Method for measuring biological rhythm

FIELD: medicine.

SUBSTANCE: invention refers to chronobiology. A method for measuring a circadian cycle on the basis of time-series data by expression levels obtained by measuring the expression levels of two clock-genes in biological samples taken from a subject three times a day. The clock-genes have different phases of the circadian measuring cycle of the expression level.

EFFECT: method provides the high accuracy measurement of the biological rhythm and minimises the quantities of samplings from the subject.

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The technical field to which the invention relates.

The present invention relates to a method of determining the biological rhythm of the subject. In particular, the present invention relates to a method for determining the biological rhythm by taking biological samples from the subject of only three times a day.

The level of technology

It is known that various biological phenomena in living organisms are "periodic rhythm, which makes the Autonomous oscillations. This periodic rhythm is called "biological rhythm". In particular, it is known that "circadian rhythm", whose period is about a day, to a large extent controls such biological phenomena as the cycle of sleep/Wake, body temperature, blood pressure and diurnal fluctuations in hormone secretion. In addition, the circadian rhythm is involved in the activity of the mind and body, athletic abilities and sensitivity to drugs.

Biological rhythm is controlled by a cluster of genes, referred to as "time genes". Clock genes act as "internal clock", independently causing periodic oscillations in the expression, activity, localization, etc. clock genes.

It is obvious that gene polymorphism and mutations in clock genes are the cause of cancer, diabetes, vascular sableman the th, neurodegenerative and other diseases. Moreover, recently it has been suggested that genetic polymorphism and mutations in clock genes are involved in causing such mental illnesses as bipolar psychosis and melancholy.

On the other hand, the biological rhythm is not only Autonomous controlled by the internal clock, but is limited because of the life in society. For example, in the cycle of sleep/wakefulness may be differences in the rhythm (phase differences) between the "cycle of going to bed/getting up in real life" and "run internal clock cycle of sleep/wakefulness" due to differences in time regular bedtime and the time of rising.

It is believed that differences in the biological rhythm of the so-called "syndrome, jet lag and sleep disorders, as well as the above mental illness. For the treatment of diseases such attempts to reconfigure abnormal internal clock using irradiation with light.

Moreover, attempts to maximize the effects of drugs with biological rhythm. Suppose that the action of drugs is also affected by the daily fluctuations due to fluctuations in the level of expression of molecules (target molecules of the drug), which are affected by the drug, and circadian rhythm enzymes (enzymes metabolism PR is parathas), metabolizing the drug. Therefore, it was suggested that the concept of "oriented by the time medical care", which seeks to maximize therapeutic effect by setting the appropriate time of administration for each drug.

In addition, in the better-known cases, using the circadian activity rhythm of the mind and body and athletic abilities began the study of this period of activity, which reaches a maximum learning ability and training, and a time of ingestion, in which labor is an increase in the weight (or easily is the weight gain).

In connection with the foregoing, we believe that an accurate assessment of the biological rhythm is positive to improve such poor physical condition as a syndrome, jet lag, prevent various diseases, conducting Pro-time medical care, display their skills and weight loss.

In PTL 1 is disclosed a method of determining the body's internal time based on the measurement of the expression product of a gene in a standard sample taken from a living individual. In this way determine the body's internal time is the table of the molecular clock to estimate the body's internal time based on the level of expression of the expression product is s (i.e. mRNA).

The list of cited documents

PTL 1: International Publication No. 2004/012128.

Disclosure of inventions

In PTL 1 is not disclosed specific gene targets for measurement. Biological rhythms are usually estimated using the clock gene as a target for measurement based on changes in the level of expression time gene in time.

However, to measure changes in the level of expression of the time of the gene in the time you need to constantly take biological samples from the subject. That is, for the assessment of biological rhythm, with great accuracy, it is necessary to take biological samples from the subject within 24 hours with an interval of several hours, to obtain time series data on the level of expression of the time of the gene.

For the subject (the individual) the taking of biological samples several times a day so very burdensome. Moreover, the subject sometimes Wake in the night to take a biological sample. This affects the cycle of sleep/wakefulness of the subject, which can lead to changes in the biological rhythm.

