– Research Plan

Integral Biomathics aims to develop a research program with the following foci:

  1. development of a theoretical and computational framework that incorporates both oracles and mechanisms whereby real-life complexity can be captured to an extent that other contemporary approaches (e.g. systems biology) do not;
  2. stepwise elimination of oracles by generalizing the theory (or theories) underlying the framework; i.e. the oracles will gradually be replaced by statements/models that lie within the mathematical and computational theories being generalized;
  3. clear definition of milestones that include the following:
  4. conceptualization and elaboration of the computational framework that includes, but also separates meta-level oracles from mechanisms;
  5. construction of experimental and validation protocols to verify the legitimacy of the oracles (or classes thereof) and their interactions with the modeled mechanisms;
  6. search of statements/models within existing theories that will eventually replace a subset (if not all) of the oracles;
  7. discover/unveil new/neglected theories in an attempt to obtain a single “unified theory”.
  8. physical or hardware implementations of oracles. 

Life and mind have been escaping all effective complete theories to this moment. Therefore, we require that Integral Biomathics be an incomplete theoretical and computational framework. It uses oracle machines, but it remains always incomplete and extendible. Without oracles, theories can only reman “more incomplete“.


1. Challenges

Abstractions used in biology can be divided into three levels, shown in Fig.1. The level ordinarily employed by practitioners consists of what can be observed, measured and affected empirically. These are the domains of the ‘omics’ (genomics, proteomics, metabolomics, etc.) and the medical imaging disciplines (radiology, pathology). Rich tools abound at this level. Being quantitative in nature, omics and imaging data is readily handled by computing systems (incl. AI/ML methods backed by topological data analysis (TDA)). By assigning semantics and implied causality, biologists can rise to the next ‘logical’ level to devise hypotheses to develop theories to then be tested against more data. Usually, life science is conducted in the cycle between these two levels.

We theorize, experiment, measure, re-theorize. A problem with this ‘life cycle’ is that observations are permeated by prior theory or experience reports (e.g. clinical findings), which (pre)define the concepts being measured and enriched by data. This limits the scope of suggested hypotheses and the derived theories. Evolutionary progress is well served, but true insight is limited. This ‘corrupting’ embeddedness of theory in measurement and observation was criticized by Ludwig von Bertalanffy ([1], p. 25) in his treatise on organismic vs. mechanistic approaches to general system theory. Summing up, reductionist theories do not sufficiently inform system level or paradigm shifting theories because fundamental concepts will be interpreted in a new context. A view of life is needed that includes the way new system-level entities and interactions emerge, and become evident (e.g. a new virus outbreak like the 2019 SARS-CoV-2). To address this, I suggest a third, epistemological level of a meta-theory – Integral Biomathics – which addresses the living entity as a whole incl. its eco-system at large and Robert Rosen’s question about (the meaning of) “life itself” [2-3] while preserving the utility of the ‘lower’ levels.

Fig. 1: Methodologies for research in life sciences

The rationale for the new level is that living systems have essential system dynamics, which overlap and often do not have clear physiological expression. To advance biology and medicine, sustainable models are needed to unite the three conceptual levels. On the one hand – the concomitance of complex information and energy flows through living systems at multiple scales from molecules to cells, tissues to organ(ism)s and (eco)systems. All need to be coherently comprehended to adequately address challenges like developmental and epigenetic disorders, autoimmune and rare diseases, virus outbreaks, etc. On the other hand, the current state of systems biology and bioinformatics will not support the development of new theories and their transition to everyday practice, no matter how advanced AI becomes. Combined with addressing vexing system-level disorders, the problem is even more demanding when adding the challenges of personalized and precision medicine. Therefore, we propose addressing the third, epistemological level of integrated research in the context of real problems, which is blending into current bioinformatics and data science to provide a robust modern construct for exploration.

Our approach is formal and goes beyond the present state of science. It has been reviewed by peers in its essential elements. Our goal is to develop advanced tools for visualization, modeling and simulation for in silico medicine and life sciences based on this general understanding of life. They are supposed to extend and guide empirical research in a methodological way which adequately reflects the complexity of the emerging problems as they progress and are being solved. This will substantiate and accelerate the development, admittance and inclusion of novel research methods, therapies and medications.


