Network structure determines patterns of network reorganization during adult neurogenesis
Casey M. Schneider-Mizell, Jack M. Parent, Eshel Ben-Jacob, Michal Zochowski, Leonard M. Sander
NNetwork structure determines patterns of networkreorganization during adult neurogenesis
Casey M. Schneider-Mizell , Jack M. Parent , Eshel Ben-Jacob ,Michal Zochowski *1,3,4,5 , Leonard M. Sander *1,5 Departments of Physics, Neurology, Biophysics Research Division, Neuroscience Graduate Program, and Michigan Center for Theoretical Physics,University of Michigan, Ann Arbor, Michigan 48109, USA; School of Physics and Astronomy, Tel-Aviv University, Tel Aviv, IsraelOctober 29, 2018
Abstract
New cells are generated throughout life and integrate into the hippocam-pus via the process of adult neurogenesis. Epileptogenic brain injury inducesmany structural changes in the hippocampus, including the death of interneu-rons and altered connectivity patterns. The pathological neurogenic nicheis associated with aberrant neurogenesis, though the role of the network-levelchanges in development of epilepsy is not well understood. In this paper, we usecomputational simulations to investigate the effect of network environment onstructural and functional outcomes of neurogenesis. We find that small-worldnetworks with external stimulus are able to be augmented by activity-seekingneurons in a manner that enhances activity at the stimulated sites withoutaltering the network as a whole. However, when inhibition is decreased or con-nectivity patterns are changed, new cells are both less responsive to stimulusand the new cells are more likely to drive the network into bursting dynam-ics. Our results suggest that network-level changes caused by epileptogenicinjury can create an environment where neurogenic reorganization can induceor intensify epileptic dynamics and abnormal integration of new cells. a r X i v : . [ q - b i o . N C ] D ec Introduction
Continuous introduction of new neurons via adult hippocampal neurogenesis is thoughtto assist memory formation and storage (1; 2; 3). While many details of neurogenesisat the molecular and cellular level are known (4), the effect of network environmenton the integration of newly born cells remains unresolved. In this paper, we use acomputational model to investigate how the established network structure can alterpatterns of neural integration and how these changes affect the evolution of structureand dynamics.Hippocampal neuroblasts arise from progenitor cells in the subgranular zone ofthe dentate gyrus (DG) and migrate a short distance into the granule layer (5; 6; 7; 8).They develop synaptic inputs from GABAergic interneurons whose activity promotesthe development of neural processes (9; 10). After weeks, they form glutamergicsynapses onto mossy cells and interneurons (11). Studies have found new granulecells to be preferentially activated by stimulation (12) and to have sensitive synapticplasticity (13). These findings show neurogenesis to be promoted by and respondspecifically to activity in the established network.Epileptogenic injury can significantly alter the neurogenic niche. Mossy fibersprouting increases the number of granule cell synaptic outputs, hilar cell deathreduces inhibition, and granule cell dispersion changes the spatial structure of thegranule cell layer (14). Additionally, seizures form a different pattern of activity. Therate of neurogenesis after status epilepticus has been observed to increase (15). Someneuroblasts migrate ectopically into the hilus and, unlike in the healthy brain (15;16; 17), appear to receive synapses from other granule cells (18).Previous computational work on neurogenesis has focused on learning and mem-ory (19; 20; 21; 22; 23). Here, we consider the general question of how the networkactivity and structure affects new cell integration and long term network activity.We build a computational model with simplified neurogenesis rules and study spa-tial patterns of integration as a function of structural characteristics of the networkenvironment. We consider two levels of inhibition: 1) when the ratio of inhibitoryto excitatory cells represents that observed in the healthy hippocampus, and 2) thatof epileptic hippocampus with a reduced inhibitory population. Under normal con-ditions, we find an optimal network topology which is dynamically and structurallyrobust to the addition of new neurons. For other network structures or decreasedinhibition, neurogenesis leads to significant structural and dynamical changes in theunderlying network. We thus postulate that there is a range of normal conditionsin which neurogenesis could enhance network performance, but if the underlyingnetwork structure is pathological, it can worsen the pathology.2
Materials and Methods
The simulation is broken into three primary aspects: creation of the establishednetwork structure, the neuronal dynamics, and the integration of new neurons. SeeTable 4 for a consolidated list of all parameters.
