Biosystems

The present study was attempted to measure whether the dynamics of elementary coordination is influenced by an overarching temporal structure that is embedded in circadian rhythms (part 1) as well as the systemic proof associated with the intelligent capabilities (part 2). For part 1, evidence of entrainment or any influence of the embedding rhythm were examined on the stability or attractor location. The estimations from the dynamics of the relative phase between the two oscillations show that while (i) circadian effects under the artificially perturbed manipulation were not straightforward along the day-night temperature cycle, (ii) the circadian effect divided by the ordinary circadian seems to be constant along the day-night cycle. Corresponding to this evidence related to performance consequences depending on the organism and environmental interaction, the part 2 determined the impact of circadian (mis)alignment on biological functions and raised the possibility that the disruption of circadian systems may contribute to physical complications. The observations entail rules that self-attunement of current performance may develop not at a single component but across many nested, inter-connected scales. These inter-dependencies from different object phase may allow a potential context-dependent explanation for goal-oriented movements and the emergent assumption of a principle of organisms embedded into their environmental contexts.

A modeling is a mathematical tool, like a microscope, which allows consequences to logically follow from a set of assumptions by which a real world problem can be described by a mathematical formulation. It has become indispensable tools for integrating and interpreting heterogeneous biological data, validating hypothesis and identifying potential diagnostic markers. The modern molecular biology that is characterized by experiments that reveal the behaviours of entire molecular systems is called systems biology. A fundamental step in synthetic biology and systems biology is to derive appropriate mathematical model for the purposes of analysis and design. This manuscript has been engaged in the use of mathematical modeling in the Gene Regulatory System (GRN). Different mathematical models that are inspired in gene regulatory network such as Central dogma, Hill function, Gillespie algorithm, Oscillating gene network and Deterministic vs Stochastic modelings are discussed along with their codes that are programmed in Python using different modules. Here, we underlined that the model should describes the continuous nature of the biochemical processes and reflect the non-linearity. It is also found that the stochastic model is far better than deterministic model to calculate future event exactly with low chance of error.

We have studied the resetting behavior of eight basic integral controller motifs with respect to different but constant backgrounds. We found that the controllers split symmetrically into two classes: one class, based on derepression of the compensatory flux, leads to more rapid resetting kinetics as backgrounds increase. The other class, which directly activates the compensatory flux, shows a slowing down in the resetting at increased backgrounds. We found a striking analogy between the resetting kinetics of vertebrate photoreceptors and controllers based on derepression, i.e. vertebrate rod or cone cells show decreased sensitivities and accelerated response kinetics as background illuminations increase. The central molecular model of vertebrate photoadaptation consists of an overlay of three negative feedback loops with cytosolic calcium [Formula], cyclic guanosine monophosphate (cGMP) and cyclic nucleotide-gated (CNG) channels as components. While in one of the feedback loops the extrusion of [Formula] by potassium-dependent sodium-calcium exchangers (NCKX) can lead to integral control with cGMP as the controlled variable, the expected robust perfect adaptation of cGMP is lost, because of the two other feedback loops. They avoid that [Formula] levels become too high and toxic. Looking at psychophysical laws, we found that in all of the above mentioned basic controllers Webers law is followed when a "just noticeable difference" (threshold) of 1% of the controlled variables set-point was considered. Applying comparable threshold pulses or steps to the photoadaptation model we find, in agreement with experimental results, that Webers law is followed for relatively high backgrounds, while Stephens power law gives a better description when backgrounds are low. Limitations of our photoadaption model, in particular with respect to potassium/sodium homeostasis, are discussed. Finally, we discuss possible implication of background perturbations in biological controllers when compensatory fluxes are based on activation.

