Part 1. Introductory remarks

TL; DR

1. Models are just simplified representation of a real world with some constraints, which quickly become obsolete and need to be updated from time to time.

2. In silico approach is the representation of complex, dynamic, normal and pathophysiological processes within mathematical and computational formalisms. Any in silico approach is an extension of QSP. In NOVA's approach this extension focuses on what matters to the patient and based on 3 main components:

   • disease model: model of biology and physiology of disease
   • treatment model: model of treatment behavior in the body
   • virtual population (VPop)

3. In silico is a helper to in vivo and in vitro research. The “traditional” studies will become confirmatory of in silico trials, rather than remain exploratory as they are today. In silico approach can also ameliorate the reproducibility crisis which has been widely accepted as a major obstacle in therapeutic R&D

What is a model?

A model is a representation of reality. According to the Robert dictionary, the definition of a model is "that which serves or must serve as an object of imitation to make or reproduce something"; it can also be “a simplified representation of a process, of a system”. The dictionary adds: "mathematical model (of a process): model formed by mathematical expressions and intended to simulate such a process".

Thus, modeling is the act of creating a model as a representation of natural phenomena which can be achieved by means of physical, mechanical or electronic processes, computational logical relationships, mathematical formulas or other techniques (see Table 1). The representation could thus be essentially visual or written only, like most current pathophysiological models.

Table 1: Examples of models, the natural phenomenon they represent and the purpose of the model

A computer simulation, from a logical and/or mathematical model of the studied process, seeks to predict output functions by modifying the inputs (e.g. the effect of the heel angle on the speed and the drift of an America's Cup competitor). That is simulating a real situation in an experimental setting on a smaller scale (with respect to time, space or both).

The above definitions give the model, and the modeling, a voluntary aspect which reflects the fact that we build a model of the process of interest for a given purpose. The model is therefore the result of an elaboration of the human mind confronted with a natural phenomenon and a challenge posed by this phenomenon to be addressed.

By extension, any reasonable construct based on knowledge concerning a given phenomenon (i.e. built through a defined collection of observations and experimental facts) can qualify as a model of this natural phenomenon.

To assess if and how well the model represents the phenomenon of interest accurately, model validity is employed. Validity is considered the quality of being true and correct and can be internal (the model “stands up”) and external (it is not in contradiction with other known facts that are not considered in the model, i.e. external to the defined collection of facts). Often the model’s internal validity derives from a theory intended to explain the phenomenon. But a model often (always?) catches more than the theory itself, because it integrates, explicitly or implicitly, the (or at least some of the) consequences of the theory. The mathematical representation of a model, when possible, allows formalization in a condensed and portable form, and lends itself to quantitative deductions. The translation of the physical or chemical processes into analytical functions allows estimation of the outputs by simulation. Simulation is obtained by artificially varying the inputs. It is indeed usually easier than analysis because, more often than not, an analytical solution is not available. The mathematical representation has enough advantages to be preferred as supported by Gilles-Gaston Granger[1]: "...mathematics is not a solitary game but a means of advancing the knowledge of the objects of the world, and of man in particular.”[2]

Two aspects of the word “model” in the context of natural and life sciences must be highlighted, because their consequences, in particular in the field of medicine and therapeutics, are crucial for its methodological approach and pivotal for its proper application.

The first aspect is that a model is always a reduction of the phenomenon studied, a simplification, which puts it within the reach of its designer and its user. Here we find the meaning of the "reduced model". Being constituted on a body of knowledge limited in comparison with the complexity and the infinite fragmentation of reality, a model is by essence a simplification.

The second aspect is a consequence of the first one: Since the underlying knowledge is constantly evolving, that representation is naturally both fragile and ephemeral. Indeed, a model will eventually become obsolete through the emergence of new knowledge as well as from both the insights obtained through confrontation of the model outcomes (outputs) with the perceptible reality (experience) and from the knowledge that was not incorporated in the model’s foundation. In this regard, the evaluation of its external validity (based on experience or observation) is crucial. This in turn will promote its replacement by a more adequate model, or at the very least guide modifications required to provide a better fit with perceived reality. But it is rare that the new model does not retain some inherent flaws of the obsolete one. As we will see later, a model, through the structure and the knowledge it integrates, is hinged on a research question which in turn fixes the model’s context of use, i.e. the space, time and other settings within which its predictions are supposed to be accurate.

The emergence of the in silico paradigm

At the end of the past century, science was challenged by the belief that reductionism, although it has paved the way for tremendous progress since the 17th century, cannot cope with the complexity of living systems. In 1999 an issue of Science (vol 284, issue 5411) translated in current biology the quotation of Poincaré. A holistic approach was called for to put together the enormous number of pieces of knowledge collected by reductionism. Thus, researchers started to show growing interest in modeling and computer-based applications in support of a paradigm shift.

