Theoretical models that explain a system using mathematical equations.

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Hill's function for translational regulation

Transcriptional regulation is generally modeled as a Hill's function (similar to Michaelis-Menten Kinetics): $$\frac{dm_X}{dt}=\alpha _{m_X}.\frac{R}{K+R} -\beta _{m_X}.m_X$$ Where $m_X$ is the mRNA ...
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20 views

about diffusion equation [closed]

consider the heat equation $u_t=a(t)u_{xx}+f(x,t)$, $0<x<L$, $0<t<T$ subject to the initial condition $u(x,0)=g(x)$ and boundary conditions $u(1,t)=0,$ $u_x(0,t)+hu(0,t)=0$ where ...
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1answer
73 views

Effects of selection on effective population size

Background The effective population size ($N_e$) is a central concept of evolutionary biology and is influenced by several parameters. For example: sex ratio bias affects $N_e$ $\left(N_e = ...
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19 views

How many traits can a multivariate breeders equation handle?

The multivariate breeders equation (MBE) by Lande predicts the change in a trait $\Delta \bar z$ (response) as $\Delta \bar z = G \beta$ where $G$ is a genetic variance-covariance matrix and ...
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23 views

What is the allelic frequency at mutation-selection-drift equilibrium?

At mutation-selection equilibrium the expected frequency $f$ of a given locus is $$f ≈ \frac{\mu}{s\cdot h}$$ , where $\mu$ is the mutation rate, $s$ is the selection coefficient and $h$ is the ...
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26 views

Calculate generations since divergence

Can the formula $\mu = k/(2t + 4Ne)$ be used to calculate the divergence time for any two species given a mutation rate, generation time and sequence divergence value?
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34 views

Modelling intracellular interactions between sender and receiver bacteria

I am involved in a modelling task of a biological process described as follows: -- "Objective: to model behavior of a sender receiver type system The process goes as follows -Pre-signal [PS] is in ...
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11 views

Mutation-drift equilibrium and among loci variance in heterozygosity

At mutation-drift balance, the increased heterozygosity brought by new mutations is exactly equal to the loss of heterozygosity due to genetic drift. At equilibrium, the expected heterozygosity for a ...
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1answer
32 views

What are the application areas of Pattern formation studies specific to biology? [closed]

I was reading about reaction-diffusion processes, morphogenesis concept by Alan Turing and works of Murray in describing pattern formation on animals etc. But one question which came to my mind was ...
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1answer
56 views

Defining dominance and selection in these formulae

This paper uses two equations to explain the different conditions under which sexually antagonistic genetic variance is maintained in a population, while allowing for unequal dominance, for ...
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44 views

How does temperature influence the rate of protein degradation?

For computer modeling purposes, I am looking for some referenced quantitative measurements of the effect(s) of temperature on biochemical reactions. Question In particular, my question is: How does ...
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1answer
50 views

Modelling how much cadmium a cell will be able to chelate with phytochelatins

I am involved in a synthetic biology project where I have to do modelling with ODEs. The biological process I want to model is the chelation of Cd2+ with phytochelatins, to know how much can be ...
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3answers
86 views

What is the smallest scale at which blood vessels, nerves and other structures are deterministic?

Super simple question, but I can't find the answer on the Internet (and I'm in a foreign country so the library is not English.) As the title says, what is the smallest scale at which blood vessels, ...
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1answer
615 views

Calculation of the bacterial growth rate from a spectrophotomer growth curve

Typically the microbial growth in liquid cultures is monitored by turbidity. Data is obtained with a spectrophotometer to measure optical density at 600nm. The slope of the bacterial kinetic curve in ...
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33 views

Based on which criteria should i choose the control sample to calculate delta_delta_Ct

I want to calculate the gene expression of an experiment with the Delta delta Ct method. I have these results from two runs of a real time PCR (one for the GOI(Gene of Interest) and one for the ...
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1answer
100 views

Start studying mathematical biology from basics

I am really passionate about theoretical and quantitative biology and I would like to build my future career around this topic. I've just got my bachelor's degree in biology (ecology) but scince I've ...
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15 views

Review articles for best practices in modelling cellular signaling networks?