We create the initial networks prior to neurogenesis by placing 1000 excitatory neu-rons and either 200 (normal conditions) or 100 (reduced inhibition) inhibitory neu-rons at random on a two-dimensional square lattice with 40 lattice sites per side andperiodic boundaries. A lattice site can hold at most one excitatory cell. Inhibitorycells are placed on a location independent of its occupancy status. We specify thateach excitatory cell will be connected to, on average, 3.5% of the other excitatorycells.We consider random networks with variable rewiring to represent connectionsbetween neurons. This type of model is well known to possess a small-world regime(24). See Figure 1 for a cartoon of the following process. For each cell we deter-mine its downstream (axonal) connections by looking within a radius (R) containingtwice the desired average number of out-connections and connecting to each withprobability 1/2. For each connection, we rewire it to a randomly chosen excitatorycell anywhere in the network with a probability, p , which we vary. For p = 0, allconnections are local, and for p = 1 all connections are random. Each excitatoryneuron is also connected to, on average, four inhibitory neurons through the sameprocedure as described above, without random rewiring. All excitatory-to-inhibitoryconnections are therefore local. Inhibitory cells send out-connections to, on average,four other inhibitory cells and 100 excitatory cells. These targets are selected purelyat random. We adopted this connectivity structure to roughly represent that of theCA3 layer of the hippocampus (25). However, the reported results are robust tochanges in these parameters (see Supplementary Data). We represent network activity with integrate-and-fire dynamics with stochastic spon-taneous firing. While integrate-and-fire is only a very rough approximation of thedynamics of real neurons, it is sufficient for the purposes of our model, for whichconnectivity, not detailed dynamics, is paramount.3n the integrate-and-fire scheme, the i th cell has a voltage V i which follows: dV k dt = ( I e/i + E k − α k V k ) + (cid:88) j w jk A jk I jsyn ( t + τ delay ) , where I e/i is the global excitability of excitatory/inhibitory neurons, depending onwhat class of neuron k belongs to. The initial potentials are distributed uniformlyat random between 0 and 1. The cellular and network parameters are adopted from(25). We use I i = 0 . I e = 0 .
73. The external stimulus is denoted by E k ,which is 0 for unstimulated cells and 0.4 for those which receive external stimulus.Stimulus occurs at the five centermost excitatory cells. The membrane leak constantis α k , drawn for each cell from a uniform distribution between 1 and 1.3. Thenetwork adjacency matrix elements are denoted by A jk , which is 1 if neuron k sendsan output to neuron j and 0 otherwise. The synaptic weight is denoted by w jk .Synaptic weight is based only on the class of the neurons involved, with w ee = 0 . w ei = 0 . w ie = − .
4, and w ii = − .
7. The negative sign represents inhibition.Synaptic weight and excitability parameters are inspired by (25), where they weretuned to give controlled dynamics. Finally, the synaptic current from the j th neuronis I jsyn ( t ), where I syn ( t ) comes from a double exponential based on the time t sinceneuron j fired plus a signaling delay τ delay = 0 . I syn ( t ) = e − t/τ S − e − t/τ F where τ S = 3 ms and τ F = 0 . ms . This spike form is taken from (26).The voltage dynamics is numerically solved using the Euler method. Membranepotentials are capped below by 0 and if V j >
1, the neuron j fires. All cells also havea probability of 0.0003 per ms of spontaneously firing, providing a mean backgroundfiring rate per cell of 0.3Hz. When a neuron fires, its potential is reset and held at 0for a refractory time of 8 ms. In order to represent neurogenesis, we introduce a new neuron every 350 ms afteran initial 1,000 ms of simulation time. A new cell is placed on a randomly chosenunoccupied lattice site. We then proceed to form inward (dendritic) and outward(axonic) connections. We form inward connections by compiling a list of all inwardconnections of neighboring cells (within radius R/
2) to the newly added one. Thislist denotes the possible in-connections. Inputs are drawn from this list by assigning4 score g i to each neuron on the list based on firing rate f i and a small amount ofrandom jitter ω drawn uniformly between 0 and 1: g i = a f i max { i } f i + (1 − a ) ω. The parameter a determines the amount of randomness in the selection process. Weuse a = 0 . g are selected to be inputs to the new cell,until the appropriate number of inputs is reached. Our results are not sensitive tomodest changes in a (see Supplementary Data).Similarly, the output connections are drawn from downstream targets of nearbycells. Connections are made to a random subset of possible outputs until the newcell has the same average number of connections as the original network.During the initial stages of its dynamics the network can undergo rapid rewiring.At intervals of 200 ms of simulation time, all output connections which do not resultin a sufficient number of coincident firing events (defined as a post-synaptic cell firingwithin 10 ms after the pre-synaptic cell fires) are broken and new connections areagain chosen at random. After 2000 ms of simulation time, the new cell either dies ifits firing rate is less than 100 times the spontaneous background firing rate (0.3Hz) ormatures and ceases to undergo changes in its connections. When a new cell survives,the total population is kept constant by killing a randomly chosen mature cell.Birth and maturation rates are chosen so that there is little interaction betweentwo immature cells and the network activity is well sampled. Spatial activity dis-tributions were not observed to change considerably for the parameters used here,except in response to new cells. Network activity can thus be well measured by 2000ms of activity, even though it is not a physiologically relevant time period.Except where noted, simulations are performed by first running dynamics on thestimulated initial network for 1000 ms to establish baseline activity. We then add 500new cells as described above, and stop the simulation 1000 ms after the last new cellhas had an opportunity to mature. Each data point represents 50 realizations. Allsimulations, data analysis, and plotting were performed in Matlab 7.7.0 (Mathworks). To measure and visualize the firing activity, survivorship, and number of reconnectionevents as a function of location, we break the space into a 20 ×
20 grid of squarescovering the network space, so that each square represents four lattice sites. Activity5nd reconnection events are both measured as the average value among all cells thatfall within a given square. For survivorship, we report the average number of cellsthat survive within a given square.
