of two independent afferents, each having different dynamics);
#1B: nonlinear input/output properties of dentate granule cells in response to microstimulation of (i) medial perforant path fibers, (ii) lateral perforant path fibers and (iii) commissural-associational afferents (asynchronous activation of three independent afferents, each having different dynamics);
#1C: nonlinear input/output properties of dentate granule cells in response to microstimulation of subpopulations of medial perforant path fibers (asynchronous activation of two or more independent afferents, each having the same dynamics).

Specific Aim #2

The primary intrinsic pathway of the hippocampus consists of trisynaptic circuit that includes excitatory perforant path input to dentate granule cells, granule cell excitation of CA3 pyramidal cells, and CA3 excitatory input to CA1 pyramidal neurons. In past studies, we have successfully completed a single-input/single-output model of medial perforant path input to the dentate gyrus. During the past four years, we also have completed a single-input/single-output model of CA3 (Schaffer collateral pathway) input to CA1. We propose to extend our analyses to dentate granule cell (mossy fiber) input to the CA3 subfield, and thus, construct a single-input/single-output model of the entire, intrinsic trisynaptic pathway of hippocampus:

#2A: We will develop a nonlinear systems model of the CA3 region based on random impulse train stimulation of the mossy fiber region (s. lucidum) just dorsal to the CA3 pyramidal layer. There is continued controversy concerning whether such a stimulation paradigm selectively activates mossy fibers or other afferents to CA3. To resolve this difficulty, during the past period of support, we have completed an extensive characterization and modeling of current source density profiles generated in CA3, and we will use results of these studies to extract the nonlinear dynamics of mossy fiber afferents. The resulting model of CA3 will be combined with our existing models of dentate and CA1 to develop a three-stage, cascade model (we also will test the possibility of a feedforward configuration, see below) of the trisynaptic pathway for which each of the three subfields has been characterized separately.
#2B: Utilizing newly developed technology for silicon-based, multi-site electrode stimulation and recording from hippocampal slices, we also will generate an input/output model of the nonlinear dynamics of the entire trisynaptic pathway based on electrical stimulation of perforant path afferents and simultaneous electrophysiological recordings from the dentate, CA3, and CA1. This will provide a model of the trisynaptic pathway in which all three subfields are characterized as a single system. The results will be compared to the three-phase, cascade model generated as part of Specific Aim #2A.;
#2C: Using novel methodology to be developed in collaboration with Dr. Marmarelis (in which variable amplitude outputs from each stage in the hippocampus are considered variable amplitude input impulses to the next subfield), we will decompose the input/output properties of the CA3 subfield from the trisynaptic model results generated as part of Specific Aim #2B. This will allow us to verify whether or not our assumptions about selective activation of mossy fiber stimulation (Specific Aim #2A) are valid.
#2D: Finally, we will test the decomposition methods developed during the past support period to test a critical hypothesis concerning the architecture of the intrinsic circuitry of hippocampus. Specifically, anatomical relations between the entorhinal cortex, dentate gyrus, and the pyramidal cell regions of the hippocampus traditionally have been conceived of as a cascade in which entorhinal input initiates a sequential excitation of the other subsystems. In other previous work, we have established that entorhinal input excites dentate and CA3 simultaneously, arguing instead for a feedforward configuration. We will test this hypothesis through theoretical evaluation of cascade and feedforward models of the perforant path, dentate, and CA3.

Specific Aim #3

Collectively, Specific Aims #1 and #2 will provide us with a nonlinear input/output model of the equivalent of one transverse slice of the hippocampus, with multiple input dynamics for the dentate gyrus, the first of the three major stages of the trisynaptic pathway. We propose to use these results as the basis for developing a large-scale, “three-dimensional” model of the hippocampal dentate gyrus, CA3, and CA1, i.e., multiple representations of the trisynaptic pathway. We also will include results of our past work that characterized GABA_A and GABA_B receptor-mediated forms of inhibition, with results from Specific Aim #1B (commissural-associational afferents) as a basis for functionally coupling the multiple transverse slice models into a system model. Although initially the large-scale model will be more complete for dentate than for other subsystems (because of the inclusion of multiple input dynamics), the CA3 and CA1 components of the model will be expanded as our multiple input studies extend to those subfields. We will verify the large-scale model by attempting to account for experimentally observed spatio-temporal patterns of excitation and inhibition evoked by multi-site electrical stimulation in vivo, and for spatio-temporal patterns of granule cell and pyramidal cell activity observed in behaving animals.

