Behavior Of Biological Systems Research Articles

Open problems in mathematical biology

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

Gas-liquid interface of a Lennard-Jones binary mixture controlled by differential activity: phase transition and interfacial stability.

We perform molecular dynamics simulations of a two-dimensional binary mixture of Lennard-Jones particles, characterized by some degree of "activity" inside. Starting from a base state that features a gas-liquid interface and a completely segregated system at thermodynamic equilibrium, we introduce differential scalar activity between the two species by prescribing two different effective temperatures. The differential activity is measured as the ratio of the two temperatures. Previous studies showed segregation in a homogeneously mixed system induced by high activity. In this study, we investigate the effect of activity on a pre-existing gas-liquid interface between two separated species. Whereas a high activity ratio induces the formation of new interfaces, we show that a low activity ratio destabilizes existing ones. Moreover, the combination of a pre-existent interface with differential activity leads to partial crystallization and thus to triple phase coexistence (solid, liquid and gas), which is observed over a wide range of moderate differential activities. Findings from this idealized system can guide our understanding of interfacial behaviors in certain biological systems.

Glückliche Fügung: Experiments' Potential to Integrate Disciplines.

This essay reviews the discipline‐connecting potential of experimentation. Two examples are used to illustrate how researchers in the first half of the twentieth century profitably combined resources from different disciplines in their experiments. These experiments were designed to test mechanism models describing chemical processes underlying the behavior of biological systems. The researchers had clear expectations about how certain interventions should affect the behavior of the organisms studied, if that behavior was indeed based on the presumed chemical processes. They manipulated the organisms in the relevant ways and determined how the behavior of the organisms changed as a result.

Optimal COVID-19 therapeutic candidate discovery using the CANDO platform.

The worldwide outbreak of SARS-CoV-2 in early 2020 caused numerous deaths and unprecedented measures to control its spread. We employed our Computational Analysis of Novel Drug Opportunities (CANDO) multiscale therapeutic discovery, repurposing, and design platform to identify small molecule inhibitors of the virus to treat its resulting indication, COVID-19. Initially, few experimental studies existed on SARS-CoV-2, so we optimized our drug candidate prediction pipelines using results from two independent high-throughput screens against prevalent human coronaviruses. Ranked lists of candidate drugs were generated using our open source cando.py software based on viral protein inhibition and proteomic interaction similarity. For the former viral protein inhibition pipeline, we computed interaction scores between all compounds in the corresponding candidate library and eighteen SARS-CoV proteins using an interaction scoring protocol with extensive parameter optimization which was then applied to the SARS-CoV-2 proteome for prediction. For the latter similarity based pipeline, we computed interaction scores between all compounds and human protein structures in our libraries then used a consensus scoring approach to identify candidates with highly similar proteomic interaction signatures to multiple known anti-coronavirus actives. We published our ranked candidate lists at the very beginning of the COVID-19 pandemic. Since then, 51 of our 276 predictions have demonstrated anti-SARS-CoV-2 activity in published clinical and experimental studies. These results illustrate the ability of our platform to rapidly respond to emergent pathogens and provide greater evidence that treating compounds in a multitarget context more accurately describes their behavior in biological systems.

Structure-activity assessment of flavonoids as modulators of copper transport.

Flavonoids are polyphenolic small molecules that are abundant in plant products and are largely recognized for their beneficial health effects. Possessing both antioxidant and prooxidant properties, flavonoids have complex behavior in biological systems. The presented work investigates the intersection between the biological activity of flavonoids and their interactions with copper ions. Copper is required for the proper functioning of biological systems. As such, dysregulation of copper is associated with metabolic disease states such as diabetes and Wilson’s disease. There is evidence that flavonoids bind copper ions, but the biological implications of their interactions remain unclear. Better understanding these interactions will provide insight into the mechanisms of flavonoids’ biological behavior and can inform potential therapeutic targets. We employed a variety of spectroscopic techniques to study flavonoid-Cu(II) binding and radical scavenging activities. We identified structural moieties important in flavonoid-copper interactions which relate to ring substitution but not the traditional structural subclassifications. The biological effects of the investigated flavonoids specifically on copper trafficking were assessed in knockout yeast models as well as in human hepatocytes. The copper modulating abilities of strong copper-binding flavonoids were largely influenced by the relative hydrophobicities. Combined, these spectroscopic and biological data help elucidate the intricate nature of flavonoids in affecting copper transport and open avenues to inform dietary recommendations and therapeutic development.