To measure the mean radial component of output connections, we first create a vectorfor each new cell that represents the average direction of all outputs. This is definedas (cid:126)v i = 1 k i (cid:88) j A ji (cid:126)x j − (cid:126)x i | (cid:126)x j − (cid:126)x i | where k i = (cid:80) j A ji is the number of out-connections from neuron i . We then measurethe inward radial component by taking the dot product of this mean direction withthe inward-pointing unit radial vector ˆ r at the location of the ith neuron and normal-izing by the magnitude of (cid:126)v i : ˆ r · (cid:126)v i / | (cid:126)v i | . This is averaged for all surviving new neuronsin each simulation. Values close to one indicate highly radial directionality amongnew neurons’ outputs. Values near zero are consistent with random directions. We use an existing measure of synchronicity of bursting based on interspike timedifferences (27). We first make an ordered list of all spike times t ν for all excitatorycells. The measure B is defined as B = 1 √ N (cid:32) (cid:112) (cid:104) τ ν (cid:105) − (cid:104) τ ν (cid:105) (cid:104) τ ν (cid:105) − (cid:33) where τ ν = t ν − t ν +1 is the time difference between subsequent firing events for on theexcitatory network and angle brackets indicate averages over all such time differences.For large N and all neurons firing as independent Poisson processes, B = 0, and forsynchronous bursting B = 1. The relative intraburst order of new and old cells is measured as the time differencebetween the onset of new cells bursting and old cells bursting. We define the onsetof a burst as the time at which the number of new or old cells firing simultaneouslyincreases past four. We make a list of the onset of all new and old bursts. For eachburst of new cells, we record the time difference to the closest old burst onset. The6onvention is chosen such that an old burst that leads a new burst has a negativetime difference.
Adult male Sprague-Dawley rats were pretreated with atropine methylbromide (5mg/kg intraperitoneally [IP]; Sigma), and 15-minutes later were given pilocarpinehydrochloride (340 mg/kg IP; Sigma) to induce SE. Seizures were terminated withdiazepam (10 mg/kg) after 90 minutes of SE as previously described (28). Controlsreceived the same treatments as experimental animals except that they were givensaline in place of pilocarpine.
Replication-incompetent recombinant RV vectors were pseudotyped by co-transfectionof GP2-293 packaging cell line (Clontech,) with plasmids containing the RV vector(RV-CAG-GFP-WPRE, gift of S. Jessberger and F. Gage) and vesicular stomatitusvirus (VSV)-G envelope protein (Clontech). The supernatant containing RV washarvested and filtered through a 0.45- µ m pore size filter (Gelman Sciences) and cen-trifuged in a Sorvall model RC 5C PLUS at 50,000xg at 4 ◦ C for 90 minutes. TheRV-containing pellet was resuspended in 1X PBS, aliquoted, and subsequently storedat -80 ◦ C until use. The concentrated RV titer was determined using NIH 3T3 cellsand found to be approximately 1-5 x 108 CFU/mL. For intrahippocampal RV injec-tions, animals were anesthetized with a ketamine/xylazine mixture and placed on awater-circulating heating blanket. After positioning in a Kopf stereotaxic frame, amidline scalp incision was made, the scalp reflected by hemostats to expose the skull,and bilateral burr holes drilled. RV vector (2.5 µ L of viral stock solution was injectedinto the left and right dentate gyri over 20 minutes each using a 5 µ L Hamilton Sy-ringe, and the micropipette left in place for an additional 2 minutes. Coordinatesfor injections (in mm from Bregma and mm depth below the skull) were caudal 3.9;lateral 2.3, depth 4.2.
Four weeks after SE, animals were deeply anesthetized and perfused with 4% paraformalde-hyde (PFA). The brains were removed, postfixed for 4-6 hours in 4% PFA, cry-oprotected in 30% sucrose and frozen. Coronal sections (40 µ m thick) were cutwith a freezing mictrotome and fluorescence immunohistochemistry was performed7n free-floating sections (15; 29) using rabbit anti-GFP primary antibody (1:1000,Invitrogen) and Alexa 488-conjugated anti-rabbit IgG secondary antibody (1:400,Invitrogen). Images were captured using a Zeiss LSM 510 confocal microscope. The purpose of the simulations was to understand how the network connectivitystructure may influence spatial patterns of network augmentation during the adultneurogenesis and the dynamical patterns of the resulting network. We investigatedthe spatial patterns of neurogenesis, their established connectivity patterns and theirdynamics with relation to the existing cells as a function of the network topology.This study was carried out for two cases: 1) when the inhibition resembles thatobserved during the normal conditions and 2) when the inhibition is reduced torepresent the situation after loss of hilar interneurons as in temporal lobe epilepsy.