We believe that it is necessary to reduce the load on the body of the subject when taking biological samples in order to expand the limits of the assessment of biological rhythm, for example, to improve such poor physical condition as a syndrome, jet lag and prevention of different Zab is problems.

Accordingly, the main purpose of the present invention to provide a method, which is achieved by the determination of the biological rhythm with great accuracy and minimizes the number of times of taking biological samples from the subject.

To achieve the above objectives the present invention provides a method for determining the biological rhythm of the subject on the basis of time series data on the levels of expression obtained in the measurement of expression levels of two clock genes in biological samples from the subject three times a day, and clock genes have different phases of the circadian cycle changes in the level of expression.

In particular, the method of determining the biological rhythm involves the following stages:

(1) taking a biological sample from the subject three times in 24 hours;

(2) measurement of expression levels of two clock genes in biological samples, and these two time gene have different phases of the circadian cycle changes in the level of expression; and

(3) calculation of circadian cycles from time series data on the levels of expression obtained in stages (1) and (2).

When measuring two clock genes, with different phases of the circadian cycle changes in the level of expression, taking biological samples from the subject can be performed only three times a day.

At stage (3) this method opredeleniiakh circadian rhythm cycles calculated from time series data on the levels of expression of the following formulas (I) and (II):

In the formula (I): E_a(t), A_a, ω and C_amean expression level, amplitude, initial phase, and the amount of displacement of one of the clock genes at time t. In the formula (II): E_b(t), A_band C_bmean expression level, amplitude, and offset of another time gene at time t. In addition, θ indicates the phase difference between two time genes.

This method of determining biological rhythm preferably includes the calculation of the simulation data from the graph, obtained by approximation of the cosine of the time series data on levels of expression, and simulation data reflect changes in the level of expression of every hour; the calculation of the sample data by three points from three arbitrary points of time and levels of expression in these points from the simulation data by the above formulas (I) and (II); calculate the difference in time between the simulation data and sample data for three points in those moments in which the levels of expression reaches a maximum; and calculating three points of time at which the average the value of the difference in time is less than 0.6, and the standard error of the difference in time is less than 0.4; and the taking of biological samples three times per day at these three time points as the point of sampling. In the lastnosti, you can define the biological rhythm with great accuracy when taking biological samples from the subject three times a day with an interval of 8 hours.

In this way determine the biological rhythm of time genes can be Per3 gene and gene Nr1d2.

In the General case "phase" means a quantity that describes, for a single period, the position of the points of the type peaks and dips at periodic change. The circadian cycle changes in the level of expression of the time of the gene can be observed in the form of the wave function of the cosine represented by the formula (III) below. Thus E(t) is the level of expression of the time of a gene at time t, A is the amplitude of the level of expression, and C is the offset value:

In the present invention the phase is given by the expression inside the parentheses of the cosine in the formula (III), namely: "2π(t+ω)/24" in the formula (III). In addition, the "initial phase" is "ω", which determines the phase at time t=0. A "phase difference" means the difference between the initial phases of ω between time genes.

In accordance with the present invention provides a method, which is achieved by the determination of the biological rhythm with great accuracy and minimizes the number of times of taking biological samples from the subject.

Brief description of figures

Figure 1 presents a graph obtained by plotting points in time at which level the expression peak in the circadian cycles of a change of expression levels of the gene Per3 gene and Nr1d2 (Example 1). On the X-axis (horizontal axis) is the time during which reaches the level of expression of the gene Per3, and on the Y-axis (vertical axis) is the time at which it reaches the maximum level of gene expression Nr1d2. In Fig. the dotted line denotes the position of the graph in the case where the time difference (phase difference) between the points is 2 hours.

Figure 2 presents a graph obtained by applying the difference in time points, in which the levels of expression reaches a maximum, between the simulation data and circadian cycles, designed for those intervals in which the samples were taken three times (example 2). In Fig. on the X-axis (horizontal axis) is the standard error of the difference in time interval of sampling, and the Y-axis (vertical axis) is the average value.

Figure 3 shows the graphs of the circadian cycle changes in the level of expression of Per3 calculated when all profiles sampling three-point interval "8:08" (A) or interval "9:15" (B) simulation data (Example 2). In Fig. figure 1 shows the circadian cycle Per3 according to the simulation, and number 2 are marked circadian cycle Nr1d2 according to the simulation. Next, figure 3 marked circadian cycle Per3 according to sampling by three points, and number 4 marked circadian cycle Nr1d2 according to sampling by three points.

