A comparison of bimolecular reaction models for stochastic reaction-diffusion systems.

Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary spatially-continuous models that have been used in recent studies: the diffusion limited reaction model of Smoluchowski, and a second approach popularized by Doi. Both models treat molecules as points undergoing Brownian motion. The former represents chemical reactions between two reactants through the use of reactive boundary conditions, with two molecules reacting instantly upon reaching a fixed separation (called the reaction-radius). The Doi model uses reaction potentials, whereby two molecules react with a fixed probability per unit time, λ, when separated by less than the reaction radius. In this work, we study the rigorous relationship between the two models. For the special case of a protein diffusing to a fixed DNA binding site, we prove that the solution to the Doi model converges to the solution of the Smoluchowski model as λ→∞, with a rigorous [Formula: see text] error bound (for any fixed ϵ>0). We investigate by numerical simulation, for biologically relevant parameter values, the difference between the solutions and associated reaction time statistics of the two models. As the reaction-radius is decreased, for sufficiently large but fixed values of λ, these differences are found to increase like the inverse of the binding radius.

The influence of volume exclusion by chromatin on the time required to find specific DNA binding sites by diffusion.

Within the nuclei of eukaryotic cells, the density of chromatin is nonuniform. We study the influence of this nonuniform density, which we derive from microscopic images [Schermelleh L, et al. (2008) Science 320:1332-1336], on the diffusion of proteins within the nucleus, under the hypothesis that chromatin density is proportional to an effective potential that tends to exclude the diffusing protein from regions of high chromatin density. The constant of proportionality, which we call the volume exclusivity of chromatin, is a model parameter that we can tune to study the influence of such volume exclusivity on the random time required for a diffusing particle to find its target. We consider randomly chosen binding sites located in regions of low (20th-30th percentile) chromatin density, and we compute the median time to find such a binding site by a protein that enters the nucleus at a randomly chosen nuclear pore. As the volume exclusivity of chromatin increases from zero, we find that the median time needed to reach the target binding site at first decreases to a minimum, and then increases again as the volume exclusivity of chromatin increases further. Random permutation of the voxel values of chromatin density abolishes the minimum, thus demonstrating that the speedup seen with increasing volume exclusivity at low to moderate volume exclusivity is dependent upon the spatial structure of chromatin within the nucleus.

Regulation of proprioceptive memory by subarachnoid regional anesthesia.

BACKGROUND: Patient perception of limb position during regional anesthesia is frequently incorrect. The existing model ascribes this misperception, or phantom sensation, as a reversion to a fixed, slightly flexed, body schema. A model was developed to evaluate the influence of limb position changes on the incidence of incorrect or phantom sensations during regional anesthesia. METHODS: Forty American Society of Anesthesiologists physical status I-III adult patients undergoing genitourinary procedures under subarachnoid anesthesia were assigned to a lidocaine or bupivacaine treatment group and randomly assigned to one of four time groups (1, 4, 7, and 10 min). After blockade, patients were placed supine and blinded to limb positioning manipulations. One leg was flexed and the contralateral leg extended, with leg positions subsequently reversed at the assigned time point. At 10 min, patients were asked to identify the position of each leg. Percentage of incorrect response was analyzed using a logistic regression model with two independent variables: treatment and time. A supplemental study was undertaken to evaluate the observed difference in incorrect perceptions relative to flexed first versus extended limb first sequencing. RESULTS: The inability to perceive a change in limb position under regional anesthesia is dependent on the time after the block that the position change is initiated in relation to the onset characteristics of the local anesthetic. A phantom sensation of an extended leg position clearly exists. The flexed-first limb has a significantly higher incidence of incorrect or phantom perceptions. CONCLUSION: Proprioceptive memory involves a dynamic neuroplastic imprinting process that is influenced by limb or joint position prior to onset of regional anesthesia. This contrasts with previously held beliefs of a purely fixed body schema.