The topology of the initial network in our model is inspired by Watts-Strogatz net-works (24). The network structure depends on a parameter, p , which controls therewiring probability of a given connection between excitatory cells. This parameterallows the connectivity of excitatory-excitatory networks to range from purely local( p = 0) to purely random ( p = 1), while preserving many other aspects of the net-work such as the degree (i.e. cell connectivity) distribution. Between the local andglobal extremes is a small-world topology. Small-world networks are characterizedby having short average path lengths between any two nodes, but a high probabilitythat the neighbors of a given node are connected to one another, as measured by theclustering coefficient (30). One can determine the range of values of p for which thenetwork exhibits small-world characteristics by measuring the clustering coefficientand mean path length (Figure 2). We observe small-world structure in our excitatorynetworks around p = 0 . We first consider how the network activity patterns respond to external stimulus fordifferent network topologies. We stimulated five excitatory neurons positioned inthe center of the network by applying an additional constant current. The spatial8istribution of activity in the network after the addition of new cells as a function ofrewiring probability p and the amount of inhibition in the original network is shownin Figure 3. For established networks with p < . p . This confirms that our neurogenesis process cansharpen the response of our network to a stimulus. Increasing the rewiring anddecreasing inhibition each result in a global increase of firing rate, with amountsvarying depending on the details of the network.We next consider the spatial patterns of survivorship of cells that we added. Weobserved that, as above, for local connectivity and normal inhibition, the location ofactive network reorganization (i.e. high survival probability for new cells) is focusedaround the stimulation area (Figure 5). This effect diminishes for more global con-nectivity and decreased inhibition. This indicates that to maintain specific activityafter incorporation of new cells, as we expect in normal hippocampal conditions, theestablished network must have relatively local connectivity of the original networkand sufficiently high levels of inhibition.We can develop a general picture of what occurs for each network structure bymeasuring the mean radius of survivors in the network calculated from the center ofthe stimulation and mean number of new cells that survive (Figure 6a and b). Tosee how initial activity affects survivorship and changes in activity, we also plot thespace-averaged correlation between initial network activity and survival probabilityas well as the correlation between initial activity and change in activity (Figure 6c andd). These measurements are done for both high inhibition regime and low inhibition.Note that the correlation between activity and change in activity is artificially low,since the locations that have the highest activity may be unable to fire faster due tothe refractory time setting a maximum frequency.We observe that under normal inhibition the smallest number of added cellssurvives when the network is in the small-world regime. Furthermore, the highestcorrelation between initial activity and survival probability also occurs for the sameregime. Peak correlation for change in activity is at a slightly different location thansurvivorship, but still in the range where the established network is small-world.Increasing the rewiring parameter p , and thus the number of random connections, anddecreasing the inhibition have similar effects of reducing correlation and increasingboth the number of surviving cells and the spatial extent of where they survive andactivate the network. 9e also considered the effect of an increase in the number of connections betweenexcitatory neurons (see Supplementary Data). We find that increasing the excitatoryto excitatory connectivity from 3.5% to 4.5% while retaining normal inhibition doesnot qualitatively change the pattern of rewiring above p = 0 .
2. However, for p ≤ . The newly born neurons are thought to have higher structural plasticity, enablingthem to rapidly form and abolish synaptic connections to other cells. This poten-tially allows the cells to optimally integrate themselves into the existing networks.In our simulation this reconnection occurs when an immature neuron is unable togenerate a sufficient number of downstream coincident firing events. We observedthat the number of activity dependent reconnection events per surviving cell is high-est for global network topologies (Figure 7d). Furthermore, networks with loweredinhibition exhibit lower rates of reconnection events for p < . p and inhibition (Figure 8). Under normal inhibition and for relatively localnetworks, cells that lie outside the immediate stimulated area undergo significantlymore reconnection events. Established cells within the stimulated region are morelikely than remote cells to respond to firing events from new cells, making it an easierregion to wire into. This effect becomes less dramatic and eventually goes away formore random network topologies as well as for networks with diminished inhibition.Another important feature of neurogenesis is the innervation pattern of the newcells. We consider each synaptic connection to be spanned by a long axon and shortdendrites, such that the direction of a connection is roughly that of the innervatingaxon. For low values of p , a clear pattern of radially oriented outputs toward thestimulation site can be observed among introduced cells (Figure 7c). This disap-pears for large p . To quantify this, we plotted the average radial component forthe output directions of all surviving new cells (Figure 7d). The networks having10ormal inhibition levels that develop the most highly ordered (i.e. directed towardstimulus) connectivity are those having small-world properties. More random net-works continue developing without any strongly ordered directionality. Additionally,low inhibition networks are not able to develop the same degree of directionality asnormal networks. We also investigated differences in the firing patterns of new and established cells inreorganized networks. If we look at traces of the cumulative activity patterns, we cansee that for small-world networks, activation of new neurons overlaps with that ofthe already existing cells (Figure 9a) without a significant lead-lag pattern emergingbetween the activations of the two populations. For random networks, bursts fromnew cells tend to lead those of the original ones (Figure 9b).To quantify this observation, we measured the time difference between the onsetof bursts of the old and new subpopulations (Figure 9c). This time difference isnegative when old cells lead and positive when new cells lead. We restrict ourselvesto data taken from the end of the simulation. We see that, in most cases, new cellswill lead bursts in the established network. The only case where the establishednetwork consistently leads bursts is for low rewiring and normal inhibition. Thetransition between which cell population leads occurs when the network is in thesmall-world regime.Notably, for low inhibition there is never a regime with a negative time difference.However, the new cell lead time is generally smaller for low inhibition because theestablished network requires less activity to be driven.