Figure 4 presents graphs ZirCAD the th cycle changes in the level of expression of the gene Per3 gene and Nr1d2, calculated at the sampling by three points with an interval of 8 hours (Example 3). In Fig. symbols a1, b1 and c1 respectively marked circadian cycles of gene Per3 when sampling at three points of the profiles a, b and c, and the symbols a2, b2 and c2 respectively marked circadian cycles of gene Nr1d2 when sampling at three points of the profiles a, b and c. Next, the symbols d1 and d2 indicated circadian cycles Per3 gene and gene Nr1d2, obtained by sampling on seven points.

The implementation of the invention

1. The method of determining the biological rhythm

The authors of the present invention found that the number of times the subject has come from biological samples can be reduced by determining the biological rhythm of the differences in the cycles of changes in the level of expression between multiple time genes, and examined this assumption. Then, the inventors have discovered that the biological rhythm can be determined with high accuracy by measuring two clock genes with different phases of the circadian cycle changes in the level of expression of taking biological samples from the subject of only three times a day. That is, in the method of determining the biological rhythm of the present invention measured the levels of expression of two clock genes with different phases of the circadian cycle changes in the level of expression for biological samples, in atih the subject three times per day, and the biological rhythm of the subject is projected on the basis of the received time series data on levels of expression.

If two time gene a and b have the different phases of the circadian cycle changes in the level of expression and the phase difference is equal to "0", circadian cycles, changes in the levels of expression of clock genes can be modeled using the following formulas cosine graphs (I) and (II):

In the formula (I): E_a(t), A_a, ω and C_amean expression level, amplitude, initial phase, and the offset time of the gene and at the moment of time t. In the formula (II): E_b(t), A_band C_bmean expression level, amplitude, and offset time gene b at time t.

In the case where the known phase difference θ between the two time genes a and b, the formula cosine graphs (I) and (II) include 5 unknown constants (ω, A_a, A_bC_aand C_b). Measuring the levels of expression of E_a(t) and E_b(t) clock genes a and b in a biological sample taken from the subject at time t, the formula cosine graphs (I) and (II), we can obtain 2 equations. Therefore, in this model, receiving 6 equations formulas cosine graphs (I) and (II) in the capture (selection) of biological samples in three different time t, can be calculated circadian cycles is izmenenii levels of expression of clock genes a and b.

Mathematically for finding unknown 5 need 5 equations. In the present invention, when modeling the circadian cycles of changes in the levels of expression of clock genes a and b with known phase difference θ between them in the above formulas cosine graphs (I) and (II), calculate unknown 5 based on 6 equations. Namely, taking the phase difference θ between time genes a and b as limiting conditions, you can more accurately calculate the unknown ω, A_a, A_bC_aand C_b. Thus, with great accuracy, it is possible to calculate the circadian cycle, the level of expression of the time of the gene, which is a biological phenomenon, the exact score which is usually carried out with difficulty.

More specifically, the method of determining the biological rhythm involves the following stages: (1) taking a biological sample from the subject three times per day; (2) measurement of expression levels of two clock genes in biological samples, and these two time gene have different phases of the circadian cycle changes in the level of expression; and (3) calculation of circadian cycles of changes in the levels of expression of clock genes from time series data on the levels of expression obtained in the previous stages.

In the method of determining the biological rhythm of the present invention examples of subjects in the broad sense to include, along with the man, and yet the laboratory animals, as mice, rats and monkeys.

2. Taking biological samples

Biological samples from the subject, have no special restrictions, if only they is a biological tissue containing the product of the expression (mRNA) time gene. In relation to ease of sampling preferably take the biological tissue from the surface of the body, such as hair, mucous membranes of the mouth or skin.

Hair can be taken by tearing out by the roots. The pulled hair roots contain hair cells handbags, and they can measure mRNA clock genes. The "cells of the hair bags" are a group of cells that form the inner lining of the roots, the outer shell of roots and buds adjacent to the roots torn from body hair.