I wonder if you could suggest an accessible review article for best practices in computational systems modelling. Specifically, I would like to try to model a cellular signalling network that would ...
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1answer
42 views

Is there a good explanation for this swarming pattern?

A film clip would be helpful here. A few days ago I noticed a swarm of newly hatched flying bugs about 20 feet away from me with the sun behind them so the shape of swarming (such as it was) was easy ...
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2answers
284 views

Help with the Price equation

The Price equation describes mathematically the evolution of a population of units from one generation to the next. $\bar{w}\Delta \bar{z}$ = $Cov (w_i,z_i) $+$ E(w_i\Delta z_i)$ I would like ...
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1answer
76 views

Coalescent theory - independence of coalescent times

Let $T_i$ be the time to coalesce from $n(t)=i+1$ to $n(t)=i$, where $n(t)$ is the number of sites that have not coalesced yet. In the below example the maximum $n(0)=6$. As I understand it, many ...
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53 views

Effects of Genetic Drift on Linkage Disequilibrium

From what I understood of @Canadianer's answer here... Genetic drift randomly causes negative or positive linkage disequilibria, by changing allele frequencies through random sampling. Natural ...
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1answer
40 views

Definition of Linkage Desiquilibrium (LD)

According to wiki, linkage disequilibrium $D$ equals $$D = x_{11} - p_1\cdot q_1$$ where: $$ \begin{matrix} \text{Haplotype} & \text{Frequency}\\ A_1B_1 & x_{11}\\ ...
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1answer
129 views

How to interpret the breeders equation?

The univariate breeders equation is defined as, $\ R = h^2 s$ where $\ R $ is the response, $\ h^2 $ is the heritability (additive genetic variation), $\ s $ is the selection differential. The ...
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1answer
133 views

Heterozygosity and overdominance

Consider $m$ loci with heterozygote advantage (overdominance) such that the fitness of the two homozygotes is $1-\frac{s}{2}$ and the fitness of the heterozygotes is $1+\frac{s}{2}$, where $s>0$. ...
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3answers
247 views

Book recommendation on population/evolutionary genetics?

I have recently been involved in collaborations that require me to model the population genetics of eukaryotic populations. I fear I may either be "re-inventing the wheel" or making conceptual ...
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2answers
90 views

Heterozygosity under genetic drift

The wright-Fisher model of genetic drift is: $$p_{ij} = \binom{2N}{j}\left(\frac{i}{2N}\right)^j \left(1- \frac{i}{2N}\right)^{2N-j} $$ ,where $\binom{2N}{j}$ is a binomial coefficient. From this ...
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1answer
56 views

Additive genetic variance with $n$ loci

The genetic variance of a quantitative trait (the quantitative trait in question is fitness) can be express as the sum of two components, the dominance and additive variance: $$\sigma_D^2 + ...
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1answer
89 views

Additive genetic variance with $n$ alleles

The genetic variance of a quantitative trait (the quantitative trait in question is fitness) can be express as the sum of two components, the dominance and additive variance: $$\sigma_D^2 + ...
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1answer
54 views

Effective population size when the population sizes varies from season to season

Let's think of a species which has four generations per year and which population size changes from season to season so that the population size is 100 in summer, 200 in spring, 50 in autumn and 20 in ...
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1answer
329 views

How much does the distance between a transcription factor binding site and a promoter influence transcription?

Assume we have a synthetic construct with a minimal (inducible) promoter that requires activation for significant transcription to occur. Realistically, how important is the distance between an ...
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2answers
92 views

Is there a standard reference for the importance of tumor heterogeneity?

In a recent post, Philip Gerlee highlighted the two biggest contributions of mathematical oncology to cancer research: (1) increasing focus on the progress of cancer as an evolutionary process, and ...
4
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1answer
67 views

What is the relation between plasmid concentration and mRNA levels?