Finding the right treatment for the right person at the right time has been the goal of precision medicine. However, the number of potentially efficacious treatments is already high, but additionally, with the advent of omics, the range and fragmentation of nosological[3] entities are staggering. This applies to diseases such as autism or leukemia, but also to rare cancers, to other diseases in need of efficient treatments (e.g. AMD, type 2 diabetes) or emerging diseases such as Covid-19, which need preventive measures or curative treatments. A new strategy needs to be crafted to handle the scattered landscape of diseases and treatment options. A promising option has presented itself with the emergence of in silico approaches, offering benefit/risk evaluation in both medicinal product discovery and development.[4] [5]

The broader concept of in silico approaches extends well beyond physiologically based pharmacokinetic (PBPK), systems biology and even the association of both, which, already have provided significant insights in new therapeutic strategies [6] [7]. The concept could be considered an extension of quantitative system biology (QSP). As will be detailed later, in the NOVA approach, this extension focuses on what matters to the patient.

The novel aspect with in silico approaches is the representation of complex, dynamic, normal and pathophysiological processes within mathematical and computational formalisms [8] [9]. Efforts to design mathematical representations of living systems is certainly not new [10] (see Box 1), the famous “Hill equation” was already developed at the beginning of the past century. Nowadays, pharmacokinetic modelling is being used on a daily basis in many academic and pharmaceutical labs. And QSP is becoming more and more popular. However, its comprehensive use in the discovery and development of new therapies or to understand complex diseases at a fundamental mechanistic level has emerged more recently at the turn of the century [8:1]. This development is mostly due to the advent of systems biology and its evolution into systems medicine and systems pharmacology. But despite their relative infancy, in silico approaches have already helped research by streamlining and accelerating innovation and development, optimizing clinical trial design and saving time and cost [11].

Box 1: A brief history of “receptor”, from intuition to concept

The classic story illustrates the interplay of various approaches to achieve significant progress. Paul Ehrlich imagined that there existed at the level of the "protoplasm" an antigen having a particular chemical and steric structure to which an equally particular structure adapts in "mirror", the antibody. He called this structure "receptor". In 1913 he extended this concept to the mode of action of the active principles of drugs which, according to him, required an interaction between the substance and the organism, an interaction implying a prior "fixation", or binding as it is referred to now. Langley imagined in 1905 that in the nerve, nicotine and curare all acted on a substance that was neither the nerve itself nor the muscle [12]. A.J. Clark completed with a quantitative vision (1937): (1) the idea that receptors represented only a very small part of biological structures; he estimated that the molecules of acetylcholine in sufficient quantity reduced the frequency of a frog’s heartbeat by 50% when covering only 0.001% of the cell surface; therefore the receptors represented only at most an equivalent fraction of the cell surface; (2) approaching the problem at the molecular level; (3) the application of the law of mass action to the active principle-receptor bond. Hence the law of Emax. The Hill equation had different origins: it was imagined to explain the release of oxygen by hemoglobin when carbon dioxide pressure varies.

The NOVA in silico approach is based on three components:

1. a mathematical representation of selected and curated knowledge about the biology and physiology of the disease system (the disease model)
2. a mathematical representation of the treatment behavior in the body and its mode of action[13] (the treatment model) - or a model of target alteration, and
3. a population of simulated patients with the condition of interest (the virtual population, VP), characterized by descriptors such as tumor cell markers, markers of T cell activation, or inflammatory markers or other model parameters.

In silico approaches have advanced enough to warrant a change in the way we identify new targets, understand mode of action and select the right candidates for clinical development, thus changing planning and implementation of clinical development[4:1] [14].

