酵母菌计数计算

質問

10ml培养基中有N个酵母菌，稀释100倍后采用16x25血细胞计数板计数，若某时刻中格细胞平均数量为25，求N的值

思考

Understanding yeast cell concentration

I’m examining a Chinese question about yeast cells and I’m translating "16×25" to average cells per square in a hemocytometer for accurate concentration calculation.

Mapping out grid intricacies

I’m working through the ambiguity of "16×25" in the question, specifically how it might relate to the subdivision of squares within a standard Neubauer chamber’s grid.

Calculating detailed volume

I’m breaking down the volume of each small square in the Neubauer chamber, figuring it’s 0.00025 µL, and tallying 400 small squares overall.

Understanding cell density

Interesting! Given the high cell density (25 cells per small square), I’m using the dilutions and a specific chamber formula to figure out the cell concentration in the original 10 ml.

Assessing calculation methods

I’m working through the options and find cell concentration methods tricky, especially with "中格" perhaps referring to a standard RBC square. I’m exploring if 10 ml of culture is specified.

Figuring out cell concentration

I’m figuring out the original cell concentration by multiplying the average cell count in a small square by the chamber factor and dilution factor, ensuring accurate adjustment.

Figuring out volume

I'm calculating the number of small squares in 1 ml by dividing the total volume of a larger square by the volume of each smaller square, leading to 4 million small squares per ml.

Calculating original concentration

I’m figuring out the original yeast cell concentration by scaling up from the diluted sample count of 25 cells per small square, leading to 1e10 cells/ml before dilution.

Calculating yeast concentration

I’m refining the yeast cell concentration calculation, interpreting "中格" as one large square, and multiplying by the dilution factor to determine the original 10 ml sample concentration.

Rethinking the calculation

I’m gathering info on the confusion surrounding "中格" and considering the standard Chinese formula for cell concentration involving 5 RBC squares and a specific dilution factor.

Figuring out concentration

Listing the steps, I'm mapping out the cell concentration calculation, using 25 cells per 1 mm^2 to estimate 2.5 x 10^5 cells/ml in the diluted sample.

Wondering about standard methods

I'm exploring the common approach in Chinese textbooks for calculating cell concentration, emphasizing the improved Neubauer chamber and the RBC counting method, despite the question's ambiguity.

Mapping out the cell count

I’m explaining the typical RBC counting method in Chinese textbooks, average cell count in 5 squares, and calculating the cell concentration using the improved Neubauer chamber and dilution factors.

Confirming the count

I’m piecing together that treating the 25 center squares as 1 mm^2 leads to a similar final cell count, consistent with standard RBC or WBC formulas.

Reaching the final count

I'm calculating the total cell quantity using both RBC and WBC formulas, adjusting for dilution, and ensuring consistency. This method clarifies the concentration calculation process.

Piecing it together

I’m working through "中格" as one of 400 small squares, calculating the cell concentration by considering the smaller volume and overall dilution factors, leading to a significantly larger final count.

Clarifying interpretations

I'm thinking through how "中格" might refer to the 1 mm x 1 mm center area divided into 25 squares or to the average cell count across these 25 squares.

Reassessing cell calculation

Recalculating by treating "中格" as averaging 25 cells per large square suggests a higher concentration in the original sample, leading to 6.25 x 10^9 cells.

Calculating diluted sample concentration

I'm working through the cell concentration in the diluted sample, concluding with 6.25 x 10^6 cells/ml by multiplying the average cells per large square by the dilution factor.

Clarifying yeast count specifics

OK, let me see. For yeast, the standard method counts the entire 1 mm^2 region with a 0.1 mm depth, leading to 6.25 x 10^9 cells.

Confirming yeast count

OK, let's clarify. Assuming "中格" means the entire 1 mm^2 center square, it results in 2.5 x 10^8 total cells in the original 10 ml sample, using the standard formula for yeast concentration.

Taking a closer look

I’m mapping out the standard RBC counting method, suggesting "中格" means the entire 1 mm^2 center square, leading to an average count of 25 for the entire region.