In parallel with the nonlinear systems approach, we also are developing an “internal” or “parametric” model of the hippocampus, i.e., a model in which each neurobiological process considered is represented explicitly through a different parameter, and the spatial relations between neurons are included as a set of geometrical constraints. For example, during the past support period, we developed a parametric model of a glutamatergic synapse, including the presynaptic terminal and the mechanisms responsible for neurotransmitter release, the relative positions of the major molecular entities within the presynaptic space, the geometry of the synaptic cleft, kinetic models of AMPA and NMDA postsynaptic receptor-channels, and their relative positions with respect to the locations of presynaptic release sites. Thus, included in the parametric model at this stage is a population of perforant path terminals and a population of granule cell bodies and dendrites; no other populations of neurons or subsystems are considered. In other words, the parametric model assumes the equivalent of an open-loop condition for granule cells -- the most simplified set of conditions we have created to date in developing the nonparametric model. Our strategy is to use both types of models in a complementary manner. The input/output model can provide an experimentally-based description of the functional interaction between components of a neural system, and in this sense, should provide useful constraints in development of a corresponding parametric model of the same system.

Specific Aim #4

We propose to expand the number of mechanisms included in the presynaptic component of the model so that we can account for additional higher order nonlinearities that the present model does not replicate, e.g., post-tetanic potentiation and augmentation that are induced by high-frequency stimulation (and that are known to optimally activate NMDA receptors). Because mobilization of reserve synaptic vesicles becomes critical to sustain release in response to higher frequencies of synaptic activation, the interaction of Ca2+ with molecular species deeper in the presynaptic terminal (e.g., synapsins) will be included in the model. We also will add other presynaptic conductances (e.g., Ca²⁺-activated K⁺ conductances) and mechanisms (mitochrondrial uptake) known to influence Ca²⁺ diffusion and release.

Specific Aim #5

In the previous support period, we developed a new generation of synaptic model that includes a representation of intracellular Ca²⁺ diffusion and molecular kinetics within the context of arbitrarily defined geometrical shapes (boundaries of the presynaptic terminal). We coupled the MATLAB PDE solver with the set of ordinary differential equations describing Ca²⁺-channel influx, Ca²⁺ diffusion, Ca²⁺ pumping and buffering, and the chemical interactions between Ca²⁺ and various intracellular molecules. Together, this capability allows the study of the effect of synaptic morphology on presynaptic distribution of calcium and thus, on neurotransmitter release. Working with collaborators conducting EM anatomical studies of synaptic morphology, we will investigate further the consequences for synaptic function of different classes of synaptic geometries.

Specific Aim #6

We will extend our modeling of Ca²⁺ influx and dynamics to include the postsynaptic spine. The goal is to begin to account for activity-dependent changes in postsynaptic Ca²⁺ that play critical roles in Ca²⁺-dependent forms of synaptic plasticity such as long-term potentiation (LTP) and long-term depression (LTD). It has long been postulated that the magnitude of NMDA receptor-channel-mediated increases in postsynaptic Ca²⁺ determines whether patterned synaptic stimulation leads to AMPA receptor-channel LTP (high Ca²⁺) or LTD (low Ca²⁺). We have published both theoretical and experimental evidence that NMDA receptor-channels themselves also undergo LTP and LTD, strongly suggesting that an initial induction of synaptic plasticity alters the presynaptic stimulus patterns required to induce further LTP or LTD. We will investigate this and other hypotheses with a new compartmental neuron model that includes both presynaptic release dynamics and postsynaptic Ca²⁺ influx and spatio-temporal distribution.

Specific Aim #7

Finally, we will begin a systematic comparison of nonparametric and parametric models. Our strategy will be to have a given nonparametric model be based on experimental characterizations of the equivalent neuronal elements and circuitry represented in a given parametric model. We will begin with a “minimal” case, namely, whole cell voltage-clamp analysis of AMPA receptor-mediated synaptic currents (recorded during pharmacological blockade of NMDA receptor-mediated currents). These conditions should be equivalent to processes included in our parametric model of presynaptic processes combined with the kinetics of the AMPA receptor-channel. We will determine whether or not such a relatively restricted release-kinetic model can account for the nonlinearities observed experimentally and represented in the nonparametric model. We then will progressively increase the complexity of our parametric model and examine how systematic variation of pre- and postsynaptic parameters alters input/output nonlinear properties.

Selected Publications

Kim, M., W. Soussou, G. Gholmieh, A. Ahuja, A.R. Tanguay Jr., T.W. Berger and R.D. Brinton. 17β-estradiol potentiates field excitatory postsynaptic potentials within each subfield of the hippocampus with greatest potentiation of the associational/commissural afferents of CA3. Neuroscience 141:391-406, 2006. [PDF – 2,212 KB]

Gholmieh, G., W. Soussou, M. Han, A. Ahuja, M.C. Hsiao, D. Song, A.R. Tanguay Jr. and T.W. Berger. Custom-designed, high-density conformal planar multielectrode arrays for brain slice electrophysiology. Journal of Neuroscience Methods 152:116-129, 2006. [PDF – 1,150 KB]

Berger, T.W., and Glanzman, D.L. Toward Replacement Parts for the Brain: Implantable Biomimetic Electronics as the Next Era in Neural Prosthetics. Cambridge, MA: MIT Press, 2005.