Proofs of concept

Several successful implementations of in silico approaches in different therapeutic areas exist[4:2] [5:1] [15] [16] [17] [18] [19]. A selection is presented here to show how they were used to answer specific questions. Only one of the following applications actually includes a disease and treatment model used with a VP to predict the efficacy on clinical outcomes[18:1]. In endometriosis, the in silico approach suggested a better biomarker for anti-oestrogen therapy[11:1]. In pain physiology, an in silico experiment demonstrated the need for considering a new and unknown degradation path for endogen cannabinoid[11:2]. In developmental physiology, in silico exploration helped to select among several hypotheses[8:2]. Von Dassow and colleagues explored the interactions among segment polarity gene products in the early D. melanogaster embryo during and after the segment polarity stage.[20] They designed a mathematical model encoding the known interactions. Regardless of the model parameter values, they could not reproduce the observed in vivo behaviour of the embryo. They hypothesized the existence of yet unknown additional, but biologically plausible, interactions. With the modified mathematical model, simulations fit with the observed behaviour of the fly embryo, indicating that the added interactions are likely to exist. In immuno-oncology, Schmidt et al. explored in silico synergistic effects of combining Ipilimumab, a CTLA-4 checkpoint inhibitor and Nivolumab, a PD-1 checkpoint inhibitor on tumour progression [19:1]. On a single virtual patient they observed a simulated marked increase in tumour shrinking compared to either compound alone. By comparing simulated compound actions on acute ischemic stroke in formally modelled human and rodent brain tissues, Dronne et al. found that the astrocyte/neuron ratio was a key factor in ion exchange modifiers efficacy on infarct size. Rodent and human brains have significantly different ratios, which explains why clinical trials with ion exchange modifiers failed, although more than 300 such compounds were successful on rodent models of ischemic stroke [17:1]. With a drug model and a disease model, Chabaud et al. simulated placebo controlled clinical trials to explore the dose-effect relation on the occurrence of effort angina pain during patient normal life of a new antianginal compound [18:2]. A virtual population was used with patient descriptor distributions derived from real data and literature. The simulated dose-effect relation was later confirmed by phase II trials. Although it concerns only a tiny part of human physiology, the last example deserves to be cited because it illustrates both the scientific process of which it is the culmination and the practical leaps, both in terms of new knowledge and in terms of aid to the development of new drugs and the advantage of a virtuous circle strategy (see below). The whole story was presented in a review paper by Denis Noble who took a large part in the development of the ionic exchange model [21]. In short, Alan Hodgkin & Andrew Huxley (HH) published in 1952 equations that described nerve conduction in the giant axon of the squid. The mathematical model correctly predicted the shape of the action potential, the impedance and the conduction velocity. For what was the first model to use mathematical reconstruction of experimentally determined kinetics of ion channel transport and gating they received the Nobel Prize for Physiology and Medicine in 1963. Later, Noble adapted the HH model to Purkinje fibres of the heart, adding new found ionic channels. Started a back and force research process, with the model predicting some experimental findings well and others poorly. The gaps between simulation outputs and in vitro results led to hypotheses on either additional properties of ionic channels already accounted for in the model or even new, unknown channels. Step by step, the process enabled the discovery of new channels or new properties and the continuous update of the model. At the end, the model reproduces well the accumulated knowledge that it was able to explain a severe cardiac event, torsades de pointe. So well that the FDA accepted the model as a way to test the arrhythmogenic cardiac toxicity of compound under development [22]. The updated model led to the discovery of new antiarrhythmic drugs. Interesting enough, a previously published phenomenological model did not lead to any of these scientific advances.

A paradigm shift is taking place with the opportunity to apply epistemological thinking into crafting the gold standard for in silico trials and to avoid the limitations of data-centric approaches which currently dominate many scientific communities. This prerequisite is a reconciliation between knowledge and data.

The in silico, in vitro and in vivo virtuous circle

Due to its nature, an in silico approach allows testing a large number and range of hypotheses in a rather limited length of time. However, this does not imply that in vitro and in vivo studies should be replaced. The well-controlled, adequately powered randomised clinical trial is and will continue to be the gold standard for showing safety and efficacy for a given treatment, regimen, and target population. But the cost, time, and other factors make the clinical trial an exceptionally inefficient tool for decisions with a broad scope (e.g. target selection, lead optimization), or where there are difficult combinatorics (combination therapies, multiple patient profiles). The in silico results can inform and improve in vitro and in vivo trials in these and other cases. For instance, the odds of estimating the optimal dose-effect relationship a priori using the traditional approach of running several dose-escalation studies are rather slim. This should result in a self-reinforcing crosstalk where hypotheses are first tested in silico. In vitro and in vivo studies in turn generate new data and knowledge which help to improve the disease and treatment models and the associated VP. This engages a virtuous circle which incorporates the in silico approach in support of traditional approaches (Figure 1). Thus, the paradigm shift here is that the “traditional” studies will become confirmatory of in silico trials, rather than remain exploratory as they are today. In this regard, in silico clinical trials have the potential to change the R&D paradigm.

There are tangible examples of the benefits of prior in silico testing to prove this point. Immunogenicity of a new recombinant protein has been predicted by an in silico model and was later confirmed in a dedicated clinical trial[23]. A dynamic biomarker of poor prognosis in neuroblastoma patients was identified by running a computational model of network that regulated stress signalling by the c-Jun N-terminal kinase (JNK) pathway and was later confirmed in a cohort of patients[24]. This model-based biomarker showed better predictive properties than current biomarkers[24:1] [25]. Another example was already mentioned previously: Dronne et al. showed by simulation the limitations of current animal models to select neuroprotective agents worth entering clinical development[17:2]. Had drug manufacturers used in silico testing at the time, their bench-to-bedside decision point would have been based on more solid evidence. Wasted time and money, and more importantly, uninformative, thus useless and thus unethical patient contributions would have been avoided.

Owing to its rigor and the need to carefully curate available knowledge to design disease models, the in silico approach can ameliorate the reproducibility crisis which has been widely accepted as a major obstacle in therapeutic R&D [26] [27] [28] [29]

Figure 1: The continuous crosstalk between in silico, in vitro and in vivo