Biological noise results from heterogeneous gene expression levels among a group of cells [1]. This heterogeneity is due to the variation in gene expression that occurs over time at the single-cell level. Some noise-filtering mechanisms like redundancy in genetic circuits have been identified. Likewise, the feed-forward loop network motif has been found to have noise-filtering capacities in animal development. On the other hand, previous studies have contradictory conclusions about the noise-filtering capacities of the feedback loop and none of them have studied this capacity in the activator-inhibitor regulatory system. Here we studied some dynamical properties, such as noise and expression levels, in self-activated and activator-inhibitor regulatory systems, both at the unicellular and multicellular levels. These systems are essential in the self-patterning and community effect processes occurring in development and differentiation. We used the three-stage model to represent the expression of a gene with promoter regulation and Hill functions to represent the regulatory connections between genes. We used Gillespies Algorithm and the Chemical Langevin Equation for simulations. The regulatory systems evaluated do not reduce the biological noise. On the contrary, the noise remains at the same level or increases in comparison with an unregulated gene. The noise levels in these systems depend on the gene expression type of both the regulator and the regulated gene. In this way, the particular forms in which genes connect to each other in these regulatory systems do not explain the noise in expression. However, the noise has a propagation pattern different for activation and inactivation types of regulation. Finally, the diffusion and colony size could be mechanisms of noise filtering in gene expression in a colony of cells. The increase in diffusion rate and colony size are necessary to synchronize gene expression and perform the community effect in embryonic development.

In the framework of resource-competition models, it has been argued that the number of species stably coexisting in an ecosystem cannot exceed the number of shared resources. However, plankton seems to be an exception of this so-called "competitive-exclusion principle". In planktic ecosystems, a large number of different species stably coexist in an environment with limited resources. This contradiction between theoretical expectations and empirical observations is often referred to as "The Paradox of the Plankton". This project aims to investigate biophysical models that can account for the large biodiversity observed in real ecosystems in order to resolve this paradox. A model is proposed that combines classical resource competition models, metabolic trade-offs and stochastic ecosystem assembly. Simulations of the model match empirical observations, while relaxing some unrealistic assumptions from previous models. Paradox: from Greek para: "distinct from", and doxa: opinion. Sainsbury (1995) defines a paradox as "an apparently unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises". Paradoxes are useful research tools as they suggest logical inconsistencies. In order to spot the flaw, the validity of all the premises has to be carefully assessed. Plankton: refers to the collection of organisms that spend part or all of their lives in suspension in water (Reynolds 2006). Plankton, or plankters, are "organisms that have velocities significantly smaller than oceanic currents and thus are considered to travel with the water parcel they occupy" (Lombard et al. 2019). Phytoplankters refer to the members of the plankton that perform photosynthesis.

The dynamic processes of multicellular organism development are regulated and coordinated by Gene Regulatory Networks (GRNs). Therefore, a sustained effort to understand the dynamical properties of these modularly structured networks has shown the great utility of experimentally grounded and dynamically characterized discrete Boolean models, as an ideal formalism based on dynamical systems modeling tool for its qualitative description. Up to now, several low-dimensional Boolean GRNs have been proposed to recover gene activation configurations observed for specific cell types, and they have been validated via robustness and mutant analyses. Nevertheless, systematic studies that elucidate the role of individual genes implicated on transitions between given attractors in the context of morphogenetic patterns of development, are still very scarce. Such sort of studies is in fact quite relevant because genes belonging to a given GRN do not work in isolation. Indeed, they could interact with others GRNs and/or with micro-environmental cues. Consequently, the structural specificities of the involved genes at the network level should be assessed in order to uncover the functional nature of the larger network involved. This is particularly meaningful when considering the role played by specific genes on transient dynamics related to cell fate specification. Following this idea, we propose here a computer-based analytical procedure intended to elucidate the role that specific genes play on the reachability properties of GRNs. As a structural property of a given dynamical network, reachability characterizes the attainability of specified attractors from given initial attractors as a consequence of the action of specific driving exogenous stimuli. Our proposal is based on algebraic systems approaches built around the Semi-Tensor Product (STP). We illustrate here our proposed procedure through the exploration of the reachability properties of the well-known Floral Organ Specification GRN of Arabidopsis thaliana (FOS-GRN), that recovers ten fixed-point attractors. Our findings suggest that there exist 79 inducible transitions among all possible pairs of attractors, with a suitable external Boolean control input over different well-characterized nodes of the network. Additionally, we found that such potentiality of these genes to produce attractor transitions is maintained by the continuous approximation model of the FOS-GRN, recovering not only qualitative but also useful quantitative information. Finally, we discussed the biological significance of our results and, even if we do not establish the specific molecular nature of the characterized exogenous control input, we concluded that reachability analysis can give us some important insights on the network level role that individual genes acquire by their collaboration with the GRN, becoming then targets in cell-fate decisions during development. Author summaryBringing to light the specific role that given genes play in gene regulatory networks is of particular importance, especially when it is necessary to quantify the influence of the environment on their dynamics. However, this becomes difficult by the fact that the genes in the network interact both nonlinearly and in the presence of feedback-based interactions. This requires then the development of methods of analysis that take into account such complex interdependencies. In this regard, Control Theory offers tools that allow characterizing the changes in the transition patterns between stable configurations (that is, cellular phenotypes) of the networks as a result of the presence of exogenous stimuli. In this work we propose a method based on the algebraic representation of small size gene regulatory networks, we first described in discrete Boolean terms, focused on delimiting the influence that specific nodes of the network play in the enhancement of transitions that define trajectories in the space of stable configurations of the state of expression of the genes involved. The proposed method uses the key control-oriented concept of reachability and is illustrated by the characterization of some induced morphogenetic trajectories that explain the development stages of Arabidopsis thaliana flower organs. Our proposal allows us to confirm that, in biological terms, the reachability analysis offers powerful tools to deepen the understanding of the interplay between the structure of specific gene regulatory networks involving both their own constitutive elements and including the networks with which they interact. This contributes to the understanding of biological development, which opens an access route to the exploration of the basic principles that associate the structure of gene regulatory processes not only with cell reprogramming and cell dedifferentiation, but also with dynamic processes underlying phenotypic plasticity and its evolutionary consequences. This is because the explanation of phenotypic change responses to environmental variability requires specifying how the constraints that govern developmental trajectories, potentially elucidated through reachability analysis, modulate the balance between phenotypic robustness and evolvability.

