Three-dimensional Migration of Neurites Is Mediated by Adhesion Site Density and Affinity

Three-dimensional neurite outgrowth rates within fibrin matrices that contained variable amounts of RGD peptides were shown to depend on adhesion site density and affinity. Bi-domain peptides with a factor XIIIa substrate in one domain and a RGD sequence in the other domain were covalently incorporated into fibrin gels during coagulation through the action of the transglutaminase factor XIIIa, and the RGD-dependent effect on neurite outgrowth was quantified, employing chick dorsal root ganglia cultured two- and three-dimensionally within the modified fibrin. Two separate bi-domain peptides were synthesized, one with a lower binding affinity linear RGD domain and another with a higher binding affinity cyclic RGD domain. Both peptides were cross-linked into fibrin gels at concentrations up to 8.2 mol of peptide/mol of fibrinogen, and their effect on neurite outgrowth was measured. Both two- and three-dimensional neurite outgrowth demonstrated a bi-phasic dependence on RGD concentration for both the linear and cyclic peptide, with intermediate adhesion site densities yielding maximal neurite extension and higher densities inhibiting outgrowth. The adhesion site density that yielded maximal outgrowth depended strongly on adhesion site affinity in both two and three dimensions, with lower densities of the higher affinity ligand being required (0.8-1.7 mol/mol for the linear peptide versus 0.2 mol/mol for the cyclic peptide yielding maximum neurite outgrowth rates in three-dimensional cultures)

Modeling Space-Time Data Using Stochastic Differential Equations

This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic differential equations to describe a latent process within a hierarchical model for the data. The intent is to view this latent process mechanistically and endow it with appropriate simple features and interpretable parameters. A motivating problem for the second setting is to model urban development through observed locations and times of new home construction; this gives rise to a space-time point pattern. We show that a spatio-temporal Cox process whose intensity is driven by a stochastic logistic equation is a viable mechanistic model that affords meaningful interpretation for the results of statistical inference. Other applications of stochastic logistic differential equations with space-time varying parameters include modeling population growth and product diffusion, which motivate our first, point-referenced data application. We propose a method to discretize both time and space in order to fit the model. We demonstrate the inference for the geostatistical model through a simulated dataset. Then, we fit the Cox process model to a real dataset taken from the greater Dallas metropolitan area.Business Administratio

Frequency control in synchronized networks of inhibitory neurons

We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively capture the frequency behavior of a larger class of neuronal models. We show that in different parameter regimes, the network frequency depends in different ways on the intrinsic and synaptic time constants. Only in one portion of the parameter space, called `phasic', is the network period proportional to the synaptic decay time. These results are discussed in connection with previous work of the authors, which showed that for mildly heterogeneous networks, the synchrony breaks down, but coherence is preserved much more for systems in the phasic regime than in the other regimes. These results imply that for mildly heterogeneous networks, the existence of a coherent rhythm implies a linear dependence of the network period on synaptic decay time, and a much weaker dependence on the drive to the cells. We give experimental evidence for this conclusion.Comment: 18 pages, 3 figures, Kluwer.sty. J. Comp. Neurosci. (in press). Originally submitted to the neuro-sys archive which was never publicly announced (was 9803001