Donald Doherty's blog

Tag: Brain Science

  • Polychronization: Playing with the Code

    Last month I reviewed the paper “Polychronization: Computation with Spikes” (published February 2006 in Neural Computation) that described a highly simplified computational model of cerebral cortex containing 1,000 neurons that included axon conductance delays and spike timing dependent plasticity (STDP). The model exhibited the spontaneous formation of neuronal groups defined as “small collectives of neurons having strong connections with matching conduction delays and exhibiting time-locked but not necessarily synchronous spiking activity” (they may fire at many different times). The author called this process polychronization (poly means many and chronous means time) and the neuronal groups it forms polychronous groups.

    Figure 1. This is a spike raster plot of data from the polychronization model spnet.cpp. The model included 1,000 neurons (y-axis) and was run for 24 hours simulation time. The plot shows the last second (in milliseconds; x-axis) of the 24 hour simulation. Neurons 0 through 799 are excitatory and 800 through 999 are inhibitory (these are fast spiking inhibitory neurons). This plot is similar to the bottom plot in Figure 5 of “Polychronization: Computation with Spikes” (published February 2006 in Neural Computation) except that in the paper the 1 second time period is extracted from the 3,600 second time point or at 1 hour of simulation time.

    C++ and MATLAB versions of the computational model are available from the SenseLab’s ModelDB repository in the “Polychronization: Computation With Spikes (Izhikevich 2005)” record. The C++ code of the standard model described in the paper is in the spnet.cpp file. Compiling the code was straight forward. I did need to modify the main() method so that it returned an int to comply with C++ coding standards. No other modifications were necessary.

    Running the spnet.cpp code resulted in a spike.dat file that, when graphed, reproduced the bottom graph in Figure 5 (see Figure 1 above) of Dr. Eugene Izhikevich’s paper “Polychronization: Computation with Spikes” (published February 2006 in Neural Computation). I created the graph by reading the contents of the spikes.dat file into an OpenOffice.org spreadsheet by using the Insert menu’s Sheet From File… command. In the Text Import dialog box use the Separated by Space option under Separator options. Delete column B, highlight all of the data, and graph by clicking on the Chart button and selecting the XY (Scatter) chart type with Points Only.

    Note: For more on the paper associated with this model please see my earlier blog post “Spontaneously Formed Neuronal Groups Far Exceed the Number of Neurons.”

    The computational model in poly_spnet.cpp is the same as in spnet.cpp. However, poly_spnet.cpp includes code for finding polychronous groups. By default the cerebral cortex simulation in poly_spnet.cpp runs for a simulated 18,000 seconds (60 seconds/minute * 60 minutes/hour * 5 hours). The program then finds the polychronous groups for you. Compiling and running poly_spnet.cpp was also straight forward. Make the same modification to the main() method. Change its return value from void to int so that it complies with C++ coding standards. I also had to remove the malloc.h header. Next we’ll take a look at the data set produced by poly_spnet.cpp.

    Other related blog posts:

    Spontaneously Formed Neuronal Groups Far Exceed the Number of Neurons

  • Memory is Replayed in the Awake and Sleeping Brain

    The hippocampus is essential in the initial encoding and subsequent consolidation and retrieval of long term memories. Both consolidation and retrieval are thought to depend on the reactivation of previously stored patterns of neural activity. Memory consolidation, however, has been primarily associated with sleep and the retrieval of memory has been primarily associated with waking behavior. A new paper “Hippocampal replay in the awake state: a potential substrate for memory consolidation and retrieval” (published February 11, 2011 in Nature Neuroscience) reviews research that has established the replay of memories during awake and behaving animals.

    Neurons in the hippocampal formation fire when an animal visits a particular place defined by a small region (firing field) and are known as place cells. An individual place cell may respond to more than one location (firing field) each known as a place field. The sequential reactivation of hippocampal place cells reflects an animal’s memory of movement through an ordered set of place fields that together form a cognitive map of locations the animal has visited.

