Special Issue "New Advances in Biocomplexity"

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: 31 March 2020.

Special Issue Editor

Prof. Mikhail Prokopenko
E-Mail Website
Guest Editor
Centre for Complex Systems, Faculty of Engineering, The University of Sydney, Sydney, New South Wales, Australia
Tel. +61-2-9351-7569
Interests: guided self-organisation; information theory; machine learning; complex networks
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

Salient evolutionary transitions, such as the emergence of genetic coding, multicellularity or language, generate higher levels of organisation, with qualitatively new properties that are not fully predictable or explainable in reductionist terms. The higher levels of biological and/or social organisation are typically associated with increased complexity, resulting from dynamic interactions between the system, its constituent parts, and the external environment.

Biocomplexity is the multidisciplinary study of macroscale complex structures and collective behaviours that arise from microscale interactions of relatively simple biological agents, across multiple levels ranging from molecules and cells to organisms and ecosystems. The key concepts and features include emergence, self-organisation, feedbacks, nonlinearity, sensitivity to initial conditions, critical dynamics, resilience, as well as adaptation and evolution. Information theory, probability theory, and complex network theory provide rigorous frameworks to study these concepts quantitatively.

The aim of this Special Issue, aligned with a topical workshop, as well as an international symposium, is to highlight advances in biocomplexity achieved both in terms of the state-of-the-art and state-of-the-practice. Several areas are of special interest: Computational epidemiology and disease control, microbial ecology and biosecurity, functional genomics and bioinformatics, systems biology and artificial life, swarm intelligence and active matter, computational neuroscience and neuro-engineering, cognitive modelling and machine learning.

Prof. Mikhail Prokopenko
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • artificial life
  • biosecurity
  • collective behavior
  • critical dynamics
  • ecology
  • emergence
  • epidemiology
  • evolution
  • neuroscience
  • self-organization
  • systems biology

Published Papers

This special issue is now open for submission, see below for planned papers.

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Prediction of Robustness and Evolvability of Biological Networks Based on Antifragility
Authors: Hyobin Kim Stalin Muñoz 1,2, Pamela Osuna 1,3 and Carlos Gershenson 1,4,5
Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, 04510 CDMX, [email protected]
2 Facultad de Ingeniería, Universidad Nacional Autónoma de México, 04510 CDMX, México
3 Faculté des Sciences et Ingénierie, Sorbonne Université, 4 place Jussieu 75005 Paris, France
4 Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, 04510 CDMX, México
5 ITMO University, St. Petersburg, 199034, Russian Federation
Abstract: Robustness and evolvability are considered essential properties of biological networks. Robustness allows the existing functions to be conserved against internal perturbations (i.e., mutations), while evolvability enables new functions to be expressed. To determine if a biological network is robust or evolvable, we need to compare the functions before and after internal perturbations. However, such calculations are computationally expensive due to the combinatorial explosion of the state space as the number of network nodes grows. In this study, we aim at developing a predictor of robustness and evolvability that does not require the explicit comparison of the functions. The predictor is based on an easily calculable measure, antifragility. It is known as a property where systems not only resist stress but also benefit from it. In the context of Boolean networks, it can be computed by our previous approach [1, 2]. For this study, we add structural or functional perturbations to 33 different Boolean network models of biological systems, and then measure the antifragility of the original and mutated networks. By comparing their attractors representing cell functions before and after the internal perturbations, we classify the robustness and evolvability of the networks into four: not robust & not evolvable, not robust & evolvable, robust and & not evolvable, and robust & evolvable. We divide the classified data into training and test sets. From the training set, we fit a convolutional neural network (CNN) model with the difference of antifragility before and after the internal perturbations as input and property classification as output. We found that the properties were correctly classified for most cases on the test set (Figure 1). It indicates that antifragility can be used as a significant predictor to estimate robustness and evolvability in Boolean network models of biological systems.

Title: Mutual entropy – a general measure of specialization in interaction networks
Authors: Gilberto Corso a, Gabriel M. F. Ferreira b, Thomas M. Lewinsohn b
Affiliations:  a  Department of Biophysics and Farmacology, Institute of Biosciences, Federal University of Rio Grande do Norte, Brazil
b  Department of Animal Biology, Institute of Biology, University of Campinas, Brazil

Abstract: Entropy-based indices are long-established measures of biological diversity. Proposed at first as simple measures of diversity in collections of organisms, nowadays they are increasingly used to gauge the relative size of partitions of diversity at different spatial scales, for instance within and among localities in a given region (alpha versus beta-diversity).

