Odorant receptors of Drosophila are sensitive to the molecular volume of odorants.

Which properties of a molecule define its odor? This is a basic yet unanswered question regarding the olfactory system. The olfactory system of Drosophila has a repertoire of approximately 60 odorant receptors. Molecules bind to odorant receptors with different affinities and activate them with different efficacies, thus providing a combinatorial code that identifies odorants. We hypothesized that the binding affinity of an odorant-receptor pair is affected by their relative sizes. The maximum affinity can be attained when the molecular volume of an odorant matches the volume of the binding pocket. The affinity drops to zero when the sizes are too different, thus obscuring the effects of other molecular properties. We developed a mathematical formulation of this hypothesis and verified it using Drosophila data. We also predicted the volume and structural flexibility of the binding site of each odorant receptor; these features significantly differ between odorant receptors. The differences in the volumes and structural flexibilities of different odorant receptor binding sites may explain the difference in the scents of similar molecules with different sizes.

Phase diagram of spiking neural networks.

In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2%, 20% of neurons are inhibitory and 80% are excitatory. These common values are based on experiments, observations, and trials and errors, but here, I take a different perspective, inspired by evolution, I systematically simulate many networks, each with a different set of parameters, and then I try to figure out what makes the common values desirable. I stimulate networks with pulses and then measure their: dynamic range, dominant frequency of population activities, total duration of activities, maximum rate of population and the occurrence time of maximum rate. The results are organized in phase diagram. This phase diagram gives an insight into the space of parameters - excitatory to inhibitory ratio, sparseness of connections and synaptic weights. This phase diagram can be used to decide the parameters of a model. The phase diagrams show that networks which are configured according to the common values, have a good dynamic range in response to an impulse and their dynamic range is robust in respect to synaptic weights, and for some synaptic weights they oscillates in α or ß frequencies, independent of external stimuli.

Simulation of droplet trains in microfluidic networks.

We show that in a microfluidic network with low Reynolds numbers, a system can be irreversible due to hysteresis effects. We simulated a network of pipes that was used in a recent experiment. The network consists of one loop connected to input and output pipes. A train of droplets enters the system at a uniform rate, but the droplets may leave the system in a periodic or even a chaotic pattern. The output pattern depends on the time interval between incoming droplets as well as the network geometry. For some parameters, the system is not reversible.

Energy-landscape networks of spin glasses.

We have studied the topology of the energy landscape of a spin-glass model and the effect of frustration on it by looking at the connectivity and disconnectivity graphs of the inherent structure. The connectivity network shows the adjacency of energy minima whereas the disconnectivity network tells us about the heights of the energy barriers. Both graphs are constructed by the exact enumeration of a two-dimensional square lattice of a frustrated spin glass with nearest-neighbor interactions up to the size of 27 spins. The enumeration of the energy-landscape minima as well as the analytical mean-field approximation show that these minima have a Gaussian distribution, and the connectivity graph has a log-Weibull degree distribution of shape kappa=8.22 and scale lambda=4.84 . To study the effect of frustration on these results, we introduce an unfrustrated spin-glass model and demonstrate that the degree distribution of its connectivity graph shows a power-law behavior with the -3.46 exponent, which is similar to the behavior of proteins and Lennard-Jones clusters in its power-law form.

Scale-free networks with an exponent less than two.

We study scale-free simple graphs with an exponent of the degree distribution gamma less than 2. Generically one expects such extremely skewed networks--which occur very frequently in systems of virtually or logically connected units--to have different properties than those of scale free networks with gamma>2: The number of links grows faster than the number of nodes and they naturally possess the small world property, because the diameter increases by the logarithm of the size of the network and the clustering coefficient is finite. We discuss a simple prototype model of such networks, inspired by real world phenomena, which exhibits these properties and allows for a detailed analytical investigation.

Three-bead rotating chain model shows universality in the stretching of proteins.

We introduce a model of proteins in which all of the key atoms in the protein backbone are accounted for, thus extending the freely rotating chain model. We use average bond lengths and average angles from the Protein Data Bank as input parameters, leaving the number of residues as a single variable. The model is used to study the stretching of proteins in the entropic regime. The results of our Monte Carlo simulations are found to agree well with experimental data, suggesting that the force extension plot is universal and does not depend on the side chains or primary structure of the proteins.