Finally we wanted to investigate how robust is the network dynamics to addingnew cells. To address this, we ran simulations that terminated when 500 new cellssurvived and were incorporated into the network, instead of 500 being introduced tothe network. Because of this, some simulations were run for longer time period thanothers. We quantified the activity patterns with the mean frequency of the networkand a measure of synchronous bursting, B .Local networks are much more robust to activity-dependent reorganization thanthose with more random connections (Figure 10). In all cases, established networkswith low p tolerate the incorporation of activity-seeking neurons with only modestincreases in activity and synchronous firing. Networks with more global connections11tart with slightly less activity, but are not able to accommodate the same number ofneurons without having increasing firing rate and spontaneous bursting. Decreasinginhibition does not qualitatively change this behavior, although the mean firing rateis generally higher. In this work, we investigated how network topology can mediate changes in networkstructural and dynamical reorganization during neurogenesis. To that effect we con-structed a simplified model incorporating activity dependent augmentation rules andinvestigated outcomes as a function of topology.We observed that the networks with sufficiently high inhibition and small-worldtopology are robust to incorporation of the new cells in terms of structural anddynamical properties. In these networks pre-existing spatial and temporal firingpatterns are reinforced by new neurons, with survival and connectivity patternshighly stimulus dependent. This is consistent with the idea that hippocampal neu-rogenesis contributes to memory formation via high stimulus dependent plasticity.Networks with less inhibition or more long range connections are unstable to activity-dependent augmentation. Activity becomes more globally synchronized and new cellsincorporate more randomly and in stimulus independent fashion. Taken together,these results indicate that structural network differences alone can be sufficient tocause qualitatively different outcomes after neurogenic reorganization. Moreover,the changes that occur in the hippocampal network after the onset of epilepsy aresimilar to the changes in our network model that induce global synchrony and erraticincorporation of new neurons.Considerable experimental (31; 32; 33) and computational work (19; 20; 21; 22;23) has focused on the role of neurogenesis in learning. While results are not entirelyconsistent in their details, there is a general consensus that the highly plastic newcells increase the ability of the hippocampus to store, maintain, and retrieve spatialmemories. In order to do this, new cells have to be able to respond with specificityto stimulus (2).We found our network to have stable, focused reorganization by neurogenesisfor a small range of rewiring probabilities near p = 0 . even more patholog-ical state. Critically, the differences in outcome can be entirely due to differences inthe initial neurogenic environment, without any changes in the underlying biochem-istry of the neurogenic process. Small-world networks with sufficiently high inhibitionwere found to be the most robust to activity dependent neurogenesis. Changes to ourinitial model network that mirrored structural changes to the DG following epilepto-genic injury resulted in changes to neurogenic patterns consistent with experimentalobservation. Connections became less focused and many more cells were able to en-ter the network. Global synchronous activity also increased. These results suggestthat neurogenesis in pathological environments can result in either the developmentor progression of epilepsy. 14 eferences James B Aimone, Janet Wiles, and Fred H Gage. Potential role for adult neuro-genesis in the encoding of time in new memories.
Nat Neurosci , 9(6):723–7, Jun2006.Alcino J Silva, Yu Zhou, Thomas Rogerson, Justin Shobe, and J Balaji. Molec-ular and cellular approaches to memory allocation in neural circuits.
Science ,326(5951):391–5, Oct 2009.C Zhao, W Deng, and F Gage. Mechanisms and functional implications of adultneurogenesis.
Cell , Jan 2008.Darrick T Balu and Irwin Lucki. Adult hippocampal neurogenesis: regulation,functional implications, and contribution to disease pathology.
Neuroscience andbiobehavioral reviews , 33(3):232–52, Mar 2009.J Altman and G D Das. Autoradiographic and histological evidence of postnatalhippocampal neurogenesis in rats.
J Comp Neurol , 124(3):319–35, Jun 1965.M S Kaplan and J W Hinds. Neurogenesis in the adult rat: electron microscopicanalysis of light radioautographs.
Science , 197(4308):1092–4, Sep 1977.H A Cameron, C S Woolley, B S McEwen, and E Gould. Differentiation of newlyborn neurons and glia in the dentate gyrus of the adult rat.
Neuroscience , 56(2):337–44, Sep 1993.H G Kuhn, H Dickinson-Anson, and F H Gage. Neurogenesis in the dentate gyrus ofthe adult rat: age-related decrease of neuronal progenitor proliferation.
J Neurosci ,16(6):2027–33, Mar 1996.Linda S Overstreet-Wadiche and Gary L Westbrook. Functional maturation ofadult-generated granule cells.
Hippocampus , 16(3):208–15, Jan 2006.S Ge, D Pradhan, G Ming, and H Song. Gaba sets the tempo for activity-dependentadult neurogenesis.
Trends Neurosci , Jan 2007.Nicolas Toni, Diego A Laplagne, Chunmei Zhao, Gabriela Lombardi, Charles ERibak, Fred H Gage, and Alejandro F Schinder. Neurons born in the adult dentategyrus form functional synapses with target cells.
Nat Neurosci , 11(8):901–7, Aug2008. 15ictor Ramirez-Amaya, Diano F Marrone, Fred H Gage, Paul F Worley, andCarol A Barnes. Integration of new neurons into functional neural networks.
JNeurosci , 26(47):12237–41, Nov 2006.Christoph Schmidt-Hieber, Peter Jonas, and Josef Bischofberger. Enhanced synap-tic plasticity in newly generated granule cells of the adult hippocampus.
Nature ,429(6988):184–7, May 2004.P S Buckmaster and F E Dudek. Network properties of the dentate gyrus in epilepticrats with hilar neuron loss and granule cell axon reorganization.
