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Modelling Bioactivities of Botanical Extracts Using Network Pharmacology and Polypharmacology.


Network pharmacology and polypharmacology are emerging as novel drug discovery paradigms. The many discovery, safety and regulatory issues they raise may become tractable with polypharmacological combinations of natural compounds found in whole extracts of edible and mixes thereof. The primary goal of this work is to get general insights underlying the innocuity and the emergence of beneficial and toxic activities of combinations of many compounds in general and of edibles in particular. A simplified model of compounds’ interactions with an organism and of their desired and undesired effects is constructed by considering the departure from equilibrium of interconnected biological features. This model allows to compute the scaling of the probability of significant effects relative to nutritional diversity, organism complexity and synergy resulting from mixing compounds and edibles. It allows also to characterize massive indirect perturbation mode of action drugs as a potential novel multi-compound-multi-target pharmaceutical class, coined Ediceuticals when based on edibles. Their mode of action may readily target differentially organisms’ system robustness as such based on differential complexity for discovering nearly certainly safe novel antimicrobials, antiviral and anti-cancer treatments. This very general model provides also a theoretical framework to several pharmaceutical and nutritional observations. In particular, it characterizes two classes of undesirable effects of drugs, and may question the interpretation of undesirable effects in healthy subjects. It also formalizes nutritional diversity as such as a novel statistical supra-chemical parameter that may contribute to guide nutritional health intervention. Finally, it is to be noted that a similar formalism may be further applicable to model whole ecosystems in general.


Network pharmacology and polypharmacology are emerging as novel drug discovery paradigms [1–4]. They hold promises for overcoming safety and efficacy pitfalls of single compound based therapeutic intervention [5–7]. Combinations of isolated synthetic or natural chemicals raises many safety issues, and for novel chemical entities, medicinal chemistry and regulatory bottlenecks are foreseeable [8, 9]. A polypharmacological alternative to combinations of drugs and/or purified natural compounds may be found in the use of (extracts of) whole edibles and mixes thereof, which form readily available complex mixes of natural compounds [10]. Their potential use in the rapid development as botanical drugs is facing regulatory challenges because their safety is questioned and their mode of action is considered as unknown [11].

Most (if not any) individual chemical substances will have a deleterious effect on an organism when exposed to a high dose of the latter, regardless of a therapeutic/nutritive effect at a therapeutic/nutritive dose. As an extreme example, many cerebral edema cases have been reported as a consequence of an excess of water intake [12]. Stated in a more general fashion, chemical compounds may induce desired and undesired effects.

Deleterious association of pharmacological actives (a fortiori drugs) is understood from a formal point of view and many examples of such are known [13]. Nevertheless, in such, association of many chemical compounds is in general far from being systematically deleterious as trivially proved by the existence in itself of edible plants (and animals).

Polypharmacology science as well as long standing drug screening observations evidenced that any chemical compound is interacting to some extent (from significant to negligible) with every constituent of an organism, resulting in desired and undesired effects [14, 15]. In order to be administrated to humans (more broadly, to animals of interest to humans), whether for therapeutic or nutritional usage, the undesired effects of chemical compounds found in foods, feeds and drugs, need to be negligible, at least with an acceptable risk/benefit ratio, at the dose where the desired effect is significant [16].

Our primary goal in this work is to get general and global insights, in opposition to detailed but highly focused molecular insights, underlying the innocuity and the emergence of absence of innocuity, i.e., a beneficial or toxic pharmacological activity, of environmental chemical exposure, e.g., foods and drugs, from a simplified theoretical framework. To do so, we define interconnected biological features and consider their departure from equilibrium to derive a simplified model of compounds’ and diseases’ interactions with an organism and of their desired and undesired effects and associated symptoms. We then use this model to compute the scaling of the probability of significant effects relative to nutritional diversity, organism complexity and synergy resulting from mixing compounds and edibles. This will allow us to compare in this aspect single chemicals (e.g., current drugs) versus mixes of chemicals (in particular edible botanicals and mixes thereof). The implication of the generalized model and of some of its properties will be discussed in regards of their medical and nutritional interest. We finally conclude on the possibility of elaborating complex mixes of extracts of edibles with desired biological and therapeutic properties and their relative a-priori risks of undesirable side effects, i.e., the risk of side-effects overwhelming therapeutic effects.


Biological Features

Here we present a simplified model of the systems functioning of an organism. It starts with the definition of an organism’s endogenous molecular and supra-molecular “biological features”. The latter arise from compounded molecular features that define additional microscopic, macroscopic and behavioral “biological features”. They can be defined not only at (macro-)molecular, sub-cellular structural and cellular levels, but also at the scale of an organ or of the whole body, and from there, also at physiological and cognitive levels. For the sake of this work, we assume that they can be quantified directly, or by some compounded calculation of one or several physical or chemical quantitative and qualitative measures (e.g., size, weight, temperature, blood-pressure, CRP level, cardiac rhythm, etc.), or by other means (e.g., mood, memory performance, level of pain, etc.).

To account for compartmentation, for every given chemical or biological characteristic, several distinct biological features may be defined for each different cellular compartment, organ, etc. The organism’s microbiota, especially its gastro-intestinal microbiota, plays a significant role in the organism’s chemical exposure. We therefore consider the microbiota, in its whole and in its microbial and chemical composition, as a set of additional endogenous biological features.