Gholmieh, G., S. Courellis, A. Dimoka, J.J. Granacki, V.Z. Marmarelis and T.W. Berger. An algorithm for real-time extraction of population EPSPs and spikes from hippocampal field potentials. Journal of Neuroscience Methods 136:111-121, 2004. [PDF - 332 KB]

Namarvar, H.H. and T.W. Berger. An efficient training algorithm for dynamic synapse neural networks using trust region methods. Neural Networks 16:585-591, 2003. [PDF - 293 KB]

Gholmieh, G., S. Courellis, S. Fakheri, E. Cheung, V.Z. Marmarelis, M.Baudry and T.W. Berger. Detection and classification of neurotoxins using a novel short-term plasticity quantification method. Biosensors and Bioelectronics 18:1467-1478, 2003. [PDF - 606 KB]

Berger, T.W., J.J. Granacki, v.Z. Marmarelis, B.J. Sheu and A.R. Tanguay, Jr. Brain-implantable biomimetic electronics as neural prosthetics. Proceedings of the 1st International IEEE EMBS Conference on Neural Engineering, 108-111, 2003.

Song, D., Z. Wang, V.Z. Marmarelis, and T.W. Berger. Non-parametric interpretation and validation of parametric models of short-term plasticity. Proceedings of the 25th IEEE-EMBS Conference, 1901-1904, 2003.

Gholmieh, G., S.H. Courellis, D. Song, Z. Wang, V.Z. Marmarelis and Berger. Characterization of short-term plasticity of the dentate gyrus-CA3 system using nonlinear systems analysis. Proceedings of the 25th IEEE-EMBS Conference, 1929-1932, 2003.

Dimoka, A., S.H. Courellis, D. Song, V.Z. Marmarelis, and T.W. Berger. Identification of lateral and medial perforant path using single- and dual-input random impulse train stimulation. Proceedings of the 25th IEEE-EMBS Conference, 1933-1936, 2003.

Song, D., Z. Wang and T.W. Berger. Contribution of T-Type VDCC to TEA-Induced long-term synaptic modification in hippocampal CA1 and dentate gyrus. Hippocampus 12:689-697, 2002. [PDF - 220 KB]

Wang, Z., D. Song and T.W. Berger. Contribution of NMDA receptor channels to the expression of LTP in the hippocampal dentate gyrus. Hippocampus 12:680-688, 2002. [PDF - 226 KB]

Song, D., X. Xiaping, Z. Wang and T.W. Berger. Differential effect of TEA on long-term synaptic modification in hippocampal CA1 and Dentate Gyrus in vitro. Neurobiology of Learning and Memory 76:375-387, 2001. [PDF - 552KB]

Alataris, K., T.W. Berger and V.Z. Marmarelis. A novel network for nonlinear modeling of neural systems with arbitrary point-process inputs. Neural Networks 13(2):255-266, 2000. [PDF - 468KB]

Foy, M., T.W. Berger and R.F. Thompson. Estrogen and neural plasticity. Current Direction in Psychological Science 9(5):148-152, 2000. [PDF - 301 KB]

Chian, M., V.Z. Marmarelis and T.W. Berger. Decomposition of neural systems with nonlinear feedback using stimulus-response data. Neurocomputing 26-27:641-654, 1999. [PDF - 347 KB]

Liaw, J.-S. and T.W. Berger. Dynamic synapse: Harnessing the computing power of synaptic dynamics. Neurocomputing 26-27:199-206, 1999.

Iatrou, M., T.W. Berger and V.Z. Marmarelis. Modeling of nonlinear nonstationay dynamic systems with a novel class of artificial neural networks. IEEE Trans. Neural Networks, 10:327-339, 1999.

Yeckel, M.F. and T.W. Berger. Spatial distribution of potentiated synapses in hippocampus: Dependence on cellular mechanisms and network properties. J. Neuroscience, 18:438-450, 1998. [PDF - 683 KB]

Tsai, R.H., J.B. Sheu and T.W. Berger. A VLSI neural network processor based on a model of the hippocampus. Analog Integrated Circuits & Signal Processing 15:201-213, 1998. [PDF - 492 KB]

Xie, X., J.-S. Liaw, M. Baudry and T.W. Berger. Novel expression mechanism for synaptic potentiation: Alignment of presynaptic release site and postsynaptic receptor. Proc. National Academy of Sciences 94:6983-6988, 1997.

Liaw, J.-S., and T.W. Berger. The dynamic Synapse: A new concept for neural representation and computation. Hippocampus, 6:591-600, 1996. [PDF - 218 KB]

Berger, T.W., B.J. Sheu, and R.H.-K. Tsai. Biologically realistic models of memory function implemented using analog VLSI technology. In: Microsystems Technology for Multimedia Applications, B. Sheu, M. Ismail, E. Sanchez-Sinencio and T. Wu (Eds.). N.Y.: IEEE Press, pp. 381-394, 1995.

Yeckel, M.Y., and T.W. Berger. Monosynaptic excitation of CA1 hippocampal pyramidal neurons by afferents from the entorhinal cortex. Hippocampus 5(2):108-114, 1995.