J Neurophysiol ,77(5):2685–96, May 1997.J M Parent, T W Yu, R T Leibowitz, D H Geschwind, R S Sloviter, and D HLowenstein. Dentate granule cell neurogenesis is increased by seizures and con-tributes to aberrant network reorganization in the adult rat hippocampus.
J Neu-rosci , 17(10):3727–38, May 1997.H E Scharfman, J H Goodman, and A L Sollas. Granule-like neurons at the hilar/ca3border after status epilepticus and their synchrony with area ca3 pyramidal cells:functional implications of seizure-induced neurogenesis.
J Neurosci , 20(16):6144–58,Aug 2000.J Parent, R Elliott, S Pleasure, and N Barbaro. Aberrant seizure-induced neuroge-nesis in experimental temporal lobe epilepsy.
Ann Neurol , Jan 2006.Joseph P Pierce, Jay Melton, Michael Punsoni, Daniel P McCloskey, and Helen EScharfman. Mossy fibers are the primary source of afferent input to ectopic granulecells that are born after pilocarpine-induced seizures.
Exp Neurol , 196(2):316–31,Dec 2005.James B Aimone, Janet Wiles, and Fred H Gage. Computational influence of adultneurogenesis on memory encoding.
Neuron , 61(2):187–202, Jan 2009.Suzanna Becker. A computational principle for hippocampal learning and neuroge-nesis.
Hippocampus , 15(6):722–38, Jan 2005.R Andrew Chambers, Marc N Potenza, Ralph E Hoffman, and Willard Miranker.Simulated apoptosis/neurogenesis regulates learning and memory capabilities ofadaptive neural networks.
Neuropsychopharmacology , 29(4):747–58, Apr 2004.16arl Deisseroth, Sheela Singla, Hiroki Toda, Michelle Monje, Theo D Palmer,and Robert C Malenka. Excitation-neurogenesis coupling in adult neuralstem/progenitor cells.
Neuron , 42(4):535–52, May 2004.Laurenz Wiskott, Malte J Rasch, and Gerd Kempermann. A functional hypothesisfor adult hippocampal neurogenesis: avoidance of catastrophic interference in thedentate gyrus.
Hippocampus , 16(3):329–43, Jan 2006.D Watts and S Strogatz. Collective dynamics of ’small-world’networks.
Nature , Jan1998.Piotr Jablonski, Gina R Poe, and Michal Zochowski. Structural network hetero-geneities and network dynamics: a possible dynamical mechanism for hippocampalmemory reactivation.
Physical review E, Statistical, nonlinear, and soft matterphysics , 75(1 Pt 1):011912, Jan 2007.T Netoff, R Clewley, S Arno, T Keck, and J White. Epilepsy in small-world net-works.
Journal of Neuroscience , Jan 2004.P H E Tiesinga and T J Sejnowski. Rapid temporal modulation of synchrony bycompetition in cortical interneuron networks.
Neural computation , 16(2):251–75,Feb 2004.Jack M Parent, Robert C Elliott, Samuel J Pleasure, Nicholas M Barbaro, andDaniel H Lowenstein. Aberrant seizure-induced neurogenesis in experimental tem-poral lobe epilepsy.
Ann Neurol , 59(1):81–91, Jan 2006.J M Parent, E Tada, J R Fike, and D H Lowenstein. Inhibition of dentate granulecell neurogenesis with brain irradiation does not prevent seizure-induced mossy fibersynaptic reorganization in the rat.
J Neurosci , 19(11):4508–19, Jun 1999.M. E. J Newman. The structure and function of networks.
SIAM Review , 45:167—256, Jan 2003.Stefano Farioli-Vecchioli, Daniele Saraulli, Marco Costanzi, Simone Pacioni, IreneCin`a, Massimiliano Aceti, Laura Micheli, Alberto Bacci, Vincenzo Cestari, andFelice Tirone. The timing of differentiation of adult hippocampal neurons is crucialfor spatial memory.
PLoS Biol , 6(10):e246, Oct 2008.Lei Cao, Xiangyang Jiao, David S Zuzga, Yuhong Liu, Dahna M Fong, DeborahYoung, and Matthew J During. Vegf links hippocampal activity with neurogenesis,learning and memory.
Nat Genet , 36(8):827–35, Aug 2004.17 van Praag, B R Christie, T J Sejnowski, and F H Gage. Running enhancesneurogenesis, learning, and long-term potentiation in mice.
Proc Natl Acad SciUSA , 96(23):13427–31, Nov 1999.Jonas Dyhrfjeld-Johnsen, Vijayalakshmi Santhakumar, Robert J Morgan, RamonHuerta, Lev Tsimring, and Ivan Soltesz. Topological determinants of epileptogenesisin large-scale structural and functional models of the dentate gyrus derived fromexperimental data.
J Neurophysiol , 97(2):1566–87, Feb 2007.Robert J Morgan and Ivan Soltesz. Nonrandom connectivity of the epileptic dentategyrus predicts a major role for neuronal hubs in seizures.
Proc Natl Acad Sci USA ,105(16):6179–84, Apr 2008.C Gong, T Wang, H Huang, and J Parent. Reelin regulates neuronal progenitormigration in intact and epileptic hippocampus.
Journal of Neuroscience , Jan 2007.J Bengzon, Z Kokaia, E Elm´er, A Nanobashvili, M Kokaia, and O Lindvall. Apop-tosis and proliferation of dentate gyrus neurons after single and intermittent limbicseizures.