For example, in the case when the subject is a person, place taking hair has no restrictions, and you can use the hair of the head, beard, legs or arms, etc. to reduce the scatter in the measurement, preferably each time take samples from areas that are close to each other.

In the case of a person approximate amount of hair taken at one time, ranging from 5 to 10 for the hair of the head, from 3 to 5 for beards and from 10 to 20 for hair hands. Using the amount of hair, greater than or equal to the above amount of hair, it is possible to extract sufficient quantities is of mRNA to quantify the levels of expression of clock genes.

Samples of oral mucosa can be obtained by scraping from the surface of the oral cavity, for example, using a brush or spatula. Thus it is possible to measure mRNA clock genes in the erased cells of the mucous membranes of the mouth.

Samples of the mucous membranes of the oral cavity preferably is obtained from the mucous membranes located on the inner lining of the cheeks. To reduce the scatter in the measurement, the samples of the mucous membranes of the oral cavity preferably taken from the mucous membranes and the left and right cheeks.

The authors of the present invention investigated, what period of time between taking samples at three sampling gives a very accurate determination of the biological rhythm. As a result, they found that greater accuracy is achieved by taking biological samples from the subject three times a day with an interval of 8 hours (see Example 2).

In other words, in the method of determining the biological rhythm of the present invention can determine the biological rhythm with the greatest accuracy at three times the sampling so that the time interval between capture of the first and second sample and the period of time between the taking of the second and third sample at the same time is 8 hours.

3. Measuring the level of expression

The level of expression of the time what s in a biological sample can be measured by a commonly known method. For example, from a biological sample extracted DNA using a commercially available kit for RNA extraction and synthesize cDNA by reverse transcription reaction, using as matrix the selected RNA. Then, quantify the level of expression using cDNA using an integrated analytical method type DNA-chips (DNA-chip) or individual analytical method type real-time PCR.

Subject to measurement clock genes may represent a group of clock genes identified to date. Representative examples of clock genes include gene Per3 (access number in NCBI NM_016831), gene Per2 (NM_022817), gene Bmal1 (NM_001030272), gene Npas2 (NM_002518), gene Nr1d2 (NM_02174), gene Nr1d2 (NM_005126), Dbp gene (NM_001352) and Cry1 gene (NM_004075).

In the method of determining the biological rhythm of the present invention measured the levels of expression of two of these clock genes to obtain time series data on the levels of expression of these two genes have different phase of daily fluctuations in the levels of expression. In the case when the subject is not human and other organisms, measured the levels of expression of homologues (homologous genes) the above time human genes in these organisms.

The combination of two clock genes can be selected freely, if only they have the different phases of the daily fluctuations in the levels of expression. Phase of daily fluctuations in the levels of expression of two freely selected clock genes can be determined, for example, by the method described below in example 1.

As a preferred combination of two clock genes can be used Per3 gene and gene Nr1d2. Gene Per3 gene and Nr1d2 stably expressed in biological samples and show large diurnal fluctuations (amplitude) levels of expression. Thus, the biological rhythm can be accurately determined by calculating the circadian cycles of a change of expression levels of the gene Per3 gene and Nr1d2 of these time series data on levels of expression.

4. The calculation of the circadian cycle

Circadian cycles of changes in the levels of expression of clock genes is calculated by the following formulas (I) and (II) from time series data on levels of expression, showing changes in the levels of gene expression in time:

In the formula (I): E_a(t), A_a, ω and C_amean expression level, amplitude, initial phase, and the offset time of the gene and at the moment of time t. In the formula (II): E_b(t), A_band C_bmean expression level, amplitude, and offset time gene b at time t. In addition, θ indicates the phase difference between two time genes.

By the aforementioned formulas (I) and (II) can be obtained 6 uravnenii the time series data on the levels of expression of two clock genes at three times the sampling. Of these 6 equations get 5 unknowns ω, A_a, A_bC_aand C_bthe method of conjugate gradients or other So you can calculate the circadian cycles of changes in the levels of expression of clock genes and circadian cycles will reflect the biological rhythm of the subject.

As described above, in the method of determining the biological rhythm of the present invention measured the levels of expression of two clock genes with different phases of the circadian cycle changes in the level of expression when sampling by three points, with great accuracy, it is possible to calculate the circadian cycles of a change of expression levels, and thus to determine the biological rhythm of the subject.

