On imposing detailed balance in complex reaction mechanisms.
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Algorithms↗
Biomedical subjects
John E Pearson
Publications and source records attributed to John E Pearson.
Messages diffuse faster than messengers.
In many cell-signaling pathways, information is transmitted by the diffusion of messenger molecules. Diffusion coefficients characterize the messenger's spatial range and the characteristic times of signal propagation. Inside cells, particles usually diffuse in the presence of immobile binding sites (or traps). It is well known that binding to traps results in an effective diffusion coefficient that is smaller than the free coefficient in media free of traps. To measure effective diffusion coefficients in cells, "tagged" particles are often used. Radioactive calcium was used in a giant squid axon and in cytosolic extracts of Xenopus laevis oocytes. Fluorescence recovery after photobleaching yields diffusion coefficients from observations of the distribution of fluorescently labeled proteins. In the absence of traps, free diffusion coefficients give both the rate at which single-particle mean square displacements increase and the rate at which information in the form of inhomogeneities in particle concentration spread out with time. We show here that, in the presence of traps, information diffuses faster than single particles. Thus, messages diffuse faster than messengers. Tagged-particle experiments give the single-particle diffusion coefficients and, thus, can underestimate the rate of diffusive signal propagation.
Animals↗
Transformations that preserve detailed balance in Markov models.
Aggregated Markov processes related by similarity transformation are equivalent in that they cannot be distinguished by steady-state experiments. We derive an explicit formula for the set of all detailed-balance preserving similarity transformations between such continuous time Markov chains with N states. The matrices that define the allowed similarity transformations are found to be a simple non-linear function applied to almost any element of the special orthogonal group in N dimensions. Since a model is identifiable only if there is no similarity transformations to an equivalent model, we expect this result to prove useful in the theory of identification of aggregated Markov chains, an enterprise of growing importance as more and more single molecules yield to observation.
Biometry↗
Phi-value analysis of a linear, sequential reaction mechanism: theory and application to ion channel gating.
We derive the analytical form of a rate-equilibrium free-energy relationship (with slope Phi) for a bounded, linear chain of coupled reactions having arbitrary connecting rate constants. The results confirm previous simulation studies showing that Phi-values reflect the position of the perturbed reaction within the chain, with reactions occurring earlier in the sequence producing higher Phi-values than those occurring later in the sequence. The derivation includes an expression for the transmission coefficients of the overall reaction based on the rate constants of an arbitrary, discrete, finite Markov chain. The results indicate that experimental Phi-values can be used to calculate the relative heights of the energy barriers between intermediate states of the chain but provide no information about the energies of the wells along the reaction path. Application of the equations to the case of diliganded acetylcholine receptor channel gating suggests that the transition-state ensemble for this reaction is nearly flat. Although this mechanism accounts for many of the basic features of diliganded and unliganded acetylcholine receptor channel gating, the experimental rate-equilibrium free-energy relationships appear to be more linear than those predicted by the theory.
Computer Simulation↗
Using independent open-to-closed transitions to simplify aggregated Markov models of ion channel gating kinetics.
Deducing plausible reaction schemes from single-channel current traces is time-consuming and difficult. The goal is to find the simplest scheme that fits the data, but there are many ways to connect even a small number of states (>2 million schemes with four open and four closed states). Many schemes make identical predictions. An exhaustive search over model space does not address the many equivalent schemes that will result. We have found a canonical form that can express all reaction schemes for binary channels. This form has the minimal number of rate constants for any rank (number of independent open-closed transitions), unlike other canonical forms such as the well established "uncoupled" scheme. Because all of the interconductance transitions in the new form are independent, we refer to it as the manifest interconductance rank (MIR) form. In the case of four open and four closed states, there are four MIR form schemes, corresponding to ranks 1-4. For many models proposed in the literature for specific ion channels, the equivalent MIR form has dramatically fewer links than the uncoupled form. By using the MIR form we prove that all rank 1 topologies with a given number of open and closed states make identical predictions in steady state, thus narrowing the search space for simple models. Moreover, we prove that fitting to canonical form preserves detailed balance. We also propose an efficient hierarchical algorithm for searching for the simplest possible model consistent with a given data set.
Algorithms↗
Sheet excitability and nonlinear wave propagation.
In the Xenopus laevis oocyte, calcium ion channels are clustered in a thin shell. Motivated by this morphology, we study a general class of reaction-diffusion systems that include most of the well-known models that support wave propagation but restricting excitability to a "sheet" of codimension 1. We find waves that undergo propagation failure with increasing diffusion coefficient and a scaling regime in which the wave speed is independent of it.
Animals↗