Session B10: Biological Physics II: Multi-scale Biophysical Models

Searching for Minimal Mechanisms that can Achieve Biological Adaptation

Adaptation is an important biological function that can be achieved through networks of enzyme reactions. These networks can be modeled as systems of coupled differential equations. There has been recent interest in identifying mechanisms that achieve adaptation. We ask what design principles are necessary for a network to adapt to an external stimulus. We use a novel approach that begins with a fully connected network and uses model reduction to remove unnecessary combinations of components, effectively constructing and tuning the network to the simplest form that still can achieve adaptation. We show that our approach can effectively identify the basic design principles behind adaptation, and we discuss the prospects of identifying similar principles for other behaviors and contexts.   

The limitations of model-based experimental design in sloppy systems

Mathematical models can help us understand complex biological systems such as gene regulatory networks and signaling pathways. These models can include hundreds of unknown parameters. Data fitting typically leads to huge uncertainties in the inferred parameter values, a phenomenon known as sloppiness. It has been suggested that model-based experimental design can help overcome this challenge. However, models of complex systems, such as those in biology, never account for all of the system's details. Designing experiments to make previously irrelevant model details become more relevant may result in the model no longer being able to fit all the data. If such is the case, the conditions would necessitate a change in the model itself. We test this by considering two models of the same cell-signaling process, each of varying complexity. Performing experimental design guided by the simple model but using the complex model as a surrogate for the actual system, we determine the limits of model-based experimental design for accurate parameter inference.   

Parameter Identifiability in the Hodgkin-Huxley Model of a Single Neuron

Neurons convey information through the propagation of an action potential across the cell membrane. The foundational model of potential propagation, formulated by Hodgkin and Huxley in 1952, involves 4 dynamical variables and 26 parameters. In contrast, most foundational theories in physics usually depend on a small number of parameters, for example, the BCS model of superconductivity has one free parameter. We consider the question: Are all of the parameters in the Hodgkin Huxley model necessary? Unnecessary parameters will be unconstrained by the model behavior. We therefore perform a parameter identifiability analysis for the spiking behavior of a Hodgkin Huxley neuron. We show that many of the parameters in the Hodgkin-Huxley model are likely unnecessary. We discuss preliminary results attempting to remove the unnecessary parameters from the model.   

Asymmetric Corrections to the West, Brown, and Enquist Model of Biological Resource Distribution Networks

Biological allometries, such as metabolic scaling, have been shown to result from a balancing between the geometrical network structure comprising an organism and a minimization of energy loss during resource transport. The West, Brown, and Enquist (WBE) model uses this approach in describing biological networks that exhibit allometric scaling, but in so doing it is assumed that the networks are perfectly symmetric with respect to their geometric properties. Our work relaxes this assumption by defining and exploring two candidates for asymmetrically bifurcating networks. We incorporate asymmetric branching into the WBE model by treating the symmetric case as a zeroth-order approximation with the necessary geometrical effects of asymmetry treated as small deviations from the symmetric model. We then impose hydrodynamic and fractal space-filling principles by the method of undetermined Lagrange multipliers, resulting in several theoretical predictions regarding how asymmetric branching is manifest as well as in a selection of one type of asymmetric network over the other. Additionally, network asymmetry can be incorporated into the many allometric relationships, and it can be shown that the 3/4ths metabolic scaling exponent from Kleiber's Law is still attainable in such networks.   

Reversible Gates in Quantum Computing, may explain the ''Dead Reckoning'' path return of Bees and other Social Insects

Reversible gates in Quantum Computing may yield a clue as to how insects, which have a fairly small Brain size, can not only find their way to food, but also return successfully and communicate that path to other Social Insects. As anyone who has studied the works of Aristotle, or George Boole knows, classical logic has a flaw in it, in that it is a many-to-one function, with the OR, NOR, AND, or NAND gate. This many-to-one cardinality means that the gates lose information as they compute, in that if you have an OR gate, 1 OR 1, 1 OR 0, 0 OR 1 (using George Boole's notation), all produce an output of 1. So if you start from the conclusion of 1, you have lost the information as to what the deduction was. Reversible gates using Reversible logic, keep the information as to the path of the Deduction. In that way Reversible Gates, don't necessarily need separate Data Stores, in that for small systems they can do the Deduction in Reverse. A Social Insect may have Reversible Gated Neurons, such that there need not be a separate Data Store, the Insect may simply run the Logic in Reverse to Return to its Hive, and it also has a complete record of its path (in its own language) store in those gates. This is a much better theory than the current ``Dead Reckoning'' theory.