Features’ equilibrium states

We are not interested in the detailed instantaneous dynamics of the organism. Instead, we will concentrate on the “steady state” of the features, regarded as the time average over a certain extended or characteristic period of time T. For humans and domestic/livestock animals, a meaningful period T is 24h. For each feature fi we define formally the corresponding steady state feature Fi as:

Health, an ultimate feature, can be seen as a desirable macroscopic state defined by a subset of (if not all) steady state features laying at any moment within some “healthy boundaries”, e.g., body temperature close to 37°C, blood pressure close to “12/8”, PSA below 3 μg, etc… Disease, another ultimate feature which could now be defined as “1.0—health” (if health is constructed as a normed feature), is, broadly speaking, an undesired macroscopic state with at least one feature outside its “healthy boundaries”. As a matter of fact, the organism is surviving without assistance over an extended period of time only when it is in a healthy state. The reciprocal may be even a better basis for definition, health being the state in which the organism can survive without assistance in a “normal” environment over an extended period of time. The environment itself can be treated formally as a set of exogeneous biological features, i.e., which are not influenced by the organism’s endogenous features, e.g., nutrients availability and temperature.

Empirically, any organism struggles to return to a healthy state if for any reason, it has been pushed by any mechanism (e.g., by an excess or shortage of nutrients) away from the healthy state. This behavior can be defined as a form of homeostasis. At the feature level, acknowledging non-linear and network/interrelationships of features, such homeostasis can be put into equation as:

where ki is the rate (ki > 0), which is also the inverse of some characteristic dynamic time scale τi of response to a perturbation, Hi({Fj(t)}{j≠i}) is the homeostatic equilibrium value of a feature to acknowledge that it, at least to some extent, defined by (dependent on) all the other features of the organism, and Pi, defined with the property Pi(0) = 1, is an empirical polynomial approximation of the non-linear part of response function Fi(t) Pi(Fi(t)).

In the following, the detailed and numerical knowledge of ki, Pi and Hi({Fj(t)}{j≠i}) is not required as we focus mostly on a small perturbation model. Hence, Eq 2 reduces into in first degree approximation for small departures from the ideal homeostatic state:

When we are considering a steady state situation where ∂t Fi(t) = 0, Eq 3 implies as expected that:

Feature sub-typing

Environmental exposure can be contemplated as exogeneous features which are imposed onto the organism’s endogenous features. For clarity of the discussion, features will be differentiated in their notation relative to their nature:

  • Nk for environmental chemical exposure, e.g., nutrients and drugs, coined “N-type” features with homeostatic (or normal/healthy) value of nk for nutrients that are necessary to maintain health and with homeostatic value of 0 for any other chemical which is not required to maintain health, e.g., “exotic” nutrients, drugs, pollutants, etc. We define the period TN for required dietary features. It will range from typically 24 hours for “energetic” nutrients (e.g., sugar) to weeks for “structural” nutrients (e.g., proteins) and “vitamins”. Here we consider vitamins in a broad sense as being any chemical substance necessary for health, thus seen as a broad class that may not be limited to vitamins in the traditional sense.

  • Dl for disease causing agents, coined “D-type” features with homeostatic (or normal/healthy) value of 0. The period for long term disease installation is coined TD and scales typically from weeks to months. We differentiate between endogenous-disease features found only in patients, e.g., mutations, injuries, accumulated toxins, etc., and exogeneous-disease features such as allergens and biological agents, e.g., viruses, micro-organisms, parasites and, by convention in this work, tumors, which can potentially all be cleared from the organism through therapeutics and the immune system.

  • Ei for organism’s endogenous “E-type” features as defined earlier. In this work, we impose that N-type and D-type features are not influenced by E-type features, i.e., they are imposed to the organism by the environment (in a broad sense, including societal/medical influence, etc.). In doing so, we leave out immunological and psychosomatic feedback loops between E-type and N-type and D-type features, e.g., the organism reacting to a shortage of nutrients, which may nevertheless be of interest for further developments of the model, e.g., for exploring placebo/nocebo effects. Illness is defined in this work as the occurrence of out-of-homeostasis state E-type features induced by excess or shortage of N-type features and by D-type induced effects.

Some endogenous E-type features are compounds that are also found in the N-type environmental chemical exposure, e.g., glucose is found in both blood and nutrients. Some exogenous D-type features may also be found in different places. In those cases, we may consider again compartmentation, e.g., the glucose in the digestive tract as an N-type feature will be differentiated from the glucose level in other organism’s compartments, which are E-type features.

Citation: Mayer P (2020) Modelling bioactivities of combinations of whole extracts of edibles with a simplified theoretical framework reveals the statistical role of molecular diversity and system complexity in their mode of action and their nearly certain safety. PLoS ONE 15(9): e0239841.

ABSTRACT: Network pharmacology and polypharmacology are emerging as novel drug discovery paradigms. The many discovery, safety and regulatory issues they raise may become tractable with polypharmacological combinations of natural compounds found in whole extracts of edible and mixes thereof.
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