Cooperation in costly-access environments

Understanding cooperative behavior in biological and social systems constitutes a scientific challenge, being the object of intense research over the past decades. Many mechanisms have been proposed to explain the presence and persistence of cooperation in those systems, showing that there is no unique explanation, as different scenarios have different possible driving forces. In this paper, we propose a model to study situations in which voluntary participation involves an access cost to the cooperative interaction, besides the cost associated with cooperation. The proposed costly-access prisoner’s dilemma (PD), a symmetric donation game with voluntary and costly participation, breaks the symmetry between abstainers and participants of the voluntary PD. A mean-field approach shows that, in well-mixed populations, the dynamic always leads the system to abstention. However, depending on the return parameter, numerical simulations in structured populations display an alternating behavior between mono-strategic, multi-stable, and coexistence phases. This behavior is fully explained through a theoretical analysis of the strategic motifs, the transitions being determined by the change in stability of those motifs.

Impact of chloride channel on firing patterns of the fractional-order Morris–Lecar model

Fractional calculus as a new approach for modeling has been used widely to study the non-linear behavior of physical and biological systems with some degrees of fractionality or fractality using differential and integral operators with non integer-orders. In this paper, to explore different dynamical classes of the Morris–Lecar neuronal model with chloride channel, we extend its integer-order domain into a new fractional-order space using fractional calculus. The nonstandard finite difference (NSFD) method following the Grünwald–Letnikov discretization may be applied to discretize the model and obtain the fractional-order form. Fractional derivative order has been used as a new control parameter to extract variety of neuronal firing patterns that happen in real world application but the integer-order operator may not be able to reveal them. To find the impact of chloride channel on dynamical behaviors of this neuronal model, the phase portrait and time series analysis have been performed for different fractional-orders and input currents. Depending on different values for γ, the fractional-order Morris–Lecar model with a chloride channel reproduces quiescent, spiking and bursting activities the same as the fractional-order Morris–Lecar model without a chloride channel. We numerically discover the occurrence of hopf bifurcation, and homoclinic bifurcation for these two models. These results show that adding a chloride channel to this neuron does not affect the overall spiking patterns of the model, however, when we add this new ionic channel, the neuron needs higher input current as stimulus to fire action potential and spike.

In situ Analysis of the Fate and Behavior of Inorganic Nanomaterials in Biological Systems by Synchrotron Radiation X-ray Probe Techniques

Background: The comprehensive understanding of nanomaterial behavior in biological systems is essential in accurately modeling and predicting nanomaterial fate and toxicity. Synchrotron radiation (SR) X-ray techniques, based on their ability to study electronic configuration, coordination geometry, or oxidative state of nanomaterials with high sensitivity and spatial resolution, have been introduced to analyze the transformation behavior of nanomaterials in biological systems. Methods: Previous research in this field are classified and summarized. Results: To start with, a brief introduction of a few widely used SR-based analytical techniques including X-ray absorption spectroscopy, X-ray fluorescence microprobe, scanning transmission X-ray microscopy and circular dichroism spectroscopy is provided. Then, the recent advances of their applications in the analysis of nanomaterial behaviors are elaborated based on different nanomaterial transformation forms such as biodistribution, biomolecule interaction, decomposition, redox reaction, and recrystallization/agglomeration. Finally, a few challenges faced in this field are proposed. Conclusion: This review summarizes the application of SR X-ray techniques in analyzing the fate of inorganic nanomaterials in biological systems. We hope it can help the readers to have a general understanding of the applications of SR-based techniques in studying nanomaterial biotransformation and to stimulate more insightful researches in relevant fields.

