Optimization of energy and time predicts dynamic speeds for human walking

  1. Rebecca Elizabeth Carlisle
  2. Arthur D Kuo  Is a corresponding author
  1. University of Calgary, Canada

Abstract

Humans make a number of choices when they walk, such as how fast and for how long. The preferred steady walking speed seems chosen to minimize energy expenditure per distance traveled. But the speed of actual walking bouts is not only steady, but rather a time-varying trajectory, which can also be modulated by task urgency or an individual’s movement vigor. Here we show that speed trajectories and durations of human walking bouts are explained better by an objective to minimize Energy and Time, meaning the total work or energy to reach destination, plus a cost proportional to bout duration. Applied to a computational model of walking dynamics, this objective predicts dynamic speed vs. time trajectories with inverted U shapes. Model and human experiment (𝑁 = 10) show that shorter bouts are unsteady and dominated by the time and effort of accelerating, and longer ones are steadier and faster and dominated by steady-state time and effort. Individual-dependent vigor may be characterized by the energy one is willing to spend to save a unit of time, which explains why some may walk faster than others, but everyone may have similar-shaped trajectories due to similar walking dynamics. Tradeoffs between energy and time costs can predict transient, steady, and vigor-related aspects of walking.

Data availability

Data (Carlisle and Kuo, 2023, https://github.com/kuo-lab/short_walk_experiment) and code (Kuo, 2023, https://github.com/kuo-lab/simplelocomotionmodel) for this study are in publicly-accessible archives.

The following data sets were generated

Article and author information

Author details

  1. Rebecca Elizabeth Carlisle

    Biomedical Engineering Program, University of Calgary, Calgary, Canada
    Competing interests
    The authors declare that no competing interests exist.
  2. Arthur D Kuo

    Biomedical Engineering Program, University of Calgary, Calgary, Canada
    For correspondence
    arthurdkuo@gmail.com
    Competing interests
    The authors declare that no competing interests exist.
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0001-5233-9709

Funding

Natural Sciences and Engineering Research Council of Canada (CRC Chair,Tier 1)

  • Arthur D Kuo

Natural Sciences and Engineering Research Council of Canada (Discovery award)

  • Arthur D Kuo

Dr. Benno Nigg Research Chair

  • Arthur D Kuo

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Ethics

Human subjects: Informed consent was provided by human participants according to University guidelines. Approval was granted by the Conjoint Health Research Ethics Board (CHREB) of University of Calgary, approval identifier REB21-1497.

Copyright

© 2023, Carlisle & Kuo

This article is distributed under the terms of the Creative Commons Attribution License permitting unrestricted use and redistribution provided that the original author and source are credited.

Metrics

  • 1,501
    views
  • 231
    downloads
  • 13
    citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Open citations (links to open the citations from this article in various online reference manager services)

Cite this article (links to download the citations from this article in formats compatible with various reference manager tools)

  1. Rebecca Elizabeth Carlisle
  2. Arthur D Kuo
(2023)
Optimization of energy and time predicts dynamic speeds for human walking
eLife 12:e81939.
https://doi.org/10.7554/eLife.81939

Share this article

https://doi.org/10.7554/eLife.81939

Further reading

    1. Computational and Systems Biology
    Nobuhisa Umeki, Yoshiyuki Kabashima, Yasushi Sako
    Research Article

    The RAS-MAPK system plays an important role in regulating various cellular processes, including growth, differentiation, apoptosis, and transformation. Dysregulation of this system has been implicated in genetic diseases and cancers affecting diverse tissues. To better understand the regulation of this system, we employed information flow analysis based on transfer entropy (TE) between the activation dynamics of two key elements in cells stimulated with EGF: SOS, a guanine nucleotide exchanger for the small GTPase RAS, and RAF, a RAS effector serine/threonine kinase. TE analysis allows for model-free assessment of the timing, direction, and strength of the information flow regulating the system response. We detected significant amounts of TE in both directions between SOS and RAF, indicating feedback regulation. Importantly, the amount of TE did not simply follow the input dose or the intensity of the causal reaction, demonstrating the uniqueness of TE. TE analysis proposed regulatory networks containing multiple tracks and feedback loops and revealed temporal switching in the reaction pathway primarily responsible for reaction control. This proposal was confirmed by the effects of an MEK inhibitor on TE. Furthermore, TE analysis identified the functional disorder of a SOS mutation associated with Noonan syndrome, a human genetic disease, of which the pathogenic mechanism has not been precisely known yet. TE assessment holds significant promise as a model-free analysis method of reaction networks in molecular pharmacology and pathology.

    1. Computational and Systems Biology
    2. Genetics and Genomics
    Eric V Strobl, Eric Gamazon
    Research Article

    Root causal gene expression levels – or root causal genes for short – correspond to the initial changes to gene expression that generate patient symptoms as a downstream effect. Identifying root causal genes is critical towards developing treatments that modify disease near its onset, but no existing algorithms attempt to identify root causal genes from data. RNA-sequencing (RNA-seq) data introduces challenges such as measurement error, high dimensionality and non-linearity that compromise accurate estimation of root causal effects even with state-of-the-art approaches. We therefore instead leverage Perturb-seq, or high-throughput perturbations with single-cell RNA-seq readout, to learn the causal order between the genes. We then transfer the causal order to bulk RNA-seq and identify root causal genes specific to a given patient for the first time using a novel statistic. Experiments demonstrate large improvements in performance. Applications to macular degeneration and multiple sclerosis also reveal root causal genes that lie on known pathogenic pathways, delineate patient subgroups and implicate a newly defined omnigenic root causal model.