Proc Natl Acad Sci USA , 94(19):10432–7, Sep 1997.L Overstreet-Wadiche, D Bromberg, and A Bensen. Seizures accelerate functionalintegration of adult-generated granule cells.
Journal of Neuroscience , Jan 2006.C E Stafstrom, A Chronopoulos, S Thurber, J L Thompson, and G L Holmes. Age-dependent cognitive and behavioral deficits after kainic acid seizures.
Epilepsia ,34(3):420–32, Jan 1993.G L Holmes. Epilepsy in the developing brain: lessons from the laboratory andclinic.
Epilepsia , 38(1):12–30, Jan 1997.S Jessberger, K Nakashima, and G Clemenson Jr. Epigenetic modulation of seizure-induced neurogenesis and cognitive decline.
Journal of Neuroscience , Jan 2007.Keun-Hwa Jung, Kon Chu, Manho Kim, Sang-Wuk Jeong, Young-Mok Song, Soon-Tae Lee, Jin-Young Kim, Sang Kun Lee, and Jae-Kyu Roh. Continuous cytosine-b-d-arabinofuranoside infusion reduces ectopic granule cells in adult rat hippocampuswith attenuation of spontaneous recurrent seizures following pilocarpine-inducedstatus epilepticus.
Eur J Neurosci , 19(12):3219–26, Jun 2004.Keun-Hwa Jung, Kon Chu, Soon-Tae Lee, Juhyun Kim, Dong-In Sinn, Jeong-MinKim, Dong-Kyu Park, Jung-Ju Lee, Seung U Kim, Manho Kim, Sang Kun Lee,18nd Jae-Kyu Roh. Cyclooxygenase-2 inhibitor, celecoxib, inhibits the altered hip-pocampal neurogenesis with attenuation of spontaneous recurrent seizures followingpilocarpine-induced status epilepticus.
Neurobiol Dis , 23(2):237–46, Aug 2006.
E EE EEEI I II : p = 0 – 1 E E E : Local
EII IIE : Random: Random
Connection Distance
Figure 1: A cartoon of the connection scheme for the established network. Connec-tions from inhibitory cells to either excitatory or other inhibitory cells are randomand excitatory cells connect only to nearby inhibitory cells. For excitatory-excitatoryconnections, the ratio of local to random connections is determined by a rewiringprobability p , which we vary. 19able 1: Model parameters Variable Description Value taken N ex Number of excitatory neurons 1000 N in Number of inhibitory neurons 200, 100 N add Number of introduced neurons 500 L Number of lattice sites per side 40 p Rewiring probability 0–1 k ee Average number of excitatory-to-excitatory connections per cell 35 k ei Average number of excitatory-to-inhibitory connections per cell 4 k ie Average number of inhibitory to excitatory connections per cell 110 k ii Average number of inhibitory to inhibitory connections per cell 4 m Radial multiplier 2 I ex Excitatory cell excitability 0.73 I in Inhibitory cell excitability 0.7 w ee Excitatory-excitatory connection weight 0.2 w ei Excitatory-inhibitory connection weight 0.4 w ie Excitatory-excitatory connection weight -0.4 w ii Inhibitory-inhibitory connection weight -0.7 α Membrane leak constant 1-1.3 E External stimulus 0.4 τ s Slow time for spike 3 ms τ f Fast time scale for spike 0.3ms τ d Spike delay 0.08 msRandom firing probability per ms 0.0003Refractory time 8 msIntegration time step 0.3 msNumber of stimulated cells 5Excitatory-excitatory connection radius 6.54 sitesNew cell “nearby” radius in units of the excitory-excitory connec-tion radius 0.5Number of reconnection chances per cell per connection 10Time to mature 2000 msThreshold firing rate for synapse survival 30 HzThreshold firing rate for cell survival 30 Hz a New cell input jitter control parameter 0.8Time between introduced cells 350 msMaximum time window between denoting firing events as causal 10 ms Student Version of MATLAB
Figure 2: Average mean path length (diamonds) and clustering coefficient (dots) asa function of rewiring probability p , normalized by the value for p = 0. All datapoints are averages over 20 simulated networks. The path length drops sharply as p increases, but the clustering coefficient has much slower decrease. The small-worldregime is defined by having large clustering but small path length, which is foundfor rewiring probabilities near p = 0 .
1. 21 ormal Inhibition Low Inhibition p = 0.0 p = 0.2p = 0.9p = 0.5 p = 0.0 p = 0.2p = 0.5 p = 0.9 p = 0.0 p = 0.2 p = 0.5 p = 0.9
Student Version of MATLAB F r equen cy ( H z ) Figure 1) Natural log of average activity from the end of the simulation for normal and low inhibition. Note the effective localization of activity for normal inhibition and low p that is not present for other parameter values.