Analysis of Neuronal Oscillations of Fractional-Order Morris-Lecar Model

Fractional calculus is a new approach for modeling biological and physical phenomena with memory effects. Fractional calculus uses differential and integral operators including non-integer orders to study the non-linear behavior of physical and biological systems with some degrees of fractionality or fractality. Since the long memory properties of neuronal responses can be better explained using fractional derivative, in this study we generalize the integer-order Morris-Lecar model in the fractional-order domain to better modeling of neuron dynamics. To investigate the complex spiking patterns of fractional-order Morris-Lecar neural system the fractional calculus has been applied to build this new mathematical model. We compare the results with integer-order Morris-Lecar model. The analytical solutions of these equations cannot explicitly be obtained. Therefore, to find the dynamical behaviors of solutions, we used approximation and numerical schemes. Depending on the different parameters values for 0<η≤1, the fractional-order Morris-Lecar reproduces quiescent, spiking and bursting activities the same as its original model but for higher input current. We numerically discover the hopf bifurcation, saddle node bifurcation of limit cycle and homoclinic bifurcation for this model for different input current and derivative orders. Taking the advantages of the fractional order derivative, for a variety of orders, we define different classes of this model which helps to better extract all the complicated dynamics of this single neuron model.

EpiBOX: An Automated Platform for Long-Term Biosignal Collection.

Biosignals represent a first-line source of information to understand the behavior and state of human biological systems, often used in machine learning problems. However, the development of healthcare-related algorithms that are both personalized and robust requires the collection of large volumes of data to capture representative instances of all possible states. While the rise of flexible biosignal acquisition solutions has enabled the expedition of data collection, they often require complicated frameworks or do not provide the customization required in some research contexts. As such, EpiBOX was developed as an open-source, standalone, and automated platform that enables the long-term acquisition of biosignals, passable to be operated by individuals with low technological proficiency. In particular, in this paper, we present an in-depth explanation of the framework, methods for the evaluation of its performance, and the corresponding findings regarding the perspective of the end-user. The impact of the network connection on data transfer latency was studied, demonstrating innocuous latency values for reasonable signal strengths and manageable latency values even when the connection was unstable. Moreover, performance profiling of the EpiBOX user interface (mobile application) indicates a suitable performance in all aspects, providing an encouraging outlook on adherence to the system. Finally, the experience of our research group is described as a use case, indicating a promising outlook regarding the use of the EpiBOX framework within similar contexts. As a byproduct of these features, our hope is that by empowering physicians, technicians, and monitored subjects to supervise the biosignal collection process, we enable researchers to scale biosignal collection.

Fluorescence Imaging of Neural Activity, Neurochemical Dynamics, and Drug-Specific Receptor Conformation with Genetically Encoded Sensors.

Recent advances in fluorescence imaging permit large-scale recording of neural activity and dynamics of neurochemical release with unprecedented resolution in behaving animals. Calcium imaging with highly optimized genetically encoded indicators provides a mesoscopic view of neural activity from genetically defined populations at cellular and subcellular resolutions. Rigorously improved voltage sensors and microscopy allow for robust spike imaging of populational neurons in various brain regions. In addition, recent protein engineering efforts in the past few years have led to the development of sensors for neurotransmitters and neuromodulators. Here, we discuss the development and applications of these genetically encoded fluorescent indicators in reporting neural activity in response to various behaviors in different biological systems as well as in drug discovery. We also report a simple model to guide sensor selection and optimization.

Influence of surface chemistry and morphology of nanoparticles on protein corona formation.

Nanomaterials offer promising solutions as drug delivery systems and imaging agents in response to the demand for better therapeutics and diagnostics. However, the limited understanding of the interaction between nanoparticles and biological entities is currently hampering the development of new systems and their applications in clinical settings. Proteins and lipids in biological fluids are known to complex with nanoparticles to form a “biomolecular corona”. This has been shown to affect particles' morphology and behavior in biological systems and their interactions with cells. Hence, understanding how nanomaterials' physicochemical properties affect the formation and composition of this biocorona is a crucial step. This work evaluates existing literature on how morphology (size and shape), and surface chemistry (charge and hydrophobicity) of nanoparticles influence the formation of protein corona. The latest evidence suggest that although surface charge promotes the interaction with proteins and lipids, surface chemistry plays a leading role in determining the affinity of the nanoparticle for biomolecules and, ultimately, the composition of the corona. More recently the study of additional nanoparticles' properties like shape and surface chirality have demonstrated a significant effect on protein corona architecture, providing new tools to tailor biomolecular corona formation.This article is categorized under:Therapeutic Approaches and Drug Discovery > Emerging TechnologiesToxicology and Regulatory Issues in Nanomedicine > Toxicology of Nanomaterials

Symmetries in Dynamic Models of Biological Systems: Mathematical Foundations and Implications

