Path to Diversity and to Resistant Uniformity: Intracellular Adaptation to Nutrient Environment


 Two adaptation strategies are known, which provide variability and resistance of population. We study the laws of adaptation by the example of proteins and changes in their conformations. The data were obtained in the experiments of V.I. Korogodin on yeast cells with mutations, which have demonstrated the effect of the culture medium on the appearance frequency of pseudo-wild type cells. Here, these archived and published data are analyzed by the statistical approach. Statistical analysis shows the emergence of a sequence of independent foci of the pseudo-wild cells induced by intracellular factor and their association with the cytosolic and nuclear-mitochondrial oxidative pathways; the foci dispersions conform the regularities of the folding energy landscape; intracellular imbalances and gene mutations affect their frequency and diversity. We conclude that the paths from diversity to uniformity of protein conformations obeys the laws of the energy landscape. The nuclear-mitochondrial machinery generates new proteins and their homogeneous foci. Variable foci consist mainly of the former conformations remodeled under ROS from several cytosolic sources. Strong gene expression induces oxidative stress, which increases the frequency of homogeneous conformations and reduces variability. Further, stress activates a new focus of new homogeneous conformations.


INTRODUCTION
In the mid-1980s, V.I. Korogodin and his colleagues examined the hypothesis that functional activity of genes increases their mutation frequency 1,2 . Scientists tested the "reversion frequency" of auxotrophic haploid yeast cells under starvation. The studies showed that adenine or leucine starvation increases occurrence frequency of pseudowild type cells (PWTC) in yeast with missense 2 and nonsense 3 mutations, but to a different extent. The authors explained this phenomenon by increased gene mutagenesis caused by changing of the conformation of functioning genes 2 , which is becoming more accessible to the intracellular influences 4 .
In the last two decades, another adaptation pathway has been intensively studied, which is associated with the conformational variability of proteins 5 . The protein three-dimensional (3D) structure is considered from the point of view of folding energy landscape 6,7 formed under intracellular environment 8 . The proteins have to be optimized to attain a defined 3D structure, which should be in agreement with its nature state and compatible with intracellular ensemble of physical, chemical and biological conditions 8,9 . Optimized protein conformation has the adapted phenotype.
In eukaryotic cells, the adaptation processes are linked with the reactive oxidative species (ROS) pathways 10,11 . The ROS produced by ionizing and UV irradiation and direct treatment of cells by oxidants induce direct damage to DNA/protein/lipids 11 ; high level of ROS can induce chromosomal rearrangements and cell death 12 . The ROS influence molecular chaperone activity 13 , induce signaling to proliferation/differentiation, apoptosis 11 , autophagy 14 , and gene expression 15 . The main adaptive function of ROS is their influence on protein folding 16,17 and activation of the unfolded protein response (UPR) 18 in the endoplasmic reticulum (ER). Nutrient imbalance influences the ROS level and protein folding. Starvation induces peroxidation of membrane lipid of eukaryotic cells 19 , 20 , which results in the cytosol oxidation and causes the gene expression 15 together with mitochondrial ROS 11 . Cytosolic and nuclear-mitochondrial ROS promote ER oxidation 17 . The ER oxidizing supports the formation of intra-and interchain disulfide bonds that serve to stabilize the protein folding 16 . In their turn, formation of each disulfide bond during oxidative folding produces a single ROS 16 . The UPR activates the adaptive signaling pathways to provide an efficient protein-folding environment 18 . Nutrient-rich conditions activate the eukaryotic target of rapamycin (TOR) complex1 that promotes cell growth 21,22,23 . The intracellular ROS production caused mainly by mitochondrial respiration and, to a lesser extent, through NADPh oxidase 24,25 . Redox conditions regulate protein folding, vacuolar autophagy and mitochondrial functions 26,27 .
Gene mutations change the protein folding. Missense mutation results in an altered DNA codon that shifts the equilibrium between different conformational substates 28 resulted in a prolonged obtaining of functioning conformation 29 . The study of the misfolded proteins demonstrate a reduction of interaction with chaperones 29, 30 , instability and degradation of their structure 31, 32 resulting in a strong ER stress 30 . It can affect the flexibility of the protein molecule 33,34 . Nonsense mutation results in a premature stop codon in the transcribed mRNA. The heritable factor [PSI+] appears when the SUP35 gene is expressed and causes mistranslation 35,36 . Sup35p is capable of adopting an aberrant conformation, which manifests as the prion-associated phenotype 37 . Sup35p possess a conserved Nterminal domain 38 , which determines the physical specificity of structural variants of yeast prions, to which the chaperone machinery must conform 39,40 . In this way, translation termination efficiency is regulated through a prionmediated mechanism that demonstrates its important part in adaptation 41,42,43 .