Figure 3: Spatial distribution of mean firing rate after introducing 500 cells for normal(left) and low inhibition (right). Note log scale. Shown are four example rewiringprobabilities for each level of inhibition. Observe that the effective localization ofactivity for normal inhibition and low p that is not present for other parametervalues. 22 = 0.0 p = 0.2p = 0.5 p = 0.9 Normal Inhibition p = 0.0 p = 0.2p = 0.5 p = 0.9
Low Inhibition C hange i n f r equen cy ( H z ) p = 0 p = 0.2p = 0.5 p = 0.9 02468 Student Version of MATLAB
Figure 4: Spatial distribution of the change in firing rate after introducing 500 cellsfor normal (left) and low inhibition (right). For normal inhibition and low p , thenetwork activity changes only near the stimulated region. However, for larger p ,thus more random connections, or decrease in inhibition, activity increases spreadthrough the network. For low inhibition and low rewiring, some regions show littlechange because the stimulus is already driving some cells near their maximum rate.23 = 0.0 p = 0.2p = 0.5 p = 0.9 p = 0.0 p = 0.2p = 0.5 p = 0.9 Normal Inhibition Low Inhibition
Student Version of MATLAB S u r v i v a l P r obab ili t y Figure 2) Survival probability in space based on fifty simulations for normal and low inhibition. Note that normal inhibition is very localized compared to either high rewiring or low inhibition.
Figure 5: Spatial distribution of the survival probability from fifty simulations fornormal (left) and low inhibition (right). Note that survival is highly localized for thesame values that gave localized activity and increased firing rate.24 − − − − − − − C o rr e l a t i on Low InhibitionNormal
Student Version of MATLAB
Figure 3) a) Mean activity at end of simulation as a function of rewiring and inhibition. b) Average number of survivors out of 500 introduced. Low values of rewiring and normal inhibition give low rates of incorporation. c) Mean radius of survivors. Again, normal inhibition and small world rewiring cause neurogenesis to respond more specifically to stimulus d) Correlation between activity at the beginning of simulation and survivorship at the end. While under normal inhibition new cells stay in the stimulated areas, for low inhibition cells can survive in distant locations because of the greater changes in activity. a) b)c) M ean S u r v i v o r s NormalLow Inhibition
Student Version of MATLAB − − − Student Version of MATLAB − − − Student Version of MATLAB d) M ean R ad i u s NormalLow Inhibition
Student Version of MATLAB A c t i v i t y - S u r v i v a l C o rr e l a t i on A c t i v i t y — C hange I n A c t i v i t y C o rr e l a t i on − − − Student Version of MATLAB S u r v i v o r s R ad i u s Figure 6: a) Mean radius of survivors as a function of p and inhibition, measured inlattice sites. The width of the network is 40 sites, so a distance near 15 is consistentwith uniform distribution. Again, normal inhibition and small-world rewiring causeneurogenesis to respond with more focus. b) Average number of survivors out of 500introduced. Low values of rewiring and normal inhibition give low rates of incorpo-ration. c) Spatial correlation between activity at the beginning of simulation andsurvival probability. While under normal inhibition new cells stay in the stimulatedareas, for low inhibition cells can survive in distant locations because of the greaterchanges in activity. d) Spatial correlation between initial activity and the change inactivity after all cells have been introduced. Again, the peak value occurs for nor-mal inhibition and a rewiring probability that puts the network into the small-worldregime. 25 M ean R ad i a l C o m ponen t NormalLow Inhibition
Student Version of MATLAB d) M ean r e w i r i ng e v en t s NormalLow Inhibition
Student Version of MATLAB a) b) p = 0 p = 0.4p = 0.7 p = 0.9
Student Version of MATLAB p = 0 p = 0.4p = 0.7 p = 0.9
Student Version of MATLAB c) p = 0 p = 0.9 Figure 7: Connection patterns of surviving cells. a) Average number of rewiringevents. Networks with low inhibition require less searching to effectively integrateinto the network. b) New granule cell (green) integration into the hippocampus isorderly and with consistent directions in normal conditions. The hilus is denotedby “h” and the granule cell layer by “gcl”. After seizures are induced, granule cellscan integrate and orient in a more random manner. See Methods for experimentdescription. c) Mean direction of output connections as a function of location fortwo different values of rewiring. Both have normal inhibition. For low rewiring, theconnections are aligned radially, whereas for higher rewiring the orientation becomesmore random. b) Average radial component of output connections. High valuesmean that connections are forming toward the stimulated region as in the p = 0example, whereas values near zero are consistent with random, as in the p = 0 . e c onne c t i on E v en t s Figure 8: Spatial distribution of mean reconnection events per surviving cell for fourexample rewiring probabilities. Note the presence of an “easy” place near the stim-ulus to incorporate into the network at low p . Large numbers of reconnection eventsmean that a new cell is not able to quickly find neighbors that it can functionallyinnervate. 27 ) b) c) − − − p M ean T i m e D i ff e r en c e NormalLow Inhibition
Student Version of MATLAB S p i k e s Student Version of MATLAB S p i k e s EstablishedIntroduced
Student Version of MATLAB S p i k e s EstablishedIntroduced
Student Version of MATLAB
Figure 9: Comparison of age-dependent burst times. a) An example of firing activityfor low rewiring ( p = 0), showing new neurons firing (green) within bursts of estab-lished neurons (blue). b) An example of firing activity for high rewiring ( p = 0 . B Student Version of MATLAB F r equen cy pNormal 0153050100 Student Version of MATLAB B Student Version of MATLAB F r equen cy Low Inhibition 0153050100
Student Version of MATLAB a)b)
Figure 10: Network dynamics as a function of surviving new neurons and rewiringprobability. a) Burst synchronicity measure B as a function of pp