scholarly journals Reduced Dimension, Biophysical Neuron Models Constructed From Observed Data

2021 ◽  
Author(s):  
Randall Clark ◽  
Lawson Fuller ◽  
Jason Platt ◽  
Henry D. I. Abarbanel
Keyword(s):  
Nonlinear Dynamics ◽  
Biological Networks ◽  
Applied Mathematics ◽  
Voltage Response ◽  
Synaptic Connections ◽  
Neuron Models ◽  
Detailed Specification ◽  
Reduced Dimension ◽  
The Many ◽  
Voltage Dynamics

AbstractUsing methods from nonlinear dynamics and interpolation techniques from applied mathematics, we show how to use data alone to construct discrete time dynamical rules that forecast observed neuron properties. These data may come from from simulations of a Hodgkin-Huxley (HH) neuron model or from laboratory current clamp experiments. In each case the reduced dimension data driven forecasting (DDF) models are shown to predict accurately for times after the training period.When the available observations for neuron preparations are, for example, membrane voltage V(t) only, we use the technique of time delay embedding from nonlinear dynamics to generate an appropriate space in which the full dynamics can be realized.The DDF constructions are reduced dimension models relative to HH models as they are built on and forecast only observables such as V(t). They do not require detailed specification of ion channels, their gating variables, and the many parameters that accompany an HH model for laboratory measurements, yet all of this important information is encoded in the DDF model.As the DDF models use only voltage data and forecast only voltage data they can be used in building networks with biophysical connections. Both gap junction connections and ligand gated synaptic connections among neurons involve presynaptic voltages and induce postsynaptic voltage response. Biophysically based DDF neuron models can replace other reduced dimension neuron models, say of the integrate-and-fire type, in developing and analyzing large networks of neurons.When one does have detailed HH model neurons for network components, a reduced dimension DDF realization of the HH voltage dynamics may be used in network computations to achieve computational efficiency and the exploration of larger biological networks.

scholarly journals Modelling co-translational dimerisation for programmable nonlinearity in synthetic biology

2020 ◽  
Author(s):  
Ruud Stoof ◽  
Ángel Goñi-Moreno
Keyword(s):  
Nonlinear Dynamics ◽  
Biological Networks ◽  
Rational Design ◽  
Fine Tuning ◽  
Genetic Circuits ◽  
On Demand ◽  
Regulatory Circuits ◽  
Protein Dimers ◽  
The Impact

AbstractNonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity remains an unmet challenge. This is largely due to a lack of mathematical modelling that accounts for the mechanistic basics of nonlinearity. We introduce a model for gene regulatory circuits that explicitly simulates protein dimerization—a well-known source of nonlinear dynamics. Specifically, our approach focusses on modelling co-translational dimerization: the formation of protein dimers during—and not after—translation. This is in contrast to the prevailing assumption that dimer generation is only viable between freely diffusing monomers (i.e., post-translational dimerization). We provide a method for fine-tuning nonlinearity on demand by balancing the impact of co- versus post-translational dimerization. Furthermore, we suggest design rules, such as protein length or physical separation between genes, that may be used to adjust dimerization dynamics in-vivo. The design, build and test of genetic circuits with on-demand nonlinear dynamics will greatly improve the programmability of synthetic biological systems.

scholarly journals A novel structure-based control method for analyzing nonlinear dynamics in biological networks

2018 ◽  
Author(s):  
Wei-Feng Guo ◽  
Shao-Wu Zhang ◽  
Tao Zeng ◽  
Yan Li ◽  
Jianxi Gao ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Nonlinear Control ◽  
Biological Networks ◽  
Control Method ◽  
Biological Systems ◽  
Network Control ◽  
Theoretical Research ◽  
Control Methods ◽  
Scale Free ◽  
Vertex Set

