We intend to use the stochastic process model to describe the mechanisms of action of various diseases and why various therapies can only expect a partial effect.

First of all, we define a cyberspace of drug action, and various specific molecular mechanisms are formed by their specific pathways. We assume that the occurrence of disease is a stochastic process, i.e., it is a sequence formation similar to the hidden Markov process, and only some specific combinations of sequences correspond to specific health and disease states, so we can find that it can form a certain probability distribution. At present, the role of the pharmacological network is broken down into the influence of certain action pathways, such as agonists/antagonists of various receptors, from the function of underlying proteins such as sodium channel proteins to traverse upward, such as the neuronal firing of epilepsy can be inhibited by blocking sodium ion channels, from the super-super-conditioning of the membrane to reduce the excitability of the membrane to the treatment of epilepsy. But at the same time, it may have various side effects, which are based on a certain high-dimensional structure, that is, the sequence of selective expression of the probability matrix, which has a certain distribution, so the specific sequence may be the role we need, but often cannot avoid the occurrence of other effects. We can selectively counteract these effects through a certain combination of drugs, but the general situation still exists, after all, the competitive game of drug preparations lies in the change of blood concentration in the body, which is difficult to achieve accurate matching. If it is an influence at a high-dimensional level, it is also difficult to change the proportion of its specific state so that it can form the sequence we want with a certain probability. In essence, the specific clinical application is also because of this sequence matching, which allows us to continuously explore new effects of existing drugs. Specific clinical applications are understood by scientific research to have higher scores for the matching scoring matrix of these sequences.

These specific sequences are like the bottom layer of the quantum that we cannot define for the time being, but we know that they can build a certain correlation with the real world, that is, the mechanism of action of our various drugs is the influence of the protein expression network of their sublayers, which can emerge with a certain probability of a certain path, and can be shown by a series of experiments to show the changes in their specific expression levels, such as the activation of various bottom sodium ion channels by drugs/ Inhibition may have other effects of upward traversal, such as inhibition of neuronal signaling, which ultimately suppresses seizures. These specific mechanisms are the various possible targets that we have. We can exert a deterministic influence on it to observe the possible needs of it, and as long as our newly discovered chemicals can have a good impact on certain animal models, further clinical trials can be carried out in humans. But the problem is that this is a lot of luck, and the appearance of various possible side effects is also very unsatisfying.

So we started thinking about synthesizing these mechanisms, and we wanted to be able to unify the knowledge that we had paid so much for in a higher dimension. In this regard, the fundamental theorem of calculus gives us a lot of inspiration, we can assume that the specific action function of this drug is continuous, and our synthesis of specific mechanisms is like the sum of infinitesimal quantities (I know this is a very unreasonable assumption, the granularity of the more specific mechanisms is still quite large, but if we do not demand precision in the first place, we can organize it into a better approximation, which is the basis of our next work), so different specific mechanisms correspond to different parts of this function, and according to various median value theorems, we know that in this continuous function, there is at least a certain point, which can refer to the properties of the whole in terms of local properties, such as the value of the point multiplied by the interval length equals the area covered by the function, and so on. Of course, it is dynamically changing in the biological network, and this point is different in different states of the body, and we may find this specific point, and then the state changes after the application of the action, and then this point changes. This situation is desperate to think about, so we intend to ignore it for the time being, assuming that it is relatively fixed or that there is a certain pattern of distribution in its variation, from a known static point of view.

But the sum of this effect is relatively static, and there may be a greater difference from the actual situation, so we introduce the concept of game, we will have a certain tendency to these possible mechanisms, that is, the pursuit of greater existence, competing with each other for limited living space, and finally being able to reach a certain equilibrium, that is, different mechanisms exist in a relatively stable proportion, which is the Nash equilibrium. The concept of Nash equilibrium is derived from Brouwer's fixed point principle, which is that in the transformation of the whole, there are changes in specific parts that are invariant, and this theorem has many interesting derivative theorems such as the hairball theorem and so on. But this is all found in the nature of the whole to the part, and we have a conjecture that we can have an effect on the whole with the influence of these parts? We make a series of inferences with this bold idea (and if this conjecture is wrong, then everything that follows is nonsense), and we can find the best treatment based on the information we know, such as various combinations of drugs.

Next, we introduce the idea of stochastic processes, because the events of biological networks are inherently probabilistic. Therefore, in the collection of the etiology of a disease, there are multiple elements, that is, possible underlying mechanisms, and we believe that the specific occurrence of the disease is a probabilistic event, which may be the result of the expression of different proportions of these underlying mechanisms, that is, the achievement of equilibrium. Therefore, according to the preceding fixed point hypothesis, we believe that there is a mechanism that can synthesize all the mechanisms in a holistic manner to a certain extent, and that the influence that we can exert on this mechanism is holistic, that is, to move the balance of the body's disease state so that the body returns to health. In the case of Alzheimer's disease, the hyperphosphorylation of Tau protein can play a x% role in this mechanism, and the deposition of Aβ protein can play a y% role in this mechanism...... , and then add up the probabilities of the above known mechanisms, and we can keep approaching 100%. After grasping this overall framework, we can think that in the occurrence of specific individual diseases, although the specific mechanism plays a different proportion, we can find its possible immobile pathway from a high-dimensional perspective, and then we can exert influence on it and play a better curative effect. I used the hidden Markov model to construct that these underlying states have a certain proportion, which can form a certain matrix of transition probabilities, and then in the formation of specific sequences, there is a competition for the sum of the probabilities of the specific formation of various sequences, and these sequences correspond to the different health conditions of the organism. The specific algorithm can refer to the dynamic programming and BLAST algorithm of bioinformatics, and we can think that it has a higher degree of matching, that is, the combination and sequence of the scores of the scoring matrix may be closer to the fixed point we need, that is, a certain probability distribution function is constructed with the matching degree.

When it was first established as a model, I was just amazed at the beautiful structure of this mathematical model, but I never understood what it was for, and I wondered if I was overly complacent. However, it has now been found that it may play a good role in the search for the mechanism of our drug treatment and the determination of the final treatment plan.

Of course, it is still a conjecture on paper, but I think that perhaps this is the underlying philosophical and mathematical tool for the application of medical big data.