Symmetries are ubiquitous in nature. Almost all organisms have some kind of “symmetry”, meaning that their shape does not change under some geometric transformation. This geometrical concept of symmetry is intuitive and easy to recognize. On the other hand, the behavior of many biological systems over time can be described with ordinary differential equations. These dynamic models may also possess “symmetries”, meaning that the time courses of some variables remain invariant under certain transformations. Unlike the previously mentioned symmetries, the ones present in dynamic models are not geometric, but infinitesimal transformations. These mathematical symmetries can be related to certain features of the system’s dynamic behavior, such as robustness or adaptation capabilities. However, they can also arise from questionable modeling choices, which may lead to non-identifiability and non-observability. This paper provides an overview of the types of symmetries that appear in dynamic models, the mathematical tools available for their analyses, the ways in which they are related to system properties, and the implications for biological modeling.

Design, Implementation and Evaluation of Core/Periphery-based Network-oriented Mixed Reality Services

Many new network-oriented services have been developed in recent years, and Multi-access Edge Computing (MEC) has been standardized to improve the responsiveness of services. When deploying services in a MEC environment, it is necessary to consider a service structure that can flexibly switch service behaviors to meet various user requests and that can change service behaviors according to the real-world environment at a low implementation cost. In this paper, we introduce a core/periphery structure for service components, which is known as a model for flexible behavior in biological systems, and design and implement a network-oriented mixed reality service based on this structure. We investigate what kinds of functions should be developed to accommodate user requests in conjunction with various types of devices and real-world environments in which users and devices are located. To utilize the flexibility of a core/periphery structure, we regard core functions as those whose behaviors remain unchanged even when there are changes in user requests or the environment. In contrast, peripheral functions are those whose behaviors can change under such circumstances. Experiments reveal that implementation costs are reduced while retaining increases in service response time to less than 31 ms. These results show that taking advantage of a core/periphery structure allows appropriate division of service functions and placement of functions in a MEC environment, with only small penalties on latency and at a low implementation cost.

Optimal Experimental Design Based on Two-Dimensional Likelihood Profiles.

Dynamic behavior of biological systems is commonly represented by non-linear models such as ordinary differential equations. A frequently encountered task in such systems is the estimation of model parameters based on measurement of biochemical compounds. Non-linear models require special techniques to estimate the uncertainty of the obtained model parameters and predictions, e.g. by exploiting the concept of the profile likelihood. Model parameters with significant uncertainty associated with their estimates hinder the interpretation of model results. Informing these model parameters by optimal experimental design minimizes the additional amount of data and therefore resources required in experiments. However, existing techniques of experimental design either require prior parameter distributions in Bayesian approaches or do not adequately deal with the non-linearity of the system in frequentist approaches. For identification of optimal experimental designs, we propose a two-dimensional profile likelihood approach, providing a design criterion which meaningfully represents the expected parameter uncertainty after measuring data for a specified experimental condition. The described approach is implemented into the open source toolbox Data2Dynamics in Matlab. The applicability of the method is demonstrated on an established systems biology model. For this demonstration, available data has been censored to simulate a setting in which parameters are not yet well determined. After determining the optimal experimental condition from the censored ones, a realistic evaluation was possible by re-introducing the censored data point corresponding to the optimal experimental condition. This provided a validation that our method is feasible in real-world applications. The approach applies to, but is not limited to, models in systems biology.

Collective Behavior of Urease pH Clocks in Nano- and Microvesicles Controlled by Fast Ammonia Transport.

The transmission of chemical signals via an extracellular solution plays a vital role in collective behavior in cellular biological systems and may be exploited in applications of lipid vesicles such as drug delivery. Here, we investigated chemical communication in synthetic micro- and nanovesicles containing urease in a solution of urea and acid. We combined experiments with simulations to demonstrate that the fast transport of ammonia to the external solution governs the pH–time profile and synchronizes the timing of the pH clock reaction in a heterogeneous population of vesicles. This study shows how the rate of production and emission of a small basic product controls pH changes in active vesicles with a distribution of sizes and enzyme amounts, which may be useful in bioreactor or healthcare applications.