DNA replication introduces a gradient of gene copy numbers, and in Bacteria it affects gene expression accordingly. In E. coli and other species, the slope of the gradient averaged over the population can be predicted on the basis of its relationship with growth rate. In this work we integrated this growth- and position-dependent gradient into a classical transcriptional regulation model, to highlight their interaction. The theoretical treatment of our model highlights that the sensitivity to transcription factor-mediated regulations acquires an additional dimension related to the position of a locus on the oriter axis and to division time. This reinforces the idea of replication as an additional layer in gene regulation. We highlight here that replication- and transcription factor-mediated regulations can in theory work in concert or counteract each other, and we discuss why this is important from an evolutionary point of view with respect to both steady state transcript abundance and its variance across conditions. Finally, we note that this treatment may improve the estimation of kinetic parameters for transcription factor activity using RNA-seq data, and the estimation of the dispersion factor in differential gene expression analysis when division time across conditions changes significantly.

Breast cancer is one of the most frequent cancers affecting women. Non-coding micro RNAs (miRNAs) seem to play an important role in the regulation of pathways involved in tumor occurrence and progression. Extending on the research in Haakensen et al., where significant miRNAs were selected as being associated with the progression from normal breast tissue to breast cancer, in this work we put forward 112 sets of miRNA combinations, each including at most 5 expressions with high accuracy in discriminating healthy breast tissue from breast carcinoma. Our results are based on a recently developed machine learning technique which, instead of selecting a single model (or combination of features), delivers a set of models with equivalent predictive capabilities that allow to interpret and visualize the interaction of these features. These results shed new light on the biological action of the selected miRNAs which can behave in different ways according to the miRNA network with which they interact. Indeed, these revealed connections may contribute to explain why, in some cases, different studies attribute opposite functions to the same miRNA. It is therefore possible to understand how the role of a genomic variable may change when considered in interaction with other sets of variables, as opposed to only considering its effect when it is evaluated within a unique combination of features. The approach proposed in this work provides a statistical basis for the notion of chameleon miRNAs and is inspired by the emerging field of systems biology. Author SummaryO_LIThe notion of a single predictive genomic (statistical) model is replaced by that of a set of models that can be considered as exchangeable due to their indistinguishable (optimal) predictive abilities; C_LIO_LIOur results indicate that the role of miRNAs cannot be interpreted independently from the combination of features with which they interact and can therefore vary considerably when considered in a network of different combinations. Some miRNAs may act as chameleons and behave in opposite manners thereby showing some kind of antagonistic duality; C_LIO_LISome miRNAs are exchangeable inside models with equivalent predictive ability and seem to point to latent biological functions. C_LI

Biological systems, at all scales of organization from nucleic acids to ecosystems, are inherently complex and variable. Therefore mathematical models have become an essential tool in systems biology, linking the behavior of a system to the interaction between its components. Parameters in empirical mathematical models for biology must be determined using experimental data, a process called regression because the experimental data are noisy and incomplete. The term "regression" dates back to Galtons studies in the 1890s. Considering all this, biologists, therefore, use statistical analysis to detect signals from the system noise. Statistical analysis is at the core of most modern biology and many biological hypotheses, even deceptively. Regression analysis is used to demonstrate association among the variables believed to be biologically related and fit the model to give the best model. There are two types of regression, linear and nonlinear regression to determine the best fit of the model. In this manuscript, we perform a least squares error fit to different models and select the best fit model using the{chi} 2-test, and determine the p-value of the selected model to data that was collected when various doses of a drug were injected into three animals, and the change in blood pressure for each animal was recorded.