AbstractExploring complex biological systems requires adequate knowledge of the system’s underlying wiring diagram but not its specific functional forms. Thus, exploration actually requires the concepts and approaches delivered by structure-based network control, which investigates the controllability of complex networks through a minimum set of input nodes. Traditional structure-based control methods focus on the structure of complex systems with linear dynamics and may not match the meaning of control well in some biological systems. Here we took into consideration the nonlinear dynamics of some biological networks and formalized the nonlinear control problem of undirected dynamical networks (NCU). Then, we designed and implemented a novel and general graphic-theoretic algorithm (NCUA) from the perspective of the feedback vertex set to discover the possible minimum sets of the input nodes in controlling the network state. We applied our NCUA to both synthetic networks and real-world networks to investigate how the network parameters, such as the scaling exponent and the degree heterogeneity, affect the control characteristics of networks with nonlinear dynamics. The NCUA was applied to analyze the patient-specific molecular networks corresponding to patients across multiple datasets from The Cancer Genome Atlas (TCGA), which demonstrates the advantages of the nonlinear control method to characterize and quantify the patient-state change over the other state-of-the-art linear control methods. Thus, our model opens a new way to control the undesired transition of cancer states and provides a powerful tool for theoretical research on network control, especially in biological fields.Author summaryComplex biological systems usually have nonlinear dynamics, such as the biological gene (protein) interaction network and gene co-expression networks. However, most of the structure-based network control methods focus on the structure of complex systems with linear dynamics. Thus, the ultimate purpose to control biological networks is still too complicated to be directly solved by such network control methods. We currently lack a framework to control the biological networks with nonlinear and undirected dynamics theoretically and computationally. Here, we discuss the concept of the nonlinear control problem of undirected dynamical networks (NCU) and present the novel graphic-theoretic algorithm from the perspective of a feedback vertex set for identifying the possible sets with minimum input nodes in controlling the networks. The NCUA searches the minimum set of input nodes to drive the network from the undesired attractor to the desired attractor, which is different from conventional linear network control, such as that found in the Maximum Matching Sets (MMS) and Minimum Dominating Sets (MDS) algorithms. In this work, we evaluated the NCUA on multiple synthetic scale-free networks and real complex networks with nonlinear dynamics and found the novel control characteristics of the undirected scale-free networks. We used the NCUA to thoroughly investigate the sample-specific networks and their nonlinear controllability corresponding to cancer samples from TCGA which are enriched with known driver genes and known drug target as controls of pathologic phenotype transitions. We found that our NCUA control method has a better predicted performance for indicating and quantifying the patient biological system changes than that of the state-of-the-art linear control methods. Our approach provides a powerful tool for theoretical research on network control, especially in a range of biological fields.

scholarly journals Analytic performance modeling and analysis of detailed neuron simulations

2020 ◽  
Vol 34 (4) ◽  
pp. 428-449 ◽  
Author(s):  
Francesco Cremonesi ◽  
Georg Hager ◽  
Gerhard Wellein ◽  
Felix Schürmann
Keyword(s):  
Biological Networks ◽  
Memory Performance ◽  
Simulation Software ◽  
Performance Model ◽  
Parallel Computer ◽  
Neuron Models ◽  
Simulation Code ◽  
Modeling And Analysis ◽  
Performance Engineering ◽  
And Performance

Big science initiatives are trying to reconstruct and model the brain by attempting to simulate brain tissue at larger scales and with increasingly more biological detail than previously thought possible. The exponential growth of parallel computer performance has been supporting these developments, and at the same time maintainers of neuroscientific simulation code have strived to optimally and efficiently exploit new hardware features. Current state-of-the-art software for the simulation of biological networks has so far been developed using performance engineering practices, but a thorough analysis and modeling of the computational and performance characteristics, especially in the case of morphologically detailed neuron simulations, is lacking. Other computational sciences have successfully used analytic performance engineering, which is based on “white-box,” that is, first-principles performance models, to gain insight on the computational properties of simulation kernels, aid developers in performance optimizations and eventually drive codesign efforts, but to our knowledge a model-based performance analysis of neuron simulations has not yet been conducted. We present a detailed study of the shared-memory performance of morphologically detailed neuron simulations based on the Execution-Cache-Memory performance model. We demonstrate that this model can deliver accurate predictions of the runtime of almost all the kernels that constitute the neuron models under investigation. The gained insight is used to identify the main governing mechanisms underlying performance bottlenecks in the simulation. The implications of this analysis on the optimization of neural simulation software and eventually codesign of future hardware architectures are discussed. In this sense, our work represents a valuable conceptual and quantitative contribution to understanding the performance properties of biological networks simulations.