    Much has been made of the reactivation of stored hippocampal representations during sleep since 1) the phenomenon was first observed during sleep and 2) sleep seems like an ideal time for memory consolidation to occur. The main thrust of the current review is to point to current evidence that shows sharp wave ripples and the replay of spatial memories occurs in awake and behaving animals. Replay has been shown to be most prevalent immediately after an experience in the awake animal and to decay with time. Nevertheless, the replay of a spatial memory may persist at above chance levels even 18–24 hours after an experience. Even more surprising, the awake replay of a remote environment has been shown to be a higher fidelity recapitulation of past experiences than when a replay was seen during quiescent, sleep­-like states.

    The authors point out that forward replay during both behavior and subsequent sleep seems well suited for consolidation of memories related to experienced trajectories and they speculate that forward replay during behavior may enable the retrieval of future paths to aid memory­ guided decision making. Reverse replay during behavior may link recently experienced sequences to their outcome.

    Other related blog posts:

    Sensation and Location in the Hippocampal Formation

  • An Electrically Interconnected Axon Microstructure Forms a Small World Network in the Brain

    My blog post from four days ago was about a paper that described a previously unknown slow integration of action potentials that resulted in the abrupt appearance of action potentials in the distant segments of CA1 hippocampal interneuron axons that continued to fire for tens of seconds to minutes. Their preliminary evidence that gap junctions between axons may be involved led me to pioneering theoretical work by Dr. Roger Traub describing the dynamics of axo-axonal gap junctions and to the recent paper “Mechanisms of very fast oscillations in networks of axons coupled by gap junctions” (published 2010 in the Journal of Computational Neuroscience).

    Experiments analyzing the dynamics of axons connected at distal segments by gap junctions were conducted using three different computational models:

    • Large network models that included 3,072 axons.
    • Small network models that included just a handful of axons for detailed analysis.
    • Cellular automata.

    In addition, they reproduced and modified the large scale biologically detailed model of Dr. Traub and colleagues from 1999.

    Note: All of the computational models, including the modified Traub model, are available from the SenseLab ModelDB repository in the “Mechanisms of very fast oscillations in axon networks coupled by gap junctions (Munro, Borgers 2010)” record. The computational models are all in the C language except for the cellular automata models, which are in MATLAB code. Data analysis code, which is included, is also written for MATLAB.

    The network exhibited three different types of behavior, depending on the gap junction conductance and the fixed somatic voltage:

    • externally driven very fast oscillations
    • re-entrant activity
    • non-oscillatory noisy activity

    The results of the large network simulations suggested that the axonal plexus exhibits different behaviors depending on the number of propagation failures in the network. There were a lot of propagation failures during noise, some during re-entrant activity, and none during externally driven very fast oscillations. The failure of action potentials in distant axon branches to reach the cell body has recently been hypothesized to be the cause of spikelets, which have been observed in many types of neurons (see “Axon Segments May Form Distinct Processing Units“).

    A major finding of this paper was that highly interconnected distal axon segments (a small subgroup of the total population of axons) were necessary for the emergence of externally driven very fast oscillations and re-entrant activity. These distal axon segments acted as gates like a highly connected node in a small world network. Their results from model networks of electrically coupled cells predict that:

    • Target patterns appear across an axon plexus when signal propagation is always reliable.
    • Spiral waves appear when propagation fails occasionally.
    • Noise appears when propagation failures are frequent.

    Interestingly, it’s when the propagation of action potentials fail frequently enough to effectively shut down the highly interconnected axons that the network exhibits noise. The simulations show an abrupt phase change from noise to the re-entrant activity that shows only occasional propagation failure. Re-entrant activity may appear as spiral waves, which have been observed in cerebral cortex of living mammals (see “Spiral Waves in the Brain“). Together these data point to the neuropil as the area where significant signal processing is taking place in the brain.

    Other related blog posts:

    Spiral Waves in the Brain

    Axon Segments May Form Distinct Processing Units