Confirming the method

I’m piecing together that treating "中格" as the entire 1 mm^2 center square, the yeast cell density is 2.5 x 10^7 cells/ml in the original 10 ml sample, using the standard formula.

Figuring out the approach

I'm thinking through if "中格" refers to the entire center square or only five squares, analyzing both interpretations to find the most straightforward approach among all possible methods.

Reaching the final step

I’m concluding that for yeast, counting the entire center grid leads to 2.5 x 10^8 cells in the original 10 ml sample, using standard textbook solutions.

Thought about yeast cell counting for 1m 59s

回答

下面给出一种常见、比较标准的解释和计算方法。由于题目中没有明确指出“中格”指的是整个 1 mm × 1 mm 的中心大方格、还是其中某个子格/小格，这里先按照在微生物/酵母计数时最常用的做法来处理：将“中格”理解为整个中心大方格(即 1 mm × 1 mm 的区域，计数板深度 0.1 mm)。如果你的实验/教材里对“中格”有其他特定定义，需根据实际情况调整，但大多数教科书型题目往往是这样处理的。

1. 已知条件

培养基体积：10 mL。
稀释倍数：100 倍。
使用改良 Neubauer 计数板（常见描述为“16×25”血细胞计数板，其中心区域是 1 mm×1 mm、深度 0.1 mm）。
计数时刻，在中心 1 mm×1 mm、深度 0.1 mm 的大方格中，平均计得酵母菌细胞数为 25 个。

我们要计算：原 10 mL 培养基里一共有多少个酵母菌 (记为 $N$ )。

2. 计数板中体积换算

改良 Neubauer 计数板中心的大方格面积是 $1\,\text{mm} \times 1\,\text{mm} = 1\,\text{mm}^2$ 。
计数板盖玻片与计数板之间的深度通常是 $0.1\,\text{mm}$ 。
因而该大方格所对应的体积是 $V_{\text{格}} \;=\; 1\,\text{mm}^2 \;\times\; 0.1\,\text{mm} \;=\; 0.1\,\text{mm}^3 \;=\; 1 \times 10^{-4}\,\text{mL}.$

3. 稀释后样品的浓度

在稀释后的样品中，取上述体积（大方格对应的 $10^{-4}\,\text{mL}$ ），平均测到 25 个细胞。于是稀释后样品的细胞浓度为：

C_{\text{稀释液}} = \frac{\text{该体积内细胞数}}{\text{该体积}} = \frac{25}{1\times10^{-4}\,\text{mL}} = 2.5 \times 10^5 \,\text{cells/mL}.

4. 推算回原液的浓度

由于题目说是稀释 100 倍之后才进行上述计数，因此原液的细胞浓度应为稀释液的 100 倍：

C_{\text{原液}} = C_{\text{稀释液}} \;\times\; 100 = 2.5 \times 10^5 \,\text{cells/mL} \;\times\; 100 = 2.5 \times 10^7 \,\text{cells/mL}.

5. 计算原液总细胞数 $N$

原液总体积是 10 mL，故原液中酵母菌总数为：

N = C_{\text{原液}} \;\times\; \text{体积} = 2.5 \times 10^7 \,\text{cells/mL} \;\times\; 10\,\text{mL} = 2.5 \times 10^8 \,\text{个细胞}.

因此，原 10 mL 培养基中酵母菌总数约为 $2.5\times 10^8$ 个。

如果“中格”指的是别的格子怎么办？

如果在你的实验/题目背景下，“中格”指的是“中心大方格里某一个 0.2 mm×0.2 mm 的中等方格”或者“最里层更小的 0.05 mm×0.05 mm 的小格”，则每个格子的体积不同，计算时需要先弄清楚所计数格子的实际体积，再进行同样的“（细胞数）/（格子体积）× 稀释倍数”推算。
不过，很多教材式练习题默认“中格”=“中心 1 mm×1 mm 的大方格”，并以此来给出一个简洁的计算过程；本题大概率就是这种情况。

6. 最终答案

\boxed{N = 2.5 \times 10^8 \text{（个酵母菌）}}

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