Chemically evolving DNA reactors in langevin dynamics simulations

A detailed molecular picture of the behavior of biological systems with spatial and temporal resolutions that are relevant to the involved processes can be provided by all-atom molecular dynamics simulations, or by more coarse-grained approaches relying on the propagation of diffusion equations (such as Langevin or Brownian dynamics). Yet, a crucial limitation of these approaches lies in their inability to explicitly account for the rupture/formation of chemical bonds, which would require in principle quantum approaches, thus preventing the study of e.g.

Quantum chemical and molecular docking studies of some phenothiazine derivatives

Phenothiazines are synthetic antipsychotics with a wide range of biological effects. Their properties are determined by the structure and variety of substituents in the heterocyclic system. It is known that various quantum chemical properties have a significant influence on drug behavior in biological systems. Because of the diversity in the chemical structure of phenothiazines and other drugs that include heterocyclic systems, quantum chemical calculations provide useful methods for predicting their effects. This study made an attempt to describe the physicochemical properties and the molecular docking simulation of phenothiazine derivatives. To predict the reactivity of phenothiazine derivatives, DFT-based descriptors including certain highest occupied molecular orbital and lowest unoccupied molecular orbital, energy gap, electronic chemical potential, chemical hardness, nucleophilicity, and electrophilicity were performed by using B3LYP / 6311 ++ G (d, p) level. The most and least active compounds were docked to the protein proteins glycosylphosphatidylinositol phospholipase D inhibitor (1GYM), anaphylatoxin receptor antagonist (6C1Q), arylacetonitrilase inhibitor (3UGC) and aspulvinone dimethylallyl transferase inhibitor (3RIX) to confirm the observations of DFT models and elucidate the mode of binding between this type of compound and the corresponding protein.

Dynamical behavior of cardiac conduction system under external disturbances: simulation based on microcontroller technology

The heart rhythm is one of the most interesting aspects of the dynamic behavior of biological systems. Understanding heart rhythms is essential in the dynamic analysis of the heart. Each type of dynamic behaviour can describe normal or pathological physiology. The heart is made up of nodes ranging from SA node (natural pacemaker) to Purkinje fibers. The electric current originates in the sinus node and travels through the heart until it reaches the Purkinje fibers, causing after its passage through each of the nodes a heartbeat thus constituting the electrocardiogram (ECG). Since the origin of the electric current is the sinus node, in this article we study numerically and experimentally by microcontroller the influence of the sinus node on the propagation of electric current through the heart. A study of the sinus node in its autonomous state shows us that in their coupled state, the nodes of the heart qualitatively reproduce the time series of the action potential of this latter, which leads to the recording of the ECG. A study when the sinus node is subjected to periodic pulsed excitation assumed to come from blood pressure, with the blood pressure, shows that for some selected frequencies, it is found that the nodes of the heart and the ECG exhibit responses having the same shape and the same frequencies as those of the pulsatile blood pressure. This suggests the possibility of using such a conversion and excitation mechanism to replicate the functioning of cardiac conduction system. The chaotic analysis of the sinus node subjected to a sinusoidal type disturbance is also presented, it shows that in its chaotic state, the nodes of the heart, as well as the ECG, provide very high frequency signals. This requires the control of the sinus node (natural pacemaker) in such a situation.

Shift-Invariant-Subspace Discretization and Volume Reconstruction for Light Field Microscopy

Light Field Microscopy (LFM) is an imaging technique that captures 3D spatial information with a single 2D image. LFM is attractive because of its relatively simple implementation and fast volume acquisition rate. Capturing volume time series at a camera frame rate can enable the study of the behaviour of many biological systems. For instance, it could provide insights into the communication dynamics of living 3D neural networks. However, conventional 3D reconstruction algorithms for LFM typically suffer from high computational cost, low lateral resolution, and reconstruction artifacts. In this work, we study the origin of these issues and propose novel techniques to improve the performance of the reconstruction process. First, we propose a discretization approach that uses shift-invariant subspaces to generalize the typical discretization framework used in LFM. Then, we study the shift-invariant-subspace assumption as a prior for volume reconstruction under ideal conditions. Furthermore, we present a method to reduce the computational time of the forward model by using singular value decomposition (SVD). Finally, we propose to use iterative approaches that incorporate additional priors to perform artifact-free 3D reconstruction from real light field images. We experimentally show that our approach performs better than Richardson-Lucy-based strategies in computational time, image quality, and artifact reduction.