This investigation focuses on the processes of adaptation to nutrient media in cells of yeast Saccharomyces cerevisiae with missense ade2-192 and nonsense leu2-1 mutations. Regression analysis shows that adaptation results in an occurrence of the time-separated foci of PWTC colonies, and sequence of the PWTC foci detects specific structure of the folding energy landscape. This suggests that the PWTC foci correspond to a set of variants of protein conformation. Statistical approach reveals the adaptation regularities: nutrient imbalance increases the PWTC production; variable cytosol oxidation provides diversity of the PWTC foci, and nuclear-mitochondrial machinery generates homogeneous conformations; missense and nonsense mutations demonstrate different relationship between variability and resistant uniformity. Stationary phase and prolonged stress decrease conformational variability, and increase possibility of generation of new foci associated with gene expression.

Foci of the PWTC occurrence.
Here, the numbers of L-and S-PWTC' colonies (Tables S1, S2) are analyzed depending on their appearance in time. The model of a single Gaussian or lognormal peak doesn't satisfy the statistical Kolmogorov-Smirnov' 44 and χ 2 criteria (≈ 100 -1000). Approximation of the experimental data by the composition model consisting of the complex of several lognormal functions satisfies the statistical criteria very well (Fig. 1). The composition model suggests that the revealed effects do not exceed the intracellular interactions. The single-peak distribution can be observed when an external source is irradiation or the chemical oxidants in cell culture that can cause DNA damages 11,45 .
ROS generation is the time-dependent intracellular factor, which determines cell paths including protein folding 11,46 both under stress and in normal conditions (Fig. 1). Difference of foci indicates different ROS pathways influencing the 3D protein structure. The PWTC occurrence can be result of ROS-depended protein misfolding 18,17 . Let's take this assumption as a working hypothesis.
Two pathways of protein misfolding. The PWTC can be divided into two groups (Fig. 1). The efficiency of the composition of two lognormal functions is greater than that of a single-peak model (χ 2 -criterion is 10 -100 times better), but worse than the several foci model.
The correlation analysis demonstrates different character of relationships between the averaged values ( ), ( ) and the initial conditions. In yeast a leu2-1 lys1-1, the dependence of the first L-group on the leucine content is nonlinear (R1 = 0.3051) and it is negative and close to linear in the second L-group (R2 = -0.9996). The partial correlation coefficient between L-groups is very small (r1,2 = -0.0262). The first and second S-groups are highly correlated (r1,2 = 0.9992). In yeast a ade2-192, the enlarged volume of the medium slightly increases the first L-group and decreases the second one; it means that the L-groups are generated by different mechanisms. S-groups are small.
The ROS production is associated with the cytosolic sources and substantially with the mitochondria 11,25 . Thus, the larger second group is associated with the nuclear-mitochondrial machinery. In the case of the S-genes, leucine content influences the cells as a whole; therefore both groups are minimal at low leucine content, and increase at extracellular leucine. The medium volume influences the groups, because metabolism depends on carbon sources 47 . Two pathways of ROS production and protein misfolding are presented in the scheme (Fig. 2).
Under starvation, the first group (dotted line) is associated with cytosol oxidation through membrane lipid peroxidation 19 . The second group (solid line) is shifted in time because it is linked with gene expression (nucleus) stimulated by cytosol oxidation 15,11 that is accompanied by the respiration (mitochondrion) and ROS production 11 . Missense mutation increases strongly gene expression, ROS production, and ER stress 30 ; nonsense mutation causes [PSI+] appearance, which induces mistranslation 35 .
Nutrient-rich media induce occurrence of the first group (dotted line) mainly through NADPh formation 25 in mitochondrial chain (mitochondrion). The second group (solid line) is linked with activation of conserved in eukaryotes TOR complex1, which controls cell growth 21 . Cell reproduction stimulates mitochondrial respiration (mitochondrion) and ROS production 25 . This pathway contributes heavily into ER oxidation.
The first pathway is associated with degrading and remodeling of the previous protein conformations, and the second includes generation and folding of the new protein structures. These paths need different time and form two separate groups of the PWTC focuses. Appearing of the misfolded proteins associated with S-genes is consistent with the similar scheme.
The frequency of PWTC colonies. The fitness of organisms to environmental conditions is described by fitness landscapes that take into account positive and negative selection 48 . Fig. 3 presents the occurrence frequency of PWTC colonies for strains a leu2-1 lys1-1 (Table S1) and a ade2-192 (Table S3). It describes the fitness landscapes because PWTC multiplication and formation of their colonies (Table S1, S3) depend on the appropriate nutrient conditions. The stress-induced landscape is small but frequency is high due to the strong gene expression and the large amount of ROS; landscapes generated by standard and rich media increase due to the contribution of cytosolic PWTC, but their frequency is lower.
