Cell Division and Population Growth

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Cell Division
and Population Growth

The simplest form of increase in the number of individuals (population growth) is binary cell division (true in all 3 domains).

Speaker Notes:

Multicellular organisms require more complicated models of population increase.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Reading Assignment

Read pages 222-228 (emphasising the genetic relationship of the two daughter cells to each other and to their parent)
Read pages 1177-1182 (section 52.2) emphasizing the parameters and variables of different equations of growth.
Read Box 11.2 ‘How bacteria divide’ p 230.

Speaker Notes:

Cultural ‘Life Cycle’

Pattern of abundance changes when small number of organisms colonize an abundant resource.
Batch culture (contrasted to continuous culture).
Sequence of stages: Lag, exponential growth, stationary, decline, death

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Speaker Notes:

Stages of growth in non-renewed resources

Lag = non-growing cells have different molecules than growing cells so there is a lag as cells ‘crank up’ to grow.
Exponential = the ‘default’ of growth
Stationary = not enough resources to grow but enough to stay alive
Decline = so few resources cells die
Death = all cells die, no ‘free energy’ left

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Speaker Notes:

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Growth and Reproduction

In the exponential growth phase of the cultural life cycle there is an increase in mass of the population and an increase in the number of cells.
Both building new macromolecules from acquired materials and assembling the macromolecules into new individuals are the essence of reproduction.

Speaker Notes:

Individuals reproduce; DNA replicates Different words for parts of the process of life.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Population Growth

In BioS 100 the processes of acquiring materials and energy and the building of new macromolecules is emphasized.
In BioS 101 we focus on the number of individuals - the size, N, of the population and rates of change of N.

Speaker Notes:

What is the difference between a growth rate and a per capita growth rate?

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Cell division in bacteria

Bacteria have circular DNA.
The 2 strands of the DNA run in opposite directions (5´-3´ & 3´-5´).
Bacterial DNA starts replication at a single spot and proceeds in both directions around the circle (Figure 14.10b).

Speaker Notes:

After the completion of replication the DNA has been duplicated.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Bacterial Division

After DNA duplication there are two identical circular pieces of DNA in a single cell.
When the cell divides in two, the crucial step is to assure that each daughter cell gets one and only one of the chromosomes.
Cellular parts besides DNA are not always divided equally among the daughter cells.

Speaker Notes:

Equality of the hereditary material in the two daughters is essential.

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UIC BioS 101 Nyberg

Eukaryotes

DNA is organized in linear pieces called chromosomes.
A complete set of information for a species requires many chromosomes, called the haploid number, n.
For humans n=23, for dogs n=36, for the fruit fly n=4, each has a particular number of chromosomes in a complete set.

Speaker Notes:

Each cell in the human body has 46 chromosomes, twice the haploid number.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Cell Division in Eukaryotes

Cell reproduction establishes a lineage with repeated events, the repetition of events defines the cell cycle.
Major stages of the cell cycle are: mitosis, G1 (gap 1), S (DNA synthesis), G2 (gap 2)
At the end of S the duplicated DNA of a chromosom is in two strands called sister chromatids.

Speaker Notes:

Stages of the Cell Cycle

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Speaker Notes:

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Cell Division in Eukaryotes II

The separation of the sister chromatids of the chromosome is done in mitosis (within cell membrane).
The physical separation of the cell into two ‘daughter’ cells is called cytokinesis.

Speaker Notes:

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Ploidy

Both haploid and diploid cells (and other ploidies) can undergoes mitosis.
Tetraploids have four sets of chromosomes.
Haploid is the minimum complete set.

Speaker Notes:

By complete we mean a set that has one of every type of gene for every function of the organism.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Increase in cell number

Given binary cell division, we expect the number of cells thru time to follow the powers of 2, namely 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, etc.
This is basic pattern of geometric growth.
There are variations among cells in the length of the cell cycle, and the pulsed nature of the increase in N smoothes into exponential growth.

Speaker Notes:

When the cells are not synchronized the rate of increase seems exponential.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Exponential growth

In exponential growth, the per capita growth rate ΔN/(N•Δt) is constant (r).
ΔN = Nfinal – Ninitial = increase in population size.
ΔN/Δt is the growth rate, where Δt is the time interval.
Dividing the growth rate by N gives the per person or per capita growth rate.

Speaker Notes:

The doubling time is constant if the population is growing exponentially.

Doubling time is the intellectual equivalent of a half-life.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Equation of Exponential Growth

Nt = N0•er•t

Where Nt is the number at time t, N0 is the number at time zero (initial number), e is 2.718…, r is a parameter of the species (with units of per time) and t is time (in same units that r is given).

Speaker Notes:

Natural logs are logarithms to the base e. What is the difference between a parameter and a variable?

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Geometric Growth equation

Nt+1 = • Nt

where Nt+1 is the number of individuals in the next (t + 1) generation, is the growth rate parameter, and Nt is the number of individuals in the tth generation, where t is any integer.

Speaker Notes:

Because of the seasonality on earth discrete, year to year, models are often very useful.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Geometric Growth, many generations

If the initial number of individuals is N0 and the discrete growth goes on for n generations then the following equation applies:
Nn = n• N0
The number of generations is indicated by t in your text (only integer values are OK).

Speaker Notes:

In the model lambda is a constant. In reality that is at best approximately true.

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Growth rate parameters

Each species has a characteristic per capita growth rate, r & , when resources are abundant.
Bacteria can double in as short as 20 minutes (=26,280 times in a year), but humans take 15 or 16 years (0.064 times per year).
= er when matches time units

Speaker Notes:

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Improved models of growth

The previous models assume that all N individuals in the population are equivalent.
Age of an individual seems intuitively important in modeling population growth.
Age is symbolized by the variable x to distinguish age from time, t.
A birth cohort (all individuals born in same year) is studied as they age.

Speaker Notes:

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Age specific patterns of death

Let N(0) be the total number of newborns in the cohort with N(x) the number of individuals surviving to age x.
As all individuals eventually die, N(x) = 0 for some large value of age = x.
Survivorship, l(x) (shown in text as lx) = N(x)/N(0), survivorship tells the probability a new born will survive to age X.

Speaker Notes:

Lecture 13 Exam 1

UIC BioS 101 Nyberg

Vocabulary

Cultural Life Cycle
Cycle
Exponential growth
Haploid number
growth rate

Mitosis
per capita growth rate
Reproduction
Survivorship

Speaker Notes:

Rates are measured over a time interval and are expressed as per unit time.