Setting that taking biological samples from the subject is performed only three times a day, you can reduce the load on the body of the subject when taking biological samples. Moreover, when sampling by three points with an interval of 8 hours, you can take samples only in the period of time when the subject is awake. Thus, it is possible to accurately determine the biological rhythm without prejudice to the cycle of sleep/wakefulness of the subject.

Example 1. Determining the phase difference between the Per3 gene and genome Nr1d2

In this example, the selected gene Per3 (hereinafter simply "Per3) and gene Nr1d2 (hereinafter simply "Nr1d2) as the two clock genes with different phase and the circadian cycle changes in the level of expression and determined the phase difference between the circadian cycles of a change of expression levels of these genes.

Took the hair from the head of the 15 men and women aged 20 to 50 years. The roots of the hair, including the attached cells of the hair bags were quickly loaded into a buffer for lysis of the cells (set RNEasy Microkit: QIAGEN) to obtain a solution of the lysate of the cells. Hair was taken with an interval of 3-4 hours, and each time took 5-20 hair.

From the solution of the lysate of cells stored at -70°C, were extracted total RNA in accordance with the methodology applied to the buffer for lysis of cells, and carried out the reaction of reverse transcription. For the quantitative determination of the levels of expression of Per3 and Nr1d2 conducted real-time PCR, using the product of reverse transcription in the amount of 1/20 of this product. Real-time PCR was performed on the unit PRISM 7300 (ABI) using a probe SYBR Green (ABI) or TaqMan MGB (ABI). The levels of expression of Per3 and Nr1d2 subjected to correction by the expression level of 18S-pPHK, which served as internal standard, receiving time series data on the levels of expression.

Built graphics on the obtained time series data on the levels of expression are approximated by the formula below cosine (IV) with a period of 24 hours nonlinear least squares method, receiving the phase difference between the circadian cycles of changes in the levels of expression of Per3 and Nr1d2:

where E(t) is the expression level at time t, A is the amplitude level of expr the hurt, ω is the initial phase, and C is the offset.

The results are presented in figure 1. The graph obtained by applying the moments of time t, in which the level of expression of E(t) has reached its maximum on the graph after the approximation of the cosine formula (IV). The moments of time t, which reached a maximum expression level E(t) gene Per3, inflicted on the X-axis and the time t, which reached a maximum expression level E(t) gene Nr1d2, inflicted on the y axis.

As can be seen from figure 1, the 15 subjects of the time t, which reached a maximum expression level E(t) gene Per3, had a wide range from 0 to 12. Similarly, the time t, which reached a maximum expression level E(t) gene Nr1d2, had a wide range from 0 to 12.

However, the time difference (phase difference) between the time t, which reached a maximum expression level E(t) gene Per3, and time t, which reached a maximum expression level E(t) gene Nr1d2, was approximately 2 hours for each subject. In figure 1 the dashed line presents the position of the graph in the case where the phase difference between Per3 and Nr1d2 is 2 hours.

The average value and the standard deviation of the phase difference between Per3 and Nr1d2 15 subjects was equal to 2.3 and 0.8, respectively. This phase difference (the phase difference θ") conducted modeling circadian cycles changes the level of the expression of Per3 and Nr1d2 on the following formula of cosine functions (V) and (VI) respectively:

where E_Per3(t) the level of expression of Per3 in time t, A_Per3the amplitude level of expression, ω is the initial phase of Per3, and C_Per3- offset;

where E_Nr1d2(t) is the expression level Nr1d2 at time t, A_Nr1d2the amplitude level of expression, θ is the phase difference between the circadian cycles of changes in the levels of expression of Per3 and Nr1d2, a C_Nr1d2- offset.

Example 2. The study of the interval between sampling

Using the above formulas, graphs of cosine (V) and (VI) can be calculated circadian cycles of changes in the level of expression of Per3 or Nr1d2 when sampling at least three times and thus to assess the biological rhythm of the subject. So, in this example, defined the time interval between the three sampling in order to accurately assess the biological rhythm. Assuming that the sampling is performed three times a day, examined all possible intervals between sampling (276 profiles).