A Course in Applied Mathematics for Teachers of Secondary Mathematics

1938 ◽  
Vol 31 (2) ◽  
pp. 51-62
Author(s):  
Cleon C. Richtmeyer
Keyword(s):  
Applied Mathematics ◽  
Secondary Mathematics ◽  
The Many

It has long been the feeling of the writer that the present curricula for teachers of secondary mathematics tend more to theory than to applications, and that a need exists for a course in which the many applications of mathematics could be considered. This feeling increased in intensity due to the following trends in teaching of secondary mathematics: (1) A shift in emphasis from disciplinary values to appreciation and application; and (2) The reorganization of secondary mathematics to include a general course for all students. These trends both imply a teacher with a broad background of knowledge of the application of mathematics.

scholarly journals Address of the president, Sir Frederick Gowland Hopkins, O. M., at the anniversary meeting, November 30, 1935

1936 ◽  
Vol 119 (813) ◽  
pp. 88-113 ◽  
Keyword(s):  
Wave Equation ◽  
Applied Mathematics ◽  
Electromagnetic Theory ◽  
Mathematical Ability ◽  
Text Book ◽  
De Vries ◽  
The Many ◽  
The University

It is my traditional duty to remind you of the losses the Society has suffered in the death of eighteen members. Four of these, Theobald Smith, Hugo de Vries, Friedrich Went, and H. F. Osborn, were distinguished Foreign Members. Among the fourteen Fellows are two who were active members of the Council, Dr. H. H. Thomas and Sir John McLennan. By the death of Sir Horace Lamb, the Society has lost a Fellow who for more than forty years was one of the most prominent and successful among the many workers in applied mathematics in this country. He was fortunate in his generation; Maxwell had shown the importance of the wave equation in electromagnetic theory; the work of Stokes, Rayleigh, and Thomson had aroused fresh interest in problems in heat and hydrodynamics, in all of which it was of importance. Lamb realized this and utilized his mathematical ability in the development of some of its many consequences. His papers on hydrodynamics and elasticity added to our knowledge in a marked degree. And in addition he was a great teacher. His text-book on “ Hydrodynamics ,” the outcome of a course of lectures to undergraduates at Cambridge in 1875, is a model of what such a book should be, and the distinction of many of his pupils is clear evidence of the value of his work as a Professor at Manchester. To quote from a resolution of the Council and Senate, “He inspired all who knew him in the University with respect and esteem, and his many friends with warm affection.”

Classification of Temporal Patterns in Dynamic Biological Networks

1998 ◽  
Vol 10 (7) ◽  
pp. 1831-1846 ◽  
Author(s):  
Patrick D. Roberts
Keyword(s):  
Graph Theory ◽  
Metric Space ◽  
Biological Networks ◽  
Temporal Patterns ◽  
State Transitions ◽  
Synaptic Connections ◽  
Functional Differences ◽  
Algebraic Properties ◽  
General Method

A general method is presented to classify temporal patterns generated by rhythmic biological networks when synaptic connections and cellular properties are known. The method is discrete in nature and relies on algebraic properties of state transitions and graph theory. Elements of the set of rhythms generated by a network are compared using a metric that quantifies the functional differences among them. The rhythms are then classified according to their location in a metric space. Examples are given, and biological implications are discussed.

scholarly journals Inferring Biological Networks by Sparse Identification of Nonlinear Dynamics

2016 ◽  
Vol 2 (1) ◽  
pp. 52-63 ◽  
Author(s):  
Niall M. Mangan ◽  
Steven L. Brunton ◽  
Joshua L. Proctor ◽  
J. Nathan Kutz
Keyword(s):  
Nonlinear Dynamics ◽  
Biological Networks

scholarly journals An efficient analytical reduction of detailed nonlinear neuron models

2018 ◽  
Author(s):  
Oren Amsalem ◽  
Guy Eyal ◽  
Noa Rogozinski ◽  
Felix Schürmann ◽  
Michael Gevaert ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cell Types ◽  
Computational Time ◽  
Neuron Models ◽  
Biologically Inspired ◽  
Transfer Impedance ◽  
Morphological Complexity ◽  
Activation Times ◽  
Voltage Dynamics ◽  
Computational Properties

AbstractDetailed conductance-based nonlinear neuron models consisting of thousands of synapses are key for understanding of the computational properties of single neurons and large neuronal networks, and for interpreting experimental results. Simulations of these models are computationally expensive, considerably curtailing their utility.Neuron_Reduceis a new analytical approach to reduce the morphological complexity and computational time of nonlinear neuron models. Synapses and active membrane channels are mapped to the reduced model preserving their transfer impedance to the soma; synapses with identical transfer impedance are merged into one NEURON process still retaining their individual activation times.Neuron_Reduceaccelerates the simulations by 40-250 folds for a variety of cell types and realistic number (10,000-100,000) of synapses while closely replicating voltage dynamics and specific dendritic computations. The reduced neuron-models will enable realistic simulations of neural networks at unprecedented scale, including networks emerging from micro-connectomics efforts and biologically-inspired “deep networks”.Neuron_Reduceis publicly available and is straightforward to implement.

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