In cells a leu2-1 lys1-1, the PWTC frequencies differ not significantly by transferring from the standard and rich MM conditions to the SM (Fig. 3a, b) due to nonsense suppression. However, starvation stress increases PWTC frequency. Yeast cells a ade2-192 with missense mutation causes much higher L-PWTC frequency by transferring from the standard and rich medium to the SM conditions than at starvation (Fig. 3e, f). It is explained by the fact that stress induces strong degradation of the cytosolic group. The S-PWTC frequency increases on the SM and in general obeys the similar regularities (Fig. 3c -h).
Variability and resistance of the PWTC. The adaptation process provides the survival of population through its diversity and its resistance to the environment conditions. Protein structure gets these properties during its folding described by energy landscape 49,6 . Conformational substates are associated with local minima of the energy landscape. The density of the minima increases exponentially with the energy 50 . Each minimum is characterized by the potential and vibration free energies, which are highly correlated 51 . The free energy specifies minima and influences the foci dispersions. In this way, the PWTC foci with different dispersions determine variability of the conformational substates. Approximation to the native state minimizes free energy of 3D protein structure, focus dispersion and PWTC variability. Fig. 4 presents L-and S-foci dispersions in dependence on their index number.
The cytosolic group is generated by several mechanisms of ROS production and consists of different large PWTC foci, which decrease with their index number. Excessive levels of the limiting metabolite (Fig. 4c) and a large volume of nutrient medium (Fig. 4d) do not increase variability. The nuclear-mitochondrial mechanisms generate ROS evenly and permanently; therefore, dispersion and variability of PWTC foci are small. High gene expression increases ROS level that decreases cytosolic group due to degradation of unusable conformations. Long-term oxidative stress select single foci, whose resistance increases due to appearance of hidden substates provided interaction with certain environmental substrates 51 . Fig. 4a shows that the more expressed L-genes correspond to the smaller variable cytosolic groups.

Specificity of nonsense and missense mutations.
In the case of nonsense mutation, a low-energy barrier between misfolded and natural protein variants creates a high probability of the different protein conformations 50 . The first foci group demonstrates several large dispersions (Fig. 4a) that means high variability 52 . The hidden protein variants are also exposed 5,53 . The foci of the second group are induced due to nuclear-mitochondrial machinery; their dispersions are small and hardly differ (Fig. 4a, c).
In the case of missense mutation, the formation of protein 3D structure requires strong gene expression to select rare stable protein conformation 54 . Due to strong ER stress, the cytosolic group has lost the first PWTC foci together with their diversity (Fig. 4b, d). Fig. 4d shows that L-and S-foci diversity depends directly on operation of the nuclear-mitochondrial machinery. Experiments with different volumes of nutrient medium show that low volume 10 ml reduced mRNA production and the nuclear-mitochondrial group, but the cytosolic group increased due to slight ROS in comparison with the standard volume 30 ml. Fig. 5 shows resistance and variability of appearance frequency in the foci of L-PWTC. Nonsense mutation stimulates variability of cytosolic group on both minimal (MM, exp) and selective (SM, exp) media in exponential phase; aging (SM, stat) reduces cytosolic PWTC frequency and variability. The stable nuclear-mitochondrial group decreases a little in the stationary phase (SM, stat). Cells with a missense mutation produce mostly nuclearmitochondrial PWTC, which are single on minimal media and multiply on selective media. These foci are resistant and enlarge (Fig. 5).

DISCUSSION
Experimental data and regression analysis revealed a set of time-separated foci of the PWTC colonies (Fig. 1), which are produced by an intracellular mechanisms, because an extracellular factor induces gene damages 11 described by a one-humped distribution 45 . This is the basis for the hypothesis that the reason for PWTC diversity is the variability of the 3D protein conformations. This hypothesis is clearly confirmed by the regularities of the foci dispersions (Fig.  5), which demonstrate the laws of the energy landscape of protein folding 6 .
The foci of misfolded proteins form two groups (Fig. 1). The first cytosolic group produces diversity associated with different sources of ROS, which induce degradation and remodeling of the earlier protein conformations (Fig. 2). The second group is associated with permanent operation of nuclear-mitochondrial machinery. This group produces uniform resistant PWTC foci, their diversity is small (Fig. 4).