First, expected hourly changes of expression levels of two genes on the cosine formula (IV)shown in example 1, and perform the approximation of the graphs of the time series data on the levels of expression of Per3 and Nr1d2. Then he selected three arbitrary points of time t and the levels of expression of V(t) in the quiet points in the data quality of the samples by three points from the calculated data modeling, representing the hourly changes of expression levels.

These three arbitrary points of time t and the levels of expression of V(t) at these points was substituted in the formulas (V) and (VI) and received amplitude levels of expression of A_Per3and A_Nr1d2the initial phase ω Per3 gene and the offset C_Per3and C_Nr1d2the method of conjugate gradients.

The method of conjugate gradients was performed according to the following method. Namely, first determined the sum of squares of d from substituted in the formulas (V) and (VI) levels of expression of V(t) and levels of expression of E(t) from simulation data representing the hourly changes of expression levels, as the distance between the data when sampling at three points and the simulation data according to the following formula (VII):

Then by the method of conjugate gradients received amplitude A_Per3and A_Nr1d2; the initial phase of ω and the offset C_Per3and C_Nr1d2that minimize the distance d. Note that in the case when we used nonlinear least squares, these unknown constants could not be obtained because the distance d does not converge to the minimum value.

Thus, when the method of conjugate gradients, the initial values of the unknown constants can significantly affect the resulting constants. So, if you choose wrong the correct initial values, the distance d converges to a local extremum and therefore it is impossible to obtain the correct circadian cycles.

Therefore, in this case as the correct initial values of the amplitudes A_Per3and A_Nr1d2took the average value of the amplitude A from simulation data representing the hourly changes of expression levels. In addition, as the initial values of the offset C_Per3and C_Nr1d2took the average value of the data when sampling by three points. Note that the ratio of amplitude A according to the simulation, the amplitude A_Per3gene Per3 was 0,8014513, and the amplitude A_Nr1d2gene Nr1d2 was 0,6402411.

In addition, the initial phase ω Per3 gene was restricted with integers from 0 to 23, to facilitate operational analysis. Then received the initial phase ω, ensuring the minimum distance d, asking one integers from 0 to 23 as the initial values, and applying the conjugate gradient method.

As described above, the received time difference between the time t, which reached a maximum level of expression of V(t) by the formula (V), which determines the amplitude A_Per3the level of expression, the initial phase ω Per3 gene and the offset value C_Per3and the point in time at which reached a maximum level of expression of V(t) according to the simulation. Then researchers is whether the interval between sampling with the in order to minimize the difference in time.

As a first time sampling took all times every hour from 0 to 23. Then explored the combination (276 profiles) of the intervals between the three moments of the sampling so that the second and third sampling was completed within 24 hours from the first. In relation to combinations of all time has gotten the average value and the standard error of the difference in time. The standard error indicates how the circadian cycle, calculated at the interval of sampling depends on the first time of sampling. And the average value indicates the accuracy of the calculated circadian cycle. Thus, we can say that the calculated circadian cycle becomes more accurate with decreasing standard errors and mean.

In tables 1-5 presents the mean values and standard errors were obtained for combinations of all intervals. The combination of all of the intervals in tables 1-5 are listed in order of decreasing standard errors and the mean of the intervals. Intervals are represented by a combination of the time interval between the first and second sampling and the time interval between the second and third sampling. For example, "13:06" in Fig. means that the interval between the first and second integration of the receiving samples is 13 hours and the interval between the second and third sampling is 6 hours.

In addition, figure 2 presents a graph in which each of the combinations of intervals applied in such a way that the standard error is given by the X-axis and the average value of the y axis.

As can be seen from tables 1-5 and figure 2, the standard error and the average value reaches a minimum in the interval "8:08". From this it is clear that the circadian cycle can be calculated with great accuracy at three times the sampling so that the interval between the first and second sampling and the interval between the second and third sampling at the same time is 8 hours.

In addition, standard error, and mean values are quite low in combinations of intervals, are shown in tables 1-4. We believe that by using these intervals sampling is possible to calculate the correct circadian cycles. On the other hand, it was found that the combination of the intervals shown in table 5, are not suitable, because the standard error and the mean value are high.