This paper introduces the notion of cumulative dose response (cDR). The cDR is the area under the plot of a response variable, an integral taken over a fixed time interval and seen as a function of an input parameter. This work was motivated by the accumulation of cytokines resulting from T cell stimulation, where a non-monotonic cDR has been observed experimentally. However, the notion is of general applicability. A surprising conclusion is that incoherent feedforward loops studied in the systems biology literature, though capable of non-monotonic dose responses, can be mathematically shown to always result in monotonic cDR.

Human-Brain Artificial-Intelligence Matrix is a new technology aims to connect the human brain with the machine for the purpose of enabling the human brain to perform defined functions even if it becomes unable to perform them such as performing the function of vision in case of blindness, the function of hearing in case of deafness, Performing the function of motion in case of paralysis and many other functions. This technology will be based on the Cognition Theory which I argue about that the whole process of cognition can be treated quantum-mechanically. The cognition starts when a neuron sends data to be processed in the brain and ends in an effector to respond. The data "action potential" is a current of particles which can be described quantum-mechanically as a wave-impulse based on the dual nature of the particles. The neurons are a net of entangled cells classically and quantum-mechanically. When the action potential changes the potential of the neurons, it creates quantum mechanical potential wells and barriers. The action potential perfectly transmits in and out the neurons through quantum mechanical tunnels. The form of energy before processing is not the same after, but the amount of energy is always conserved. Since the neurons are entangled during the action potential transmission, the brain and effector will be entangled during the action potential processing. The effectors cognition of data must be a discrete cognition of single-valued data from its self-adjoint matrix which entangled with brain matrix.

The ability of some microorganisms to switch from respiration to fermentation in the presence of oxygen-the so-called Crabtree effect-has been a fascinating subject of study at the theoretical and experimental fronts. Game-theoretical approaches have been routinely used to examine and explain the way a microorganism, such as yeast, would switch between the two ATP-producing pathways, i.e., respiration and fermentation. Here we attempt to explain the switch between respiration and fermentation in yeast by constructing a simple metabolic switch. We then utilise an individual-based model, in which each individual is equipped with all the relevant chemical reactions, to see how cells equipped with such metabolic switch would behave in different conditions. We further investigate our proposed metabolic switch using the game-theoretical approach. Based on this model, we postulate that individuals play a mixed game of glucose metabolism in the population. This approach not only sheds some light in the varieties of metabolic regulations that can be utilised by the individual in the population in competition with others for a common resource, it would also allow a better understanding of the causes of the Warburg effect and similar phenomena observed in nature.

Formal interaction networks are well suited for representing complex biological systems and have been used to model signalling pathways, gene regulatory networks, interaction within ecosystems, etc. In this paper, we introduce Sign Boolean Networks (SBNs), which are a uniform variant of Threshold Boolean Networks (TBFs). We continue the study of the complexity of SBNs and build a new framework for evaluating their ability to extend, i.e. the potential to gain new functions by addition of nodes, while also maintaining the original functions. We describe our software implementation of this framework and show some first results. These results seem to confirm the conjecture that networks of moderate complexity are the most able to grow, because they are not too simple, but also not too constrained, like the highly complex ones. Biological Regulation, Biological Networks, Sign Boolean Networks, Complexity, Extensibility, Network Growth