Suppose a simple synthetic construct, consisting of a constitutive promoter and a single gene: One of the simplest ways to model GFP transcription is to use an ODE: $\frac{d [GFP_{mRNA}]}{dt} = a - ...
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1answer
68 views

Visualisation of phylogeography

I am working on phylogeography on one model species and I am a beginner. You can imagine one species that came on locality more than 5 mya (million years ago). It was a good environment, so the ...
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1answer
185 views

Why does the slope of parent-offspring regression equals the heritability in the narrow sense?

Background ---- Notations and assumptions ---- let $W_{ij}$ be the fitness associated to the genotype $AiAj$. $x$ is the frequency of the allele $A1$ in the population. The frequency of the allele ...
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1answer
439 views

Natural examples of XOR functions at the cellular level

We can often think of cells as a sort of circuit on macromolecules, and can show that they can accurately and robustly implement functions like $\text{MAJ}(x_1,...,x_n)$ (return $1$ if more than half ...
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1answer
75 views

Chaos theory and population cycles

I have just begun to read about Chaos theory and have come across the statement that "Period three implies chaos." My question: Does any odd period imply chaos or only 3? If so, how can populations ...
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1answer
38 views

An over-simplified model of cell division and its relation to stem cells

I am a mathematician, and I decided to try to model cell division with math and see what conclusions came out of it. I had some questions concerning stem cells that came up in the model. In an ...
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2answers
145 views

The Assumption of Weak Selection?

I was reading this question and I failed to fully understand the introductory part of it. The OP (@Artem Kaznatcheev) says: Most analytic models like to assume weak selection because it allows ...
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1answer
149 views

Definitions and examples of some math-releated ecology branches

I would like to have an example of application and a brief description/definition (two or three lines) of the following fields. I would like to understand the exact differences between them. Other ...
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2answers
292 views

Survivorship Curves: Type II curve mortality rate is not constant?

In graphs of survivorship curves, I'm seeing that the Type II curves are straight lines, and the supplementary text says that the mortality rate is constant (i.e. the slope of the line is constant). ...
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314 views

Could be an union/synergy between Math, Computer Science and Marine Biology?

I'm studing for my bachelor's degree in Natural Science and I have to chose the path for my future life. I have to chose the right kind of graduate studies. Since I love computer science, maths and ...
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1answer
155 views

Genetic Drift: Models, assumptions and empirical observations

There two main mathematical models to describe the process of genetic drift are Moran model and Wright-Fisher model. My questions concern the assumptions of these models, the existence of other ...
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2answers
112 views

Examples of references for mathematical approaches in bioinformatics that are applicable to linguistics?

Do you have any classic references for mathematical approaches in bioinformatics that are applicable to linguistics (or vice versa)? EDIT I am mainly interested in approaches to reconstruct the ...
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85 views

Model for fluctuating selection

Is there any mathematical model to predict the behaviour and long-term consequence of counter-acting selection at different time scale? For example, let's consider the bi-allelic gene $A$, with ...
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1answer
122 views

Suggestions for an experiment? [closed]

I would appreciate suggestions for my year-long AP Biology project. Such a project would consists of a standard experiment, to be done over the period of a year, so it would have >to be fairly ...
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1answer
114 views

Population genetics and the fitness probability distribution. Why is the arithmetic mean all we need?

When recording change in allele frequency in diploid, bi-allelic, infinite and panmixic population we usually use this kind of equation: $\delta_p = \frac{p * q *( p (w11 - w12) + q * (w12 - ...
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1answer
90 views

Modeling yeast biochemical pathway using enzyme kinetics

I need enzyme concentration and metabolites concentration values to en-corporate these values in my model and do some simulation. I searched through some database yeast metabolome database ...
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66 views

Eye color genetics

I am trying to find a model to link the phenotype eye color to its genotypes. I know that there exists a simple model from Davenport, which explains {brown,blue} eyes. Further, there is an extended ...
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107 views

Understanding SIR models in epidemiology

We are doing research on a SIR model of an epidemic. For one of the subsections, we are talking about saturation content rate of a human. We would like to know if anyone has an understanding of ...
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53 views

Reverse complement of reconstruction model for assembling reads

One way to assemble fragments produced by DNA sequencing (often called reads) is to seek for the shortest common superstring that contains all the reads of a given set of reads. One model for this ...