Figure 3 presents the circadian cycle changes in the level of expression of Per3 calculated when all profiles sampling by three points for the interval "8:08" (A) or interval "9:15" (In) according to the simulation. In Fig. figure 1 shows the circadian cycle Per3 according to the simulation, and number 2 are marked circadian cycle Nr1d2 according to the simulation. Next, figure 3 marked circadian cycle Per3 according to sampling by three points, and number 4 marked circadian cycle Nr1d2 according to sampling by three points.

As can be seen from figure 3(A),in the case when the interval between the first and second sampling and the interval between the second and third sampling at the same time is 8 hours, circadian cycles Per3 and Nr1d2 on data modeling and data sampling for the three points are in good agreement with each other, which means that circadian cycles can be calculated with great precision.

On the other hand, in the case where the interval between the first and second sampling is 9 hours, and the interval between the second and third sampling is 15 hours, circadian cycles Per3 and Nr1d2 on data modeling and data sampling for the three points are not consistent with each other, which means that circadian cycles cannot be calculated.

Example 3. Evaluation of biological rhythm when sampling by three points

From the above Example 2 results found that the circadian cycle can be calculated with great accuracy when sampling three times at intervals of 8 hours. Therefore, an attempt was made to determine the biological rhythm in the actual implementation of sampling by three points with an interval of 8 hours. Sampling by three points was performed on the three profiles below in table 6.

When sampling at three points of the profiles a-c in each moment quantify the levels of expression of Per3 and Nr1d2 the method described in Example 1. Then by the same method described in Example 2, in formula (V) and (VI) substituted three points of time t and the levels of expression of E(t) at these points and the received amplitude A_Per3and A_Nr1d2levels of expression, the initial phase ω Per3 gene and the offset C_Per3and C_Nr1d2the method of conjugate gradients. Thus the expected circadian cycles changes in the levels of expression of Per3 and Nr1d2.

The results are presented in figure 4. In Fig. symbols a1, b1 and c1 respectively marked circadian cycles of gene Per3 when sampling at three points of the profiles a, b and c, and the symbols a2, b2 and c2, respectively, about the right circadian cycles of gene Nr1d2 when sampling at three points of the profiles a, b and c. Next, the symbols d1 and d2 indicated circadian cycles, obtained by approximation by the above formula cosine (IV) nonlinear least-squares time-series data on the levels of expression obtained by sampling seven times from 12:00 to 36:00. Symbol d1 marked circadian cycle Per3, and the symbol d2 marked circadian cycle Nr1d2.

As can be seen from figure 4, when sampling at three points of the profiles a-c circadian cycles changes in the levels of expression of Per3 and Nr1d2 were calculated with high reproducibility. The phase error between the circadian cycles of changes in the levels of expression of Per3 and Nr1d2 when sampling at three points of the profiles a-c and circadian cycles (see symbols d1 and d2 in Fig.) when sampling seven times amounted to an average of 0.75 hours.

As can be seen from this result, when sampling at three points in relation to levels of gene expression Per3 and Nr1d2 with different phases of the circadian cycle changes in the level of expression appeared that were calculated circadian cycles of a change of expression levels, which, with great accuracy, it is possible to determine the biological rhythm of the subject.

Industrial applicability

The method of determining the biological rhythm of the present invention may be used for the implementation of the medical service time, display their skills and weight loss. Moreover, ways which can be used to prevent various diseases, caused by the displacement of the biological rhythm, and to improve such poor physical condition, as the symptoms of jet lag.

1. The method of determining the circadian cycle of the subject on the basis of time series data on the levels of expression obtained in the measurement of expression levels of two clock genes in biological samples from the subject three times a day, and clock genes have different phases of the circadian cycle changes in the level of expression, including:
(1) the stage of taking biological samples from the subject three times per day;
(2) phase measurement of expression levels of two clock genes in biological samples, and these two time gene have different phases of circadian cycles of a change of expression levels; and
(3) the stage of calculation of circadian cycles from time series data on the levels of expression obtained in stages (1) and (2), in which in stage (3) circadian cycles calculated from time series data on the levels of expression of the following formulas (I) and (II):