Here, we tackle the problem of measuring the diversity of interactions among two distinct sets of organisms, such as plants and their pollinators or their herbivores. Sets of actual interactions in ecological communities are depicted as bipartite networks or, equivalently, as interaction matrices. Recent studies [both theoretical and empirical] have concentrated on distinctive structural patterns, such as nestedness or modularity, that are found in different modes of interaction. By contrast, we investigate the potential of mutual entropy as a general measure of structure in interactive networks. Mutual entropy (ME) is the fraction of total interaction entropy in which there is reciprocal matching; it measures the degree of reciprocal specialization between interacting organisms. In order to ascertain its usefulness as a general measure, we (a) propose analytical solutions for different sorts of models whenever possible; (b) examine the variation of ME with network dimensional parameters (size, size asymmetry and occupancy); (c) explore the sensitivity of ME to differences in matrix patterns, especially in nested, modular, and compound matrices.

As a general measure, ME should be insensitive or adjustable to dimensional or structural attributes. This enables conceptually and empirically fruitful and important comparative analyses, such as: (i) within similar ecological networks, along a geographical gradient or subject to different kinds or degrees of disturbance; (ii) over a range of increasing spatial scales or at increasing geographical distances; (iii) among different modes of ecological interactions, e.g. mutualistic or antagonistic networks. A general measure of structure, or reciprocal specialization, is a useful complement to other measures which pinpoint more specific attributes of particular networks.

Title: Phase transitions in spatial connectivity during influenza pandemics
Authors: Nathan Harding (1), Richard E Spinney (1), Mikhail Prokopenko (1,2)
(1) Centre for Complex Systems, Faculty of Engineering, University of Sydney, Darlington, NSW, 2008, Australia
(2) Marie Bashir Institute for Infectious Diseases and Biosecurity, The University of Sydney, Westmead, NSW, 2145, Australia
Abstract: We investigate phase transitions in spatial connectivity during influenza pandemics, relating epidemic thresholds to the formation of clusters defined in terms of average infection. The study is centred on a large scale agent-based model of influenza spread at a national level: the Australian Census-based Epidemic Model (AceMod). In using the AceMod simulation framework, which leverages the 2016 Australian census data and generates a surrogate population of ~23.4 million agents, we comprehensively analyse the spread of simulated epidemics across geographical regions defined according to the Australian Statistical Geography Standard. We consider the adjacent geographic regions with prevalence above a certain level as connected, and the resultant spatial connectivity is then analysed at specific time points of the epidemic. Specifically, we focus on the times when the epidemic prevalence peaks, either nationally (first wave) or at a community level (second wave). Using methods of percolation theory, we obtain probability distributions of cluster sizes, quantify the connectivity and identify critical regimes corresponding to abrupt changes in patterns of the spatial distribution of infection. The analysis of criticality is further confirmed by computing the Fisher Information in a model-independent way. The results suggest that the post-critical phase is characterised by different spatial patterns of infection developed during the first or second waves (distinguishing urban and rural epidemic peaks). Furthermore, we show that the gradient of infection connectivity is steeper in the post-critical phase driven by the second wave (rural) in comparison to the first wave (urban).

Title: Stochastic stability of a mathematical model of lac operon with multiple time delays: investigation of the bistable region
Authors: Maia Angelova; Asma Ahmed Ben-Halim; Krishna Busawon; Tania Pencheva; Sergiy Shelyag
Affiliation: 1. Deakin University, Australia 2. Northumbria University, UK 3. Bulgarian Academy of Sciences, Bulgaria
Abstract: The aim of this study is to investigate the stability properties of a model of the lac operon with multiple time delays, enhanced with stochastic perturbations. New sufficient conditions of exponential mean square stability are derived and threshold values are established analytically for this model. Numerical investigation of the bistability is performed with respect to the lactose concentration and noise terms. We demonstrate that the noise affects the behaviour in the bistable region, including switching due to the lactose concentration. The effect of noise represented by stochastic perturbation is investigated with respect to production of lactose in the lac operon system.

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