2. Goals

Currently we are pursuing two distinct goals to support future personalized and precision medicine:

  1. Practical application in research of modern relational mathematics including category theory. We expect secondary goals of:
    • creating a precedent for the use of mathematically grounded methodology in medical diagnostics;
    • reducing the need for animal models in research.
  2. Demonstration of an elegant biomathematical solution to a challenging disorder involving complex systems biology that resists solution by current methods. Several disorders are candidates. A secondary goal is:
    • generation and validation of an overarching and easily comprehensible model for personalized medicine to target more reliable diagnosis and therapy.

Our approach is theory-driven and mathematical, i.e. (data) deductive, not (data) inductive like current AI/ML developments. Data is integrated a posteriori to validate the models. The ultimate goal pursued with this work is the development of a highly sophisticated decision support system for life sciences and medicine.


3. Approach

Integral Biomathics [4-11] was proposed as a unifying framework for both top-down and bottom-up research, addressing the third level and integrating with the other two levels shown in Fig. 1. Since 2010 this program has collected views of leading scientists, mathematicians and philosophers to reach beyond the current state of the art. The common goal is to devise a new paradigm for biomedical research that addresses a unified theory of life. Four large volumes constitute the collected results [5, 7, 9, 11]. Integral Biomathics is a continuation and extension of the research line traced by Rashevsky, Waddington-Goodwin, Varela-Maturana-Uribe, Rosen-Louie and others, in line with Wigner’s directives [12]. The core insight is that the clue to understanding living systems is their structured development as ‘organic’ multi-level complexes, captured by means of appropriate biomathematical and biocomputational formalisms.

The goal of the Integral Biomathics collaboration is to examine suitably eligible applications of mathematics and computation to biology. That is, the participants are looking for patterns in biology – called diagrams in mathematics – that can be informed by computable mathematics. Empirically observed relationships between the elements at many different levels must be preserved in all transforms among levels. It is not just making higher mathematics and theoretical computer science available for studying biology in a new way, rather a matter of finding just what (and which) kinds of fields fit in the problem descriptions and ‘solve’ them. (Note: We should keep in mind that there are also incomputable branches of physics and biology.) As a result, Integral Biomathics is substantially different from systems biology today and claims to be a new, extended branch of theoretical biology as it was envisioned some 50 years ago [13]. It comprises not only the relational aspect of theoretical biology, but also its experienced, first person (phenomenological) aspect in the models. Most characteristic is that it differentiates the proposed work from mainstream systems approaches. These either ignore Aristotle’s final causes (and hence the reality of life) or reduce them to nothing more than the effect of cybernetics.

Integral Biomathics is prepared to demonstrate powerful research capabilities at all levels [14-17]. Therefore, this field was expanded to also include: 

  1. the factual[1] “middle-out”/“inside-out”[2] causation, which takes into account the evolution of structure and function based on loss of homeostatic control -> based on cell-cell signalling -> mediated by soluble growth factors and their cognate receptors -> based on developmental and phylogenetic singling mechanisms for morphogenesis; and
  2. the “outside-in” causation, which takes into account the impact of mental, environmental and social factors on the health-disease toggle state of the organism.

This approach is novel because it assumes that health and disease are a continuum across all subsumptive hierarchies [22, 23] of a living organism, not ‘disease as the absence of health’, allowing for early detection and molecularly-targeted treatment, potentially alleviating the symptomology of disease, [24]. Thus, the “middle-out”/”inside-out” approach offers the opportunity to exploit novel biomarkers that would, lead to truly pre-emptive preventive medicine, [25]. For instance, when a patient is biopsied, in addition to the usual suspects, a whole new cadre of indicators consistent with the basic science of disease etiology could be employed. This would greatly reduce both the morbidity and mortality encountered by conventional medicine in which symptoms determine the diagnosis and treatment of disease. Thus, this is truly ‘personalized medicine’.

The larger project reaches beyond assumptions from current quantitative and experimental science to consider what and whether it is worth being investigated. It not only pursues Schelling’s call for a new dynamic mathematics that allows radically new theories adequate to life to be developed ([26], p. 9), but also makes this practically relevant with the further exploration of Rosen’s relational biology [27-28].