where in the formula (I): E_a(t), A_a, ω and C_amean expression level, amplitude, initial phase, and the amount of displacement of one of the clock genes at time t; in the formula (II): E_b(t), A_band C_bmean expression level, amplitude, and offset of another time gene at the time the belts t; and θ denotes the phase difference between two time genes,
where the interval between the taking of samples chosen from:
8:08, 7:09, 9:08, 8:07, 9:07, 7:08, 8:09, 7:07, 7:10, 10:07, 9:06, 6:09, 9:09, 6:08, 10:06, 8:10, 8:06, 6:10, 10:08, 11:07, 6:11, 7:06, 11:06, 7:11, 6:07, 5:10, 9:10, 10:05, 5:09, 10:09, 9:05, 6:12, 6:06, 12:06, 5:11, 11:08, 8:05, 11:05, 8:11. 5:08, 7:12, 12:05, 5:07, 5:12, 12:07, 7:05, 5:13, 13:06, 6:05, 6:13,13:05, 5:06, 4:10, 10:10, 10:04, 9:04, 4:11, 11:09, 4:09, 9:11, 11:04, 12:08, 4:12, 8:04, 8:12, 4:08, 12:04, 5:05, 14:05, 5:14, 13:04, 7:13, 4:07, 4:13, 7:04, 13:07, 6:14, 14:04, 4:06, 6:04, 4:14, 14:06, 4:05, 5:15, 15:04, 5:04, 15:05, 4:15, 10:11, 3:10, 11:03, 3:11, 11:10, 10:03, 9:12, 3:09, 12:03, 12:09, 3:12, 9:03, 13:03, 8:13, 3:08, 13:08, 3:13, 8:03, 7:14, 14:03, 3:07, 3:14, 14:07, 7:03, 4:16, 4:04, 15:06, 6:03, 6:15, 15:03, 3:06, 17:04, 4:03, 3:17, 3:05, 16:03, 5:16, 3:16, 16:05, 5:03, 4:17, 3:04, 17:03, 3:03, 18:03, 3:18, 17:05, 16:06, 6:02, 2:16, 5:02, 2:17, 4:02, 2:18, 2:01, 18:04, 1:20, 3:01, 20:03, 2:03, 3:19, 19:02, 2:04, 18:02, 4:18, 18:05, 1:18, 5:01, 2:19, 3:02, 19:03, 2:11, 11:02, 11:11, 1:21, 16:02, 2:06, 6:16, 17:02, 5:17, 2:20, 14:02, 2:08, 8:14, 16:04, 3:15, 2:02, 20:02, 8:02, 2:05, 10:12, 2:10, 12:02, 7:02, 2:15, 15:07, 7:01, 16:07, 1:16, 2:12, 12:10, 10:02, 2:14, 14:08, 13:09, 2:13, 9:13, 2:09, 13:02, 9:02, 9:01, 14:09, 1:14, 15:02, 7:15, 2:07, 21:02, 22:01, 15:08, 1:15, 8:01, 6:17, 1:06, 17:01, 21:01, 8:15, 15:01, 1:08, 6:01, 17:06, 1:17, 1:22, 1:01, 20:01, 3:20, 1:03, 18:01, 1:05, 5:18, 19:01, 4:19, 1:13, 10:01, 2:21, 13:10, 1:09, 14:01, 9:14, 16:01, 1:07, 7:16, 1:02, 1:19, 19:04, 4:01, 1:04, 13:01, 1:10, 10:13, 1:12, 11:01, 12:11, 1:11, 12:01, 11:12.

2. The method according to claim 1, including:
the calculation of the simulation data from the graph, obtained by approximation of the cosine of the time series data on levels of expression, and simulation data reflect changes in the level of expression of every hour;
calculation of sample data by three points from three arbitrary that the EC of time and levels of expression in these points from the simulation data by the above formulas (I) and (II);
calculating the difference in time between the simulation data and sample data for three points in those moments in which the levels of expression reaches a maximum; and
the calculation of the three time points, in which the average value of the difference in time is less than 0.6, and the standard error of the difference in time is less than 0.4; and the taking of biological samples three times per day at these three time points as the point of sampling.

3. The method according to claim 2, in which the biological sample from the subject taken three times a day with an interval of 8 hours.

4. The method according to claim 1, in which the clock genes using gene Per3 gene and Nr1d2.