The changes of protein conformations depend on the intracellular imbalance (Fig. 2). Stress influences both PWTC groups. The stronger the stress, the higher the frequency of PWTC (Fig. 3) induced by high gene expression. The same reason increases mitochondrial ROS production, which decreases diversity of PWTC foci (Fig. 4) caused by degradation of some conformations of the cytosolic group. Stress is a factor, which reduces the variability of the 3D protein structure and increases uniformly stable nuclear-mitochondrial group. However, the stress-induced environment modifications can cause an appearance of a new focus in the nuclear-mitochondrial group (Fig. 5). Overrich environment does not influence the variability (Fig. 4) and PWTC frequency (Fig. 3) in comparison with the standard conditions. Gene mutations effect on the adaptation pathway differently. Nonsense mutations trigger a mechanism of nonsense suppression 35 , therefore the PWTC frequency coincides practically on the minimal and selective media (Fig.  3a, b). The cytosolic group contributes into PWTC variability (Fig. 4a, c); the nuclear-mitochondrial group increases homogeneous stable PWTC frequency (Fig. 3a). Variability of protein conformations is described in 37,42,39 . Missense mutation induces instability and overexpression of gene to get stable protein conformation 31 . Instability reduces strongly the cytosolic PWTS group; the nuclear-mitochondrial group has small variations (Fig. 4d). Missense mutation increases resistance 34,28 .
In 1967, the theory of r/K-selection was published 55 , which had described quality and quantity strategies of adaptation. In proteins, the adaptation process is associated with their three-dimensional structures (Fig. 1). Fig. 5 illustrates regularities of intracellular adaptation process in cells with missense and nonsense mutations, variability and resistance of the L-PWTC foci. Prolonged stress and stationary phase decrease the number and diversity of cytosolic groups. Nuclear-mitochondrial group is stable and uniform, but splits out two or three subgroups under prolonged stress or aging, which change intracellular environment.
External sources induce like scheme of adaptation 45,56 . For example, radiation induces mutations, which divide the population into two subpopulations, -sensitive variable and resistant ones; prolonged radiation and aging stimulate appearance of new subpopulations. This scheme is general in nature.

CONCLUSIONS
The transition from diversity to uniformity of protein conformations obeys the laws of the energy landscape of protein folding. The changing intracellular environment and genetic disorders adjust the energy landscape and thereby affect the variability of protein conformations. These factors influence two paths of the protein population to variability and uniform resistance. The nuclear-mitochondrial path generates new proteins and homogeneous conformations in the uniform foci. Variable foci consist mainly of the former conformations that remodeled due to ROS from several sources in the cytosolic path. Strong gene expression induces heavily oxidative stress, which increases the frequency of homogeneous protein conformations and reduces variability. Moreover, stress induces the formation of a new focus of new homogeneous conformations.
Differentiation and calculation of the PWTC. Yeast cells were seeded on minimal salt medium (MM), then the grown colonies were smeared and transferred to selective medium (SM) for a given time intervals. The worked methods 2 made it possible to separate the PWTC emerged on the MM and the SM condition. The PWTC were differentiated as "locus" (L) and "suppressor" (S) ones 57 . This was checked by phenotypic analysis consisting of the determination of the biochemical requirements of the PWTC. In the case of Ade + PWTC, the color of the colonies can be used to differentiate L-and S-type of PWTC 58  are published 2, 3 , and archival material is presented in the Tables S1; S3. Unpublished archived data (Table S2) show the dependence of the occurrence of Ade + PWTC on different volumes of medium. The errors in estimating the number of PWTC colonies were 10-12%. PWTC frequency estimation errors were 10-15%.
Statistical approach. A statistical approach was used to study the regularities of PWTC occurrence. The lognormal law effectively describes the division/reproduction processes 59 . This model is presented here, although the Gaussian and geometric laws were examined too. Scientific data analysis and graphing were performed by SigmaPlot13 package. The experimental data were described by the sum of lognormal distributions: is the number of the PWTCs identified in the k foci; Ai is the value of the ith focus, and µi and σi are the parameters of the lognormal distributions. The verification of the fitting efficiency was fulfilled using the Kolmogorov-Smirnov (KS) test 44  Estimation of the foci dispersions. The foci dispersions (L) and (S) (Fig. 4a, b) were estimated in the exponential phase as averaged values over three nutrient media Cleu = 3, 30, 300 mg/l in the MM and SM conditions (a) and over two volumes of medium VMM = 10, 30 ml/dish in the SM conditions (b). The foci dispersions (L) (Fig.  4c, d) were determined for three initial leucine concentrations Cleu = 3; 30; 300 mg/l, each of them were averaged over the MM and SM conditions in the exponential and stationary phases (c), and for two volumes VMM = 10, 30 ml/dish in the SM conditions (d). Figure 1. Experimental distributions of the Leu + 3 (a) and Ade + (b) PWTC occurrence in yeast a leu2-1 lys1-1 (Table  S1) and a ade2-192 (Table S2) in time and their approximations by the composition model of several and two lognormal functions. Experimental data are presented with standard errors (SE). Regression by the n-peaks model corresponds to the Kolmogorov-Smirnov -and χ 2 -criteria: 5%. Regression by the two-peaks model corresponds to the Kolmogorov-Smirnov criteria: 5%.   (Table S1) -and Ade + 2 (Table S3)