4. Solution

The core insight of Integral Biomathics is that the clue to understanding living systems is their structured development as ‘organic’ multi-level complexes, captured by means of appropriate biomathematical and biocomputational formalisms. Empirically observed relationships between the elements at many different levels must be preserved in all transforms among levels. Within this context, Simeonov and Ehresmann proposed a novel theory, being a synthesis of biomathematics and bio-computation: WLIMES, the Wandering Logic Intelligence Memory Evolutive Systems [29-31], a synergy between:

  • a non-axiomatic (i.e. “rigid but flexible”, [32]), multivalent higher-order situation and context aware spatiotemporal logic for self-organizing systems, WLI, [33-36], and
  • a dynamic category theory for multi-level, multi-agents, ME(N)S, [37-39].

This formal framework represents a sophisticated hybrid design methodology and framework for modeling the concepts and dynamics of multi-level complex living systems. The result of this effort shall be demonstrated by a practical implementation in bioscience, Fig. 2.

Fig. 2: The potential contributions of Integral Biomathics and WLIMES to personalized medicine and virtual oncology through iterative object model and process simulation enhancement with real data: life cycle steps 5-9.


A novel visual-haptic tool will be developed to allow scientists and practicing physicians to visually theorize, interact with ideas, and experience mathematical operations in a virtual and augmented reality context. Its major advantage is the capacity for smooth integration of mathematical deductive models into the traditional workflow of conventional inductive and abductive diagnostics and therapy [31]. Researchers will, jointly develop models from observed phenomena iteratively enhanced with real data. I envision a prototype implementation of the WLIMES formalism for virtual oncology, a Shared Augmented Reality Diagnosis Assistant (SARDA), illustrated in the top green colored side of Fig. 2. This tool will help physicians develop models of complex biological objects, their underlying processes and methods for their understanding and treatment. The suggested system architecture on the left-hand side of Fig. 2 goes beyond the present state of technology used for theoretical research in life sciences and personalized medicine. 

Equipped with this toolset, physicians will be able to address new challenges in their research practice. For instance, a key problem in tumor genesis and tumor dynamics is how the different tumor stem cells relate morphologically and biochemically among themselves and their environment. Obtaining a general system view from a multitude of elementary dynamics requires the use of abstract biomathematical tools such as the proposed relational mathematics and computation. These achieve an elegant system-state control based on purpose-driven visualization and affordances of objects and processes at the levels of Fig. 1.

The core of the suggested WLIMES solution is its visual language and calculus (VLC) embedded in an SARDA interactive environment. This approach can be applied in other fields such as virtual oncology, virology and immunology. A goal is for this innovation to lead a new generation of analytical and modeling tools urgently needed for creative and effective research not only in life sciences and medicine, but also other domains. This work proposal is novel and does not continue a currently funded effort.


[1] The first such diagnostic was based on the risk of newborns developing the chronic lung disease Bronchopulmonary Dysplasia (BPD), characterized by the proliferation of myofibroblasts as the dominant connective tissue phenotype in the alveolar wall, consistent with both developmental and phylogenetic processes, [18]. The myofibroblast phenotype is characterized by Wingless/int signaling. The same phenomenology occurs in chronic diseases of the kidney, liver, and gut, given that their development, homeostasis, and injury-repair are based on the evolution of cell-cell signaling for the establishment or recrudescence of homeostatic control.

[2] While Denis Noble accentuates on ‘Downward Causation’ as antipole to ‘Upward Causation’ in hierarchical systems, Sydney Brenner favors the intracellular ‘middle-out’ approach, [19]. In contrast, John Torday explored the relevance of the extracellular environment and the cell-to-cell signaling for determining the structure/function applied to development and phylogeny, [20, 21]. His approach revealed the actual mechanisms involved, and eliminated the artificial role of phenotypes. Based on epigenetic inheritance, Torday has concluded that the phenotype is not a ‘thing’, but rather a ‘process’ by which the organism collects epigenetic data from the environment that is assimilated by the egg and sperm during meiosis. It is the transcendent approach, cross-cutting spacetime via cell-to-cell signaling that is the key to Torday’s ‘middle-out’ causative approach, which is called ‘inside-out’ in Integral Biomathics. 




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