Did you know the story of blind men and an elephant? The question is: is
synchrony relevant for understanding the brain function? Perhaps, and perhaps
not! It depends on what data you examine and how you interpret it. But coherent
firing of neurons is often a significant phenomenon in the brain. For example,
in models of Parkinson's disease, there is an enhancement of coherence among
neuronal activity. If you trust that activity at the level of single neurons is
indeed important for brain function, then you must make a connection between
single neuron behavior and population behavior that might show coherence or
incoherence. Coupled oscillator theory comes handy in addressing this question.
Arthur Winfree made singular contribution to understanding dynamics of coupled
biological oscillators [The Geometry of Biological Time, 2nd Edition, Springer, 2000.
when each oscillator is treated as a phase variable. Using neuronal response
to isolated stimuli (phase response curves or PRCs), Bard Ermentrout
software book link], and
others advanced the understanding of synchrony among phase coupled oscillators.
In this research we use PRCs to systematically investigate how their shapes
(that emerge from the properties of single neurons) affect synchrony among coupled
Winfree's definition: (p. 591)
Entrainment = phase-locking at a common frequency,
Synchronization = phase-locking at a common frequency and with zero phase difference.
Noise is not noise is not noise. The brain is noisy, of course. But noise can enhance some phenomena, and it might also disrupt some phenomena. There are various attempts in the field in understanding how noise is generated, how noise affects a certain phenomenon, and how noise modifies neuronal behavior. In this research, we study how noise modifies single neuron behavior, as well as how noise affects synchronization between coupled neurons. We find that if the noise is of the type that suppresses neuronal firing, then (1) it could actually enhance coherence of neuronal output, and (2) it could disrupt synchronization of even identical neurons.
How do you find signal in noisy data? If that data is an event data, i.e. like
a sequence of spike times recorded from brain neurons, the first thing you
would try is using autocorrelation or cross-correlation methods which require you
to pool a large number of data points. Using a gazillion data points should
not be a choice, because the signal buried in short sequences of events would
be masked and overwhelmed by what the long sequence of events behaves like.
Moreover do you think that the brain keeps collecting events for an hour and do
the computation then? No! You must use brief sequences and process that data
and make a decision. Here we introduce a "phase function" to compute simple
correlations in a sequence of discrete events - this method can be used for
short or long sequences.
A popular method to visualize event data is using scattergrams that show the spread of points in a two-dimensional plane, and also show a possible relation between the horizontal and vertical axes variables. If there is no apparent linear relationship between the two variables, would you not still like to quantify the spread somehow? For example, if you find a Pearson coefficient of 0.4, then it might not mean anything except that there is no reliable linear relationship. Here we introduce a quantification of the entire scattergram based on the distribution of the density in the plane. It systematically computes a weighted sum of the clusters at various length scales, and provides a single number for clustering coefficient at a given length scale, as well as a distribution of such clustering density.
Next time you think of picking up an object from the table (a voluntary movement), think of basal ganglia. Basal ganglia are like a man-in-the-middle actively participating between your idea of a concious movement and the actual movement. The movement may go wrong as in a number of movement disorders such as Parkinson's disease, Huntington's disease, and dystonia. Basal ganglia consists of neurons from a number of interconnected nuclei displaying various levels of decorrelations among their spike timing. [A review here]. The broader question is to figure out what these decorrelations mean to the normal and diseased brain function. For that you need to first get hold of the basic function of the neurons and their diversity present in each of these nuclei. Here our focus is to investigate the cell variety of an important nucleaus, the globus pallidus neurons in slices, how to model their spiking behavior, and how this nucleus in consort with another important nucleus, the subthalamic nucleus (STN) generates rhythms and coherent patters.
Neurons behave a lot like little children. If you give them candy, they are too excited and jump around. If you take away their candy they are depressed. How about taking away their candy for now, and wait a while before you give them back just a little candy, not as much as they had earlier but a little less? Well, they might just be too happy, as happy as they were when they had loads of candy. Try it out!
We did exactly this kind of thing in some neuronal models by appropriately delaying a weak excitatory stimulus after first causing a depression with an inhibitory stimulus. Bingo, the neurons fired! We showed this experimentally as well. Finally we also showed that if such inhibition arrives randomly mixed with random excitation, which by itself would not have caused great activity, would now enhance the firing rate. Our posters document more interesting stuff.
Did you figure out where that annoying cricket was hiding last time when you were disturbed from your sleep? The reason why it is difficult to spot such sounds is because they are of high frequency. But if somebody was dragging a big table on the street, you know exactly from were to where they are dragging, and you might be able to tell, without looking, where exactly the sound is coming from. Low frequency sounds are detected by our auditory system taking advantage of the little (often microsecond) delay that our head size would introduce between the sound arrived at the two ears. This delay is encoded in the medial superior olive (MSO) neurons of the auditory pathway. The encoding involves enhancement of temporal integration of inputs arriving at these neurons. Our study focusses on certain currents that enhance such integration as well as modeling that shows how such enhancement occurs due to combination of arriving inputs.
Did you ever wonder how those dozen or two of young violinists performing Mozart's symphony No. 40 pull it off so perfectly? Or how those wonderful singers turned the air into magic in a choir? Well they are real examples of coherent behavior, or synchrony. Coherent behavior is also ubiquitous in nature and across sciences such as in flashing fireflies, coupled lasers, coupled magnetrons, Josephson junctions, coupled chemical reactions, coupled biological cells, and electronic oscillators. Simple mathematical models in the form of coupled oscillators serve quite well in understanding the basic principles of phase-locking. Arthur Winfree [book link here], Yoshiki Kuramoto [book link here], Steven Strogatz [book link here] and many others propelled this work enormously in the field. Our main focus is to address the role of communication delay between the oscillator units in the synchronization of them. We show that delay could cause oscillator death, and explore the implications of time delay in other phase-locked solutions.
We know how heat is transmitted from the sun to the earth. It's by radiation. We solved the big problem! Next, did you hear of blowing hot winds causing death? Yes, we know how heat is transmitted there. It's by convection or movement of fluids. Then we are left with the last battle ground: How does heat get transmitted from one end of a metal to another? The atoms do not flow from the hot end to the cold end. They have to transmit the vibrations from one to another via the coupling they might have between them. If the coupling enables a linear transmission, then an immediate transmission of heat might take place, i.e. it would take no time to feel the heat of stove when you stick a spoon in it. Obviously that is not the case. So a nonlinear transmission takes place that gives the heat a finite speed. Here we construct a model to study the head transfer. Good reviews: (i) J. Ford. The Fermi-Pasta-Ulam problem: Paradox turns discovery, Physics Reports 213:271-310, 1992. (link) (ii) G. Gallavotti (Ed.) The Fermi-Pasta-Ulam Problem: A Status Report, Lecture notes in physics, Vol. 728, Springer, 2008. (link)