Cell signaling systems are involved in sensing changes in the environment by activating a set of transcription factors (TF) that typically diffuse within the nucleus to trigger transcription of the required genes. The TFs can diffuse randomly in and out of the nucleus leading to fluctuations in different components which severely limits the accuracy of estimating environmental input. The diffusion usually happens through the nuclear pore complexes which enables the tf protein to enter the nucleus either passively or actively depending on its size. In this study, we explored the role of diffusion on the information transmission capacity of a set of tfs using a coupled mathematical and machine learning approaches to experimental data in yeast under several stress conditions. We found that the the activation followed by biased diffusion of transcription factors (TF) towards the nucleus triggers amplifying magnitude of the overall TF currents towards the nucleus as well as reduces the fluctuations. In fact, to our surprise the diffusion rate estimated from the data is found to be positively correlated with the protein mass, indicating the possibility of active diffusion since a negative correlation is expected in case of passive diffusion. The active diffusion in fact facilitates faster entry to the nucleus enabling faster information transmission with nuclear protein concentration as output. Additionally, higher copy number of the TF also improves information transmission by reducing overall noise in the output. However, improved information owing to faster active diffusion and higher copy number comes at an extra cost of increased entropy production due to the inherent thermodynamic uncertainty relation (TUR)for non-equilibrium systems. A linear optimization analysis demonstrates a corelation between the protein size and the optimized protein number which corroborates the actual observation. Thus, experimental measurements coupled with diffusion based theoretical models demonstrate the role of diffusion on optimizing cellular information processing.

The differentiation of the two cell types of the root epidermis, atrichoblasts, which give rise to hair cells, and atrichoblasts, which do not develop as hair cells, is determined by a complex regulatory network of transcriptional factors and hormones that act in concert in space and time to define a characteristic pattern of rows of hair cells and non-hair cells interspersed with each other throughout the root epidermis of Arabidopsis thaliana. Previous models have defined a minimal regulatory network that recovers the Wild Type phenotype and some mutants but fails to recover most of the mutant phenotypes, thus limiting its ability to spread. In this work, we propose a diffusion-coupled regulatory genetic network or meta-Gene Regulatory Network model extended to the model previously published by our research group, to describe the patterns of organization of the epidermis of the root epidermis of Arabidopsis thaliana. This network fully or partially recovers loss-of-function mutants of the identity regulators of the epidermal cell types considered within the model. Not only that, this new extended model is able to describe in quantitative terms the distribution of trichoblasts and atrichoblasts defined at each cellular position with respect to the cortex cells so that it is possible to compare the proportions of each cell type at those positions with that reported in each of the mutants analyzed. In addition, the proposed model allows us to explore the importance of the diffusion processes that are part of the lateral inhibition mechanism underlying the network dynamics and their relative importance in determining the pattern in the Wild Type phenotype and the different mutants.

Based on the expression patterns, genomes are viewed as a collection of protein-coding, RNA-coding, and non-expressing DNA sequences. Unlike most prokaryotes, eukaryotic gene expression comes with an additional step called alternative splicing. During the maturation process, different combinations of exons are spliced out and joined together resulting in the formation of mRNA isoforms. After removal from pre-mRNA, introns may be degraded by cellular exonucleases or form long non-coding RNAs (lncRNAs), or temporarily retained in the nucleus for regulating gene expression. We asked: Do introns have an unutilized potential for encoding proteins? If introns had an opportunity of getting translated, what kind of peptides or proteins, would they make? This study is based on the hypothesis of making functional proteins from leftover introns and is an extension of the original work of making functional proteins from the E. coli intergenic sequences (Dhar et al., 2009). Here full-length introns were computationally translated into proteins to study their potential structural, physicochemical, functional, and cellular location properties. Experimental validation is underway for a detailed understanding of the biology of intronic proteins. A synthetic intronic protein repository would provide an opportunity to design first-in-the-class molecules toward functional endpoints.

Resistance to several antibiotics against Mycobacterium tuberculosis is a serious problem to be solved worldwide. In the present work, we made the statistical analysis of the gene regulatory network of Mycobacterium tuberculosis and of the Mycobacterium tuberculosis-macrophage interactome to find the probable cause of this resistance. The results from this analysis show that both the gene regulatory network and the interactoma have a hierarchical free scale modular structure that assures a high degree of resilience of these networks against external perturbations. In particular, the interactome is a complex hybrid network that results from the formation of novel links between the Mycobacterium tuberculosis and macrophage proteins and from the modification of the previously existing links between the native macrophage proteins, which give rise to novel negative and positive feedback loops that modify the dynamical behavior of the interactome and protect the mycobacterium against the attack with antibiotics by taking control of the macrophage immune response and apoptosis. The statistical analysis of the interactome shows that the highly connected mycobacterium proteins inhA, ahpC, kasA, katG and rpsL exert this control by creating new links with the host proteins FAS and NF-{kappa}B. These new hybrid circuits embedded in the hierarchical scale-free modular molecular structure of the interactome produce its high resistance to external perturbations like antibiotics. As consequence, the present work proposes the hypothesis that Mycobacterium tuberculosis antibiotic resistance in vivo during chronic tuberculosis is only a particular case of a more complex problem that is the interactome resilience against antibiotics. Thus, new strategies of drug design are necessary to shatter the complex structure of the Mycobacterium tuberculosis-macrophage interactome.

Habit formation is a process in which an action becomes involuntary. While goal-directed behavior is driven by its consequences, habits are elicited by a situation rather than its consequences. Existing theories have proposed that actions are controlled by corresponding two distinct systems. Although canonical theories based on such distinctions are starting to be challenged, a few theoretical frameworks that implement goal-directed behavior and habits within a single system. Here, we propose a novel theoretical framework by hypothesizing that behavior is a network composed of several responses. With this framework, we have shown that the transition of goal-directed actions to habits is caused by a change in a single network structure. Furthermore, we confirmed that the proposed network model behaves in a manner consistent with the existing experimental results reported in animal behavioral studies. Our results revealed that habit could be formed under the control of a single system rather than two distinct systems. By capturing the behavior as a single network change, this framework provides a new perspective on studying the structure of the behavior for experimental and theoretical research. Author summaryTo obtain the desired consequences, organisms need to respond based on the knowledge of the consequences obtained by the response and the change in the environment caused by it. Such a process is called goal-directed behavior, which is flexible, but requires high computational cost. Once the same response is repeatedly performed under the same environment, the response becomes automatic, and transforms into a habit. In the canonical views, such a change from goal-directed response to habit was explained by the associative structures between the corresponding systems, goal-directed, and habit systems. However, the dichotomy in the mechanisms of behavior between goal-directed responses and habits has recently been challenged. Here, we show that, instead of assuming two explicitly distinguished mechanisms as in the canonical views, behavior is regarded as a network consisting of multiple responses, and that changes in the structure of the network cause two behavioral features, goal-directed behavior and habit. The transition from goal-directed behavior to habit has been operationally defined by sensitivity to the reward obtained by the response. We replicate such an experimental paradigm in the simulation and show that the behavioral network model can reproduce the empirical results on habit formation obtained from animal experiments. Our results demonstrate that habit formation can be explained in terms of changes in the network structure of behavior without assuming explicitly distinct systems and thus, provide a new theoretical framework to study the psychological, biological, and computational mechanisms of the behavior.

Based on the expression blueprint encoded in the genome, three groups of sequences have been identified - protein encoding, RNA encoding, and non-expressing. We asked: Why did nature choose a particular DNA sequence for expression? Did she sample every possibility, approving some for RNA synthesis, some for protein synthesis, and retiring/ignoring the rest. If evolution randomly selected sequences for metabolic trials, how much non-utilized (not-expressing) and under-utilized (only RNA encoding) information is currently available for innovations? These questions lead us to experimentally synthesizing functional proteins from intergenic sequences of E.coli (Dhar et al 2009). The current work is an extension of this original report and takes into consideration natural protein-coding sequences read backward to generate a new possibility. Reverse proteins are full-length translation equivalents of the existing protein-coding genes read in the -1 frame. The structural, functional and interaction predictions of reverse proteins in E.coli, S.cerevisiae and D.melanogaster, open up a new opportunity of producing first-in-the-class proteins towards functional endpoints. This study points to a large untapped genomic space from the fundamental biology and applications perspectives.

How did the complex structure of telencephalon evolve? Existing explanations are based on phenomena and lack the first principle. The Darwinian dynamics and the endogenous network theory established a few years ago provide a mathematical and theoretical framework of a dynamical structure, and a general constitutive structure for theory-experiment coupling, respectively, for answering this question from the first principle perspective. By revisiting a gene network that explains the anterior-posterior patterning of the vertebrate telencephalon, we found that with the increase of the cooperative effect in this network, the fixed points gradually evolve, accompanied by the occurrence of two bifurcations. The dynamic behavior of this network consists with the knowledge obtained from experiments on telencephalon evolution. Furtherly, our work drew an answer quantitatively of how the telencephalon anterior-posterior patterning evolved from the pre-vertebrate chordate to the vertebrate and gave a series of verifiable predictions in a first principle manner. Figure Abstract O_FIG_DISPLAY_L [Figure 1] M_FIG_